<div class="xblock xblock-public_view xblock-public_view-vertical" data-usage-id="block-v1:MITx+8.02.2x+2T2018+type@vertical+block@vert-lesson15-textbooklinks" data-graded="True" data-runtime-class="LmsRuntime" data-course-id="course-v1:MITx+8.02.2x+2T2018" data-block-type="vertical" data-request-token="a285686afe6b11ee8e28026cc65ec0d9" data-has-score="False" data-runtime-version="1" data-init="VerticalStudentView">
<h2 class="hd hd-2 unit-title">Textbook Links</h2>
<div class="vert-mod">
<div class="vert vert-0" data-id="block-v1:MITx+8.02.2x+2T2018+type@html+block@html-lesson15-textbooklinks">
<div class="xblock xblock-public_view xblock-public_view-html xmodule_display xmodule_HtmlBlock" data-usage-id="block-v1:MITx+8.02.2x+2T2018+type@html+block@html-lesson15-textbooklinks" data-graded="True" data-runtime-class="LmsRuntime" data-course-id="course-v1:MITx+8.02.2x+2T2018" data-block-type="html" data-request-token="a285686afe6b11ee8e28026cc65ec0d9" data-has-score="False" data-runtime-version="1" data-init="XBlockToXModuleShim">
<script type="json/xblock-args" class="xblock-json-init-args">
{"xmodule-type": "HTMLModule"}
</script>
<p>This lesson explores simple circuits with just batteries and resistors.</p>
<p>Textbook Links</p>
<ul>
<li><a href="https://openlearninglibrary.mit.edu/courses/course-v1:MITx+8.02.2x+2T2018/pdfbook/0/#viewer-frame" target="[object Object]">Chapter 7.1-7.5: Introduction to DC Circuits</a></li>
</ul>
</div>
</div>
</div>
</div>
<div class="xblock xblock-public_view xblock-public_view-vertical" data-usage-id="block-v1:MITx+8.02.2x+2T2018+type@vertical+block@vert-html-lesson15_01" data-graded="True" data-runtime-class="LmsRuntime" data-course-id="course-v1:MITx+8.02.2x+2T2018" data-block-type="vertical" data-request-token="a285686afe6b11ee8e28026cc65ec0d9" data-has-score="False" data-runtime-version="1" data-init="VerticalStudentView">
<h2 class="hd hd-2 unit-title">Introduction to DC Circuits</h2>
<div class="vert-mod">
<div class="vert vert-0" data-id="block-v1:MITx+8.02.2x+2T2018+type@html+block@lesson15_01">
<div class="xblock xblock-public_view xblock-public_view-html xmodule_display xmodule_HtmlBlock" data-usage-id="block-v1:MITx+8.02.2x+2T2018+type@html+block@lesson15_01" data-graded="True" data-runtime-class="LmsRuntime" data-course-id="course-v1:MITx+8.02.2x+2T2018" data-block-type="html" data-request-token="a285686afe6b11ee8e28026cc65ec0d9" data-has-score="False" data-runtime-version="1" data-init="XBlockToXModuleShim">
<script type="json/xblock-args" class="xblock-json-init-args">
{"xmodule-type": "HTMLModule"}
</script>
<center><b>Introduction to DC Circuits</b></center><p> The goal of this week is to be able to calculate the current flowing through different resistors and capacitors connected together to a power supply that is constant with time. These type of circuits are called Direct Current (DC) circuits because the resulting currents do not change direction with time. When the circuit only contains resistors the resulting current is also constant in time. In the next lesson, we will consider circuits with capacitors, where the current can be time dependent. </p><p> The figure below is an electric circuit with three resistors. A battery, not shown in the picture, is connected to the circuit via two clips at the top and bottom right. Underneath the white board, there are conducting wires connecting each horizontal row of holes and so the ends of the two resistors are connected together, as are the end of the white wire and the red clip and the bottom end of resistor 3 and the black clip. Below the picture there is a <b>circuit diagram</b> representing the real circuit.</p><center><img src="/asset-v1:MITx+8.02.2x+2T2018+type@asset+block/images_html_lesson15_01b.png"/><img src="/assets/courseware/v1/f5210f8a18682f4cc518af93140b8938/asset-v1:MITx+8.02.2x+2T2018+type@asset+block/images_html_lesson15_01_c2.png" width="300"/></center><p> This week we will analyze circuits connecting batteries to resistors, capacitors and switches. The symbols used in a circuit diagram to represent these elements are shown in the left table below.</p><center><img src="/assets/courseware/v1/9769d7e29d6a4c562b2f5fe04feede6e/asset-v1:MITx+8.02.2x+2T2018+type@asset+block/images_circuitElements.svg" width="600"/></center><p> To build a circuit, the different elements are connected together with conducting wires. We will assume that the wires have negligibly small resistance, and therefore the electric potential at any point in the connecting ideal wire is the same. A connecting wire in a circuit diagram is represented by a straight line.</p><p>In the figure below the real circuit is shown again. This time we have drawn lines to show the hidden conducting wires that are connecting the resistors together to the battery. We have also included the circuit diagram in the same picture for comparison. Note that the battery shown in the figure is off to the right in the photo.</p><center><img src="/assets/courseware/v1/81f42d4a4d1916cee780928d684f8bda/asset-v1:MITx+8.02.2x+2T2018+type@asset+block/images_html_lesson15_01b2.png"/></center><p> The red positive clip is connected to the positive terminal of the battery. Points <b>a</b> , <b>b</b> and <b>c</b> are at the same potential as the positive terminal. Point <b>c</b> is a point where three elements are connected: the battery, resistor 1 and resistor 2. This is called a <b>junction</b>. Point <b>d</b> is another junction. At this point, resistors 1, 2 and 3 are connected. Points <b>e</b> and <b>f</b> are at the same electric potential as the negative terminal of the battery. </p><p> We use the term <b>branch</b> to describe the wires and the element or elements of the circuit between two junctions. There are three branches in this circuit. One consists of resistor 1 between junctions <b>d</b> and <b>c</b>, the second one connects through resistor 2 between junctions <b>c</b> and <b>d</b>, and the third one connects resistor 3 and the battery starting at junction <b>d</b> and travelling successively through resistor 3, then junctions <b>e</b> and <b>f</b>, then the battery, followed by junctions <b>a</b> and <b>b</b> and then ending at junction <b>c</b>. </p><p> One important feature of a single branch is that there are no junctions except at the ends where more than 2 elements or one element and a wire come together, i.e. there are no places where current could split. For example, you cannot consider the path from junction <b>c</b> through resistor 1 and then through resistor 3 to junction <b>e</b> as a single branch because there is a split at junction <b>d</b></p>
</div>
</div>
</div>
</div>
<div class="xblock xblock-public_view xblock-public_view-vertical" data-usage-id="block-v1:MITx+8.02.2x+2T2018+type@vertical+block@vert-L15v01" data-graded="True" data-runtime-class="LmsRuntime" data-course-id="course-v1:MITx+8.02.2x+2T2018" data-block-type="vertical" data-request-token="a285686afe6b11ee8e28026cc65ec0d9" data-has-score="False" data-runtime-version="1" data-init="VerticalStudentView">
<h2 class="hd hd-2 unit-title">L15v1: Batteries</h2>
<div class="vert-mod">
<div class="vert vert-0" data-id="block-v1:MITx+8.02.2x+2T2018+type@video+block@L15v01">
<div class="xblock xblock-public_view xblock-public_view-video xmodule_display xmodule_VideoBlock" data-usage-id="block-v1:MITx+8.02.2x+2T2018+type@video+block@L15v01" data-graded="True" data-runtime-class="LmsRuntime" data-course-id="course-v1:MITx+8.02.2x+2T2018" data-block-type="video" data-request-token="a285686afe6b11ee8e28026cc65ec0d9" data-has-score="False" data-runtime-version="1" data-init="XBlockToXModuleShim">
<script type="json/xblock-args" class="xblock-json-init-args">
{"xmodule-type": "Video"}
</script>
<h3 class="hd hd-2">L15v01: Circuits and Batteries</h3>
<div
id="video_L15v01"
class="video closed"
data-metadata='{"end": 0.0, "speed": null, "ytTestTimeout": 1500, "publishCompletionUrl": "/courses/course-v1:MITx+8.02.2x+2T2018/xblock/block-v1:MITx+8.02.2x+2T2018+type@video+block@L15v01/handler/publish_completion", "ytApiUrl": "https://www.youtube.com/iframe_api", "showCaptions": "true", "streams": "1.00:nBv5xpEhIb4", "poster": null, "saveStateEnabled": false, "start": 0.0, "completionPercentage": 0.95, "transcriptAvailableTranslationsUrl": "/courses/course-v1:MITx+8.02.2x+2T2018/xblock/block-v1:MITx+8.02.2x+2T2018+type@video+block@L15v01/handler/transcript/available_translations", "autoplay": false, "transcriptLanguages": {"en": "English"}, "autohideHtml5": false, "transcriptTranslationUrl": "/courses/course-v1:MITx+8.02.2x+2T2018/xblock/block-v1:MITx+8.02.2x+2T2018+type@video+block@L15v01/handler/transcript/translation/__lang__", "ytMetadataEndpoint": "", "generalSpeed": 1.0, "lmsRootURL": "https://openlearninglibrary.mit.edu", "autoAdvance": false, "completionEnabled": false, "savedVideoPosition": 0.0, "saveStateUrl": "/courses/course-v1:MITx+8.02.2x+2T2018/xblock/block-v1:MITx+8.02.2x+2T2018+type@video+block@L15v01/handler/xmodule_handler/save_user_state", "captionDataDir": null, "sources": ["https://d2f1egay8yehza.cloudfront.net/MITx8.02.2x-V000100/MITx8.02.2x-V000100.m3u8"], "transcriptLanguage": "en", "recordedYoutubeIsAvailable": true, "prioritizeHls": false, "duration": null}'
data-bumper-metadata='null'
data-autoadvance-enabled="False"
data-poster='null'
tabindex="-1"
>
<div class="focus_grabber first"></div>
<div class="tc-wrapper">
<div class="video-wrapper">
<span tabindex="0" class="spinner" aria-hidden="false" aria-label="Loading video player"></span>
<span tabindex="-1" class="btn-play fa fa-youtube-play fa-2x is-hidden" aria-hidden="true" aria-label="Play video"></span>
<div class="video-player-pre"></div>
<div class="video-player">
<div id="L15v01"></div>
<h4 class="hd hd-4 video-error is-hidden">No playable video sources found.</h4>
<h4 class="hd hd-4 video-hls-error is-hidden">
Your browser does not support this video format. Try using a different browser.
</h4>
</div>
<div class="video-player-post"></div>
<div class="closed-captions"></div>
<div class="video-controls is-hidden">
<div>
<div class="vcr"><div class="vidtime">0:00 / 0:00</div></div>
<div class="secondary-controls"></div>
</div>
</div>
</div>
</div>
<div class="focus_grabber last"></div>
<h3 class="hd hd-4 downloads-heading sr" id="video-download-transcripts_L15v01">Downloads and transcripts</h3>
<div class="wrapper-downloads" role="region" aria-labelledby="video-download-transcripts_L15v01">
<div class="wrapper-download-transcripts">
<h4 class="hd hd-5">Transcripts</h4>
<ul class="list-download-transcripts">
<li class="transcript-option">
<a class="btn btn-link" href="/courses/course-v1:MITx+8.02.2x+2T2018/xblock/block-v1:MITx+8.02.2x+2T2018+type@video+block@L15v01/handler/transcript/download" data-value="srt">Download SubRip (.srt) file</a>
</li>
<li class="transcript-option">
<a class="btn btn-link" href="/courses/course-v1:MITx+8.02.2x+2T2018/xblock/block-v1:MITx+8.02.2x+2T2018+type@video+block@L15v01/handler/transcript/download" data-value="txt">Download Text (.txt) file</a>
</li>
</ul>
</div>
</div>
</div>
</div>
</div>
<div class="vert vert-1" data-id="block-v1:MITx+8.02.2x+2T2018+type@video+block@Krishana-W10D2-01">
<div class="xblock xblock-public_view xblock-public_view-video xmodule_display xmodule_VideoBlock" data-usage-id="block-v1:MITx+8.02.2x+2T2018+type@video+block@Krishana-W10D2-01" data-graded="True" data-runtime-class="LmsRuntime" data-course-id="course-v1:MITx+8.02.2x+2T2018" data-block-type="video" data-request-token="a285686afe6b11ee8e28026cc65ec0d9" data-has-score="False" data-runtime-version="1" data-init="XBlockToXModuleShim">
<script type="json/xblock-args" class="xblock-json-init-args">
{"xmodule-type": "Video"}
</script>
<h3 class="hd hd-2">Introduction to Circuits and Batteries</h3>
<div
id="video_Krishana-W10D2-01"
class="video closed"
data-metadata='{"end": 0.0, "speed": null, "ytTestTimeout": 1500, "publishCompletionUrl": "/courses/course-v1:MITx+8.02.2x+2T2018/xblock/block-v1:MITx+8.02.2x+2T2018+type@video+block@Krishana-W10D2-01/handler/publish_completion", "ytApiUrl": "https://www.youtube.com/iframe_api", "showCaptions": "true", "streams": "1.00:peOCDwt0AcQ", "poster": null, "saveStateEnabled": false, "start": 0.0, "completionPercentage": 0.95, "transcriptAvailableTranslationsUrl": "/courses/course-v1:MITx+8.02.2x+2T2018/xblock/block-v1:MITx+8.02.2x+2T2018+type@video+block@Krishana-W10D2-01/handler/transcript/available_translations", "autoplay": false, "transcriptLanguages": {"en": "English"}, "autohideHtml5": false, "transcriptTranslationUrl": "/courses/course-v1:MITx+8.02.2x+2T2018/xblock/block-v1:MITx+8.02.2x+2T2018+type@video+block@Krishana-W10D2-01/handler/transcript/translation/__lang__", "ytMetadataEndpoint": "", "generalSpeed": 1.0, "lmsRootURL": "https://openlearninglibrary.mit.edu", "autoAdvance": false, "completionEnabled": false, "savedVideoPosition": 0.0, "saveStateUrl": "/courses/course-v1:MITx+8.02.2x+2T2018/xblock/block-v1:MITx+8.02.2x+2T2018+type@video+block@Krishana-W10D2-01/handler/xmodule_handler/save_user_state", "captionDataDir": null, "sources": [], "transcriptLanguage": "en", "recordedYoutubeIsAvailable": true, "prioritizeHls": false, "duration": null}'
data-bumper-metadata='null'
data-autoadvance-enabled="False"
data-poster='null'
tabindex="-1"
>
<div class="focus_grabber first"></div>
<div class="tc-wrapper">
<div class="video-wrapper">
<span tabindex="0" class="spinner" aria-hidden="false" aria-label="Loading video player"></span>
<span tabindex="-1" class="btn-play fa fa-youtube-play fa-2x is-hidden" aria-hidden="true" aria-label="Play video"></span>
<div class="video-player-pre"></div>
<div class="video-player">
<div id="Krishana-W10D2-01"></div>
<h4 class="hd hd-4 video-error is-hidden">No playable video sources found.</h4>
<h4 class="hd hd-4 video-hls-error is-hidden">
Your browser does not support this video format. Try using a different browser.
</h4>
</div>
<div class="video-player-post"></div>
<div class="closed-captions"></div>
<div class="video-controls is-hidden">
<div>
<div class="vcr"><div class="vidtime">0:00 / 0:00</div></div>
<div class="secondary-controls"></div>
</div>
</div>
</div>
</div>
<div class="focus_grabber last"></div>
</div>
</div>
</div>
<div class="vert vert-2" data-id="block-v1:MITx+8.02.2x+2T2018+type@video+block@Krishana-W10D2-01b">
<div class="xblock xblock-public_view xblock-public_view-video xmodule_display xmodule_VideoBlock" data-usage-id="block-v1:MITx+8.02.2x+2T2018+type@video+block@Krishana-W10D2-01b" data-graded="True" data-runtime-class="LmsRuntime" data-course-id="course-v1:MITx+8.02.2x+2T2018" data-block-type="video" data-request-token="a285686afe6b11ee8e28026cc65ec0d9" data-has-score="False" data-runtime-version="1" data-init="XBlockToXModuleShim">
<script type="json/xblock-args" class="xblock-json-init-args">
{"xmodule-type": "Video"}
</script>
<h3 class="hd hd-2">different ending to batteries</h3>
<div
id="video_Krishana-W10D2-01b"
class="video closed"
data-metadata='{"end": 0.0, "speed": null, "ytTestTimeout": 1500, "publishCompletionUrl": "/courses/course-v1:MITx+8.02.2x+2T2018/xblock/block-v1:MITx+8.02.2x+2T2018+type@video+block@Krishana-W10D2-01b/handler/publish_completion", "ytApiUrl": "https://www.youtube.com/iframe_api", "showCaptions": "true", "streams": "1.00:y6XKpmJjJhs", "poster": null, "saveStateEnabled": false, "start": 0.0, "completionPercentage": 0.95, "transcriptAvailableTranslationsUrl": "/courses/course-v1:MITx+8.02.2x+2T2018/xblock/block-v1:MITx+8.02.2x+2T2018+type@video+block@Krishana-W10D2-01b/handler/transcript/available_translations", "autoplay": false, "transcriptLanguages": {"en": "English"}, "autohideHtml5": false, "transcriptTranslationUrl": "/courses/course-v1:MITx+8.02.2x+2T2018/xblock/block-v1:MITx+8.02.2x+2T2018+type@video+block@Krishana-W10D2-01b/handler/transcript/translation/__lang__", "ytMetadataEndpoint": "", "generalSpeed": 1.0, "lmsRootURL": "https://openlearninglibrary.mit.edu", "autoAdvance": false, "completionEnabled": false, "savedVideoPosition": 0.0, "saveStateUrl": "/courses/course-v1:MITx+8.02.2x+2T2018/xblock/block-v1:MITx+8.02.2x+2T2018+type@video+block@Krishana-W10D2-01b/handler/xmodule_handler/save_user_state", "captionDataDir": null, "sources": [], "transcriptLanguage": "en", "recordedYoutubeIsAvailable": true, "prioritizeHls": false, "duration": null}'
data-bumper-metadata='null'
data-autoadvance-enabled="False"
data-poster='null'
tabindex="-1"
>
<div class="focus_grabber first"></div>
<div class="tc-wrapper">
<div class="video-wrapper">
<span tabindex="0" class="spinner" aria-hidden="false" aria-label="Loading video player"></span>
<span tabindex="-1" class="btn-play fa fa-youtube-play fa-2x is-hidden" aria-hidden="true" aria-label="Play video"></span>
<div class="video-player-pre"></div>
<div class="video-player">
<div id="Krishana-W10D2-01b"></div>
<h4 class="hd hd-4 video-error is-hidden">No playable video sources found.</h4>
<h4 class="hd hd-4 video-hls-error is-hidden">
Your browser does not support this video format. Try using a different browser.
</h4>
</div>
<div class="video-player-post"></div>
<div class="closed-captions"></div>
<div class="video-controls is-hidden">
<div>
<div class="vcr"><div class="vidtime">0:00 / 0:00</div></div>
<div class="secondary-controls"></div>
</div>
</div>
</div>
</div>
<div class="focus_grabber last"></div>
</div>
</div>
</div>
</div>
</div>
<div class="xblock xblock-public_view xblock-public_view-vertical" data-usage-id="block-v1:MITx+8.02.2x+2T2018+type@vertical+block@vert-html-lesson15_02" data-graded="True" data-runtime-class="LmsRuntime" data-course-id="course-v1:MITx+8.02.2x+2T2018" data-block-type="vertical" data-request-token="a285686afe6b11ee8e28026cc65ec0d9" data-has-score="False" data-runtime-version="1" data-init="VerticalStudentView">
<h2 class="hd hd-2 unit-title">Kirchhoff's Circuit Rules</h2>
<div class="vert-mod">
<div class="vert vert-0" data-id="block-v1:MITx+8.02.2x+2T2018+type@html+block@lesson15_02">
<div class="xblock xblock-public_view xblock-public_view-html xmodule_display xmodule_HtmlBlock" data-usage-id="block-v1:MITx+8.02.2x+2T2018+type@html+block@lesson15_02" data-graded="True" data-runtime-class="LmsRuntime" data-course-id="course-v1:MITx+8.02.2x+2T2018" data-block-type="html" data-request-token="a285686afe6b11ee8e28026cc65ec0d9" data-has-score="False" data-runtime-version="1" data-init="XBlockToXModuleShim">
<script type="json/xblock-args" class="xblock-json-init-args">
{"xmodule-type": "HTMLModule"}
</script>
<center><p><b>Kirchhoff's Loop Rule</b></p></center><p> To analyze circuits we will use two circuit rules. These rules are a consequence of conservation of charge and conservation of energy and they are known as Kirchhoff's Circuits Rules.</p><p><b> Kirchhoff's first rule, Junction Rule:</b> The sum of all currents entering a junction must be equal to the sum of all the currents leaving the junction. This is a statement of charge conservation. At the junction no charge is created or destroyed.</p><p><b>Kirchhoff's second rule, Loop Rule:</b> The sum of the change in potential across the elements in a closed circuit loop is zero. This is a consequence of conservation of energy.</p>
</div>
</div>
</div>
</div>
<div class="xblock xblock-public_view xblock-public_view-vertical" data-usage-id="block-v1:MITx+8.02.2x+2T2018+type@vertical+block@vert-L15v02" data-graded="True" data-runtime-class="LmsRuntime" data-course-id="course-v1:MITx+8.02.2x+2T2018" data-block-type="vertical" data-request-token="a285686afe6b11ee8e28026cc65ec0d9" data-has-score="False" data-runtime-version="1" data-init="VerticalStudentView">
<h2 class="hd hd-2 unit-title">L15v2: Kirchhoff's Loop Rule</h2>
<div class="vert-mod">
<div class="vert vert-0" data-id="block-v1:MITx+8.02.2x+2T2018+type@html+block@lesson15_03">
<div class="xblock xblock-public_view xblock-public_view-html xmodule_display xmodule_HtmlBlock" data-usage-id="block-v1:MITx+8.02.2x+2T2018+type@html+block@lesson15_03" data-graded="True" data-runtime-class="LmsRuntime" data-course-id="course-v1:MITx+8.02.2x+2T2018" data-block-type="html" data-request-token="a285686afe6b11ee8e28026cc65ec0d9" data-has-score="False" data-runtime-version="1" data-init="XBlockToXModuleShim">
<script type="json/xblock-args" class="xblock-json-init-args">
{"xmodule-type": "HTMLModule"}
</script>
<center><p><b>Kirchhoff's Loop Rule</b></p>.
</center><p> The sum of the change of voltage across the elements on a closed loop is zero:</p>
\[\sum_{\text{closed loop}} \Delta V = 0\]
<p><b>Kirchhoff's Junction Rule</b></p>
<p> The sum of the currents into a node must be equal to the sum of the currents out of the node:</p>
\[\sum I_{in} = \sum I_{out}\]
<p> A node is formed by the junction of three or more current carrying
wires. In the circuit shown in the figure, current \(I_1\) is flowing into the node, and currents \(I_2\) and \(I_3\) are flowing out, therefore:
\[I_1 = I_2+I_3\]
</p>
<center><img src="/assets/courseware/v1/6ffec176efe6ed15661aa3cb1d04430c/asset-v1:MITx+8.02.2x+2T2018+type@asset+block/images_html_lesson15_02.svg" width="300"/></center>
</div>
</div>
<div class="vert vert-1" data-id="block-v1:MITx+8.02.2x+2T2018+type@video+block@L15v02">
<div class="xblock xblock-public_view xblock-public_view-video xmodule_display xmodule_VideoBlock" data-usage-id="block-v1:MITx+8.02.2x+2T2018+type@video+block@L15v02" data-graded="True" data-runtime-class="LmsRuntime" data-course-id="course-v1:MITx+8.02.2x+2T2018" data-block-type="video" data-request-token="a285686afe6b11ee8e28026cc65ec0d9" data-has-score="False" data-runtime-version="1" data-init="XBlockToXModuleShim">
<script type="json/xblock-args" class="xblock-json-init-args">
{"xmodule-type": "Video"}
</script>
<h3 class="hd hd-2">L15v02: Kirchhoff's Loop Rule</h3>
<div
id="video_L15v02"
class="video closed"
data-metadata='{"end": 0.0, "speed": null, "ytTestTimeout": 1500, "publishCompletionUrl": "/courses/course-v1:MITx+8.02.2x+2T2018/xblock/block-v1:MITx+8.02.2x+2T2018+type@video+block@L15v02/handler/publish_completion", "ytApiUrl": "https://www.youtube.com/iframe_api", "showCaptions": "true", "streams": "1.00:5F-TBCgodYg", "poster": null, "saveStateEnabled": false, "start": 0.0, "completionPercentage": 0.95, "transcriptAvailableTranslationsUrl": "/courses/course-v1:MITx+8.02.2x+2T2018/xblock/block-v1:MITx+8.02.2x+2T2018+type@video+block@L15v02/handler/transcript/available_translations", "autoplay": false, "transcriptLanguages": {"en": "English"}, "autohideHtml5": false, "transcriptTranslationUrl": "/courses/course-v1:MITx+8.02.2x+2T2018/xblock/block-v1:MITx+8.02.2x+2T2018+type@video+block@L15v02/handler/transcript/translation/__lang__", "ytMetadataEndpoint": "", "generalSpeed": 1.0, "lmsRootURL": "https://openlearninglibrary.mit.edu", "autoAdvance": false, "completionEnabled": false, "savedVideoPosition": 0.0, "saveStateUrl": "/courses/course-v1:MITx+8.02.2x+2T2018/xblock/block-v1:MITx+8.02.2x+2T2018+type@video+block@L15v02/handler/xmodule_handler/save_user_state", "captionDataDir": null, "sources": [], "transcriptLanguage": "en", "recordedYoutubeIsAvailable": true, "prioritizeHls": false, "duration": null}'
data-bumper-metadata='null'
data-autoadvance-enabled="False"
data-poster='null'
tabindex="-1"
>
<div class="focus_grabber first"></div>
<div class="tc-wrapper">
<div class="video-wrapper">
<span tabindex="0" class="spinner" aria-hidden="false" aria-label="Loading video player"></span>
<span tabindex="-1" class="btn-play fa fa-youtube-play fa-2x is-hidden" aria-hidden="true" aria-label="Play video"></span>
<div class="video-player-pre"></div>
<div class="video-player">
<div id="L15v02"></div>
<h4 class="hd hd-4 video-error is-hidden">No playable video sources found.</h4>
<h4 class="hd hd-4 video-hls-error is-hidden">
Your browser does not support this video format. Try using a different browser.
</h4>
</div>
<div class="video-player-post"></div>
<div class="closed-captions"></div>
<div class="video-controls is-hidden">
<div>
<div class="vcr"><div class="vidtime">0:00 / 0:00</div></div>
<div class="secondary-controls"></div>
</div>
</div>
</div>
</div>
<div class="focus_grabber last"></div>
<h3 class="hd hd-4 downloads-heading sr" id="video-download-transcripts_L15v02">Downloads and transcripts</h3>
<div class="wrapper-downloads" role="region" aria-labelledby="video-download-transcripts_L15v02">
<div class="wrapper-download-transcripts">
<h4 class="hd hd-5">Transcripts</h4>
<ul class="list-download-transcripts">
<li class="transcript-option">
<a class="btn btn-link" href="/courses/course-v1:MITx+8.02.2x+2T2018/xblock/block-v1:MITx+8.02.2x+2T2018+type@video+block@L15v02/handler/transcript/download" data-value="srt">Download SubRip (.srt) file</a>
</li>
<li class="transcript-option">
<a class="btn btn-link" href="/courses/course-v1:MITx+8.02.2x+2T2018/xblock/block-v1:MITx+8.02.2x+2T2018+type@video+block@L15v02/handler/transcript/download" data-value="txt">Download Text (.txt) file</a>
</li>
</ul>
</div>
</div>
</div>
</div>
</div>
</div>
</div>
<div class="xblock xblock-public_view xblock-public_view-vertical" data-usage-id="block-v1:MITx+8.02.2x+2T2018+type@vertical+block@vert-checkpoint_w6_9" data-graded="True" data-runtime-class="LmsRuntime" data-course-id="course-v1:MITx+8.02.2x+2T2018" data-block-type="vertical" data-request-token="a285686afe6b11ee8e28026cc65ec0d9" data-has-score="False" data-runtime-version="1" data-init="VerticalStudentView">
<h2 class="hd hd-2 unit-title">L15Q1: Difference in Potential</h2>
<div class="vert-mod">
<div class="vert vert-0" data-id="block-v1:MITx+8.02.2x+2T2018+type@problem+block@checkpoint_w6_9">
<div class="xblock xblock-public_view xblock-public_view-problem xmodule_display xmodule_ProblemBlock" data-usage-id="block-v1:MITx+8.02.2x+2T2018+type@problem+block@checkpoint_w6_9" data-graded="True" data-runtime-class="LmsRuntime" data-course-id="course-v1:MITx+8.02.2x+2T2018" data-block-type="problem" data-request-token="a285686afe6b11ee8e28026cc65ec0d9" data-has-score="True" data-runtime-version="1" data-init="XBlockToXModuleShim">
<script type="json/xblock-args" class="xblock-json-init-args">
{"xmodule-type": "Problem"}
</script>
<div id="problem_checkpoint_w6_9" class="problems-wrapper" role="group"
aria-labelledby="checkpoint_w6_9-problem-title"
data-problem-id="block-v1:MITx+8.02.2x+2T2018+type@problem+block@checkpoint_w6_9" data-url="/courses/course-v1:MITx+8.02.2x+2T2018/xblock/block-v1:MITx+8.02.2x+2T2018+type@problem+block@checkpoint_w6_9/handler/xmodule_handler"
data-problem-score="0.0"
data-problem-total-possible="1.0"
data-attempts-used="0"
data-content="
<h3 class="hd hd-3 problem-header" id="checkpoint_w6_9-problem-title" aria-describedby="block-v1:MITx+8.02.2x+2T2018+type@problem+block@checkpoint_w6_9-problem-progress" tabindex="-1">
Difference in potential
</h3>
<div class="problem-progress" id="block-v1:MITx+8.02.2x+2T2018+type@problem+block@checkpoint_w6_9-problem-progress"></div>
<div class="problem">
<div>
<center>
<img src="/assets/courseware/v1/a9bdafd0acd55c3c058b4b2e16ffade9/asset-v1:MITx+8.02.2x+2T2018+type@asset+block/images_checkpoint_w6_9.svg" width="330"/>
</center>
<p>
The circuit shown consists of four different resistors and a battery. You do not know the strength of the battery or the values of any of the four resistances. Select the expressions that will be equal to [mathjaxinline]{\cal E}[/mathjaxinline], the emf across the battery. </p>
<p>
For the choices below, [mathjaxinline]\Delta V_1[/mathjaxinline] represents the magnitude of the difference in potential across resistance [mathjaxinline]R_1[/mathjaxinline], etc. </p>
<p>
<div class="wrapper-problem-response" tabindex="-1" aria-label="Question 1" role="group"><div class="choicegroup capa_inputtype" id="inputtype_checkpoint_w6_9_2_1">
<fieldset aria-describedby="status_checkpoint_w6_9_2_1">
<div class="field">
<input type="checkbox" name="input_checkpoint_w6_9_2_1[]" id="input_checkpoint_w6_9_2_1_choice_0" class="field-input input-checkbox" value="choice_0"/><label id="checkpoint_w6_9_2_1-choice_0-label" for="input_checkpoint_w6_9_2_1_choice_0" class="response-label field-label label-inline" aria-describedby="status_checkpoint_w6_9_2_1">
<text>1. [mathjaxinline]{\cal E}=\Delta V_1+\Delta V_2[/mathjaxinline]</text>
</label>
</div>
<div class="field">
<input type="checkbox" name="input_checkpoint_w6_9_2_1[]" id="input_checkpoint_w6_9_2_1_choice_1" class="field-input input-checkbox" value="choice_1"/><label id="checkpoint_w6_9_2_1-choice_1-label" for="input_checkpoint_w6_9_2_1_choice_1" class="response-label field-label label-inline" aria-describedby="status_checkpoint_w6_9_2_1">
<text>2. [mathjaxinline]{\cal E}=\Delta V_1+\Delta V_3[/mathjaxinline]</text>
</label>
</div>
<div class="field">
<input type="checkbox" name="input_checkpoint_w6_9_2_1[]" id="input_checkpoint_w6_9_2_1_choice_2" class="field-input input-checkbox" value="choice_2"/><label id="checkpoint_w6_9_2_1-choice_2-label" for="input_checkpoint_w6_9_2_1_choice_2" class="response-label field-label label-inline" aria-describedby="status_checkpoint_w6_9_2_1">
<text>3. [mathjaxinline]{\cal E}=\Delta V_2+\Delta V_3[/mathjaxinline]</text>
</label>
</div>
<div class="field">
<input type="checkbox" name="input_checkpoint_w6_9_2_1[]" id="input_checkpoint_w6_9_2_1_choice_3" class="field-input input-checkbox" value="choice_3"/><label id="checkpoint_w6_9_2_1-choice_3-label" for="input_checkpoint_w6_9_2_1_choice_3" class="response-label field-label label-inline" aria-describedby="status_checkpoint_w6_9_2_1">
<text>4. [mathjaxinline]{\cal E}=\Delta V_1+\Delta V_2+\Delta V_3[/mathjaxinline]</text>
</label>
</div>
<div class="field">
<input type="checkbox" name="input_checkpoint_w6_9_2_1[]" id="input_checkpoint_w6_9_2_1_choice_4" class="field-input input-checkbox" value="choice_4"/><label id="checkpoint_w6_9_2_1-choice_4-label" for="input_checkpoint_w6_9_2_1_choice_4" class="response-label field-label label-inline" aria-describedby="status_checkpoint_w6_9_2_1">
<text>5. [mathjaxinline]{\cal E}=\Delta V_1+\Delta V_2+\Delta V_3+\Delta V_4[/mathjaxinline]</text>
</label>
</div>
<div class="field">
<input type="checkbox" name="input_checkpoint_w6_9_2_1[]" id="input_checkpoint_w6_9_2_1_choice_5" class="field-input input-checkbox" value="choice_5"/><label id="checkpoint_w6_9_2_1-choice_5-label" for="input_checkpoint_w6_9_2_1_choice_5" class="response-label field-label label-inline" aria-describedby="status_checkpoint_w6_9_2_1">
<text>6. [mathjaxinline]{\cal E}=\Delta V_1+\Delta V_4[/mathjaxinline]</text>
</label>
</div>
<div class="field">
<input type="checkbox" name="input_checkpoint_w6_9_2_1[]" id="input_checkpoint_w6_9_2_1_choice_6" class="field-input input-checkbox" value="choice_6"/><label id="checkpoint_w6_9_2_1-choice_6-label" for="input_checkpoint_w6_9_2_1_choice_6" class="response-label field-label label-inline" aria-describedby="status_checkpoint_w6_9_2_1">
<text>7. [mathjaxinline]{\cal E}=\Delta V_4[/mathjaxinline]</text>
</label>
</div>
<span id="answer_checkpoint_w6_9_2_1"/>
</fieldset>
<div class="indicator-container">
<span class="status unanswered" id="status_checkpoint_w6_9_2_1" data-tooltip="Not yet answered.">
<span class="sr">unanswered</span><span class="status-icon" aria-hidden="true"/>
</span>
</div>
</div></div>
</p>
<p>
<div class="solution-span">
<span id="solution_checkpoint_w6_9_solution_1"/>
</div></p>
</div>
<div class="action">
<input type="hidden" name="problem_id" value="Difference in potential" />
<div class="submit-attempt-container">
<button type="button" class="submit btn-brand" data-submitting="Submitting" data-value="Submit" data-should-enable-submit-button="True" aria-describedby="submission_feedback_checkpoint_w6_9" >
<span class="submit-label">Submit</span>
</button>
<div class="submission-feedback" id="submission_feedback_checkpoint_w6_9">
<span class="sr">Some problems have options such as save, reset, hints, or show answer. These options follow the Submit button.</span>
</div>
</div>
<div class="problem-action-buttons-wrapper">
</div>
</div>
<div class="notification warning notification-gentle-alert
is-hidden"
tabindex="-1">
<span class="icon fa fa-exclamation-circle" aria-hidden="true"></span>
<span class="notification-message" aria-describedby="checkpoint_w6_9-problem-title">
</span>
<div class="notification-btn-wrapper">
<button type="button" class="btn btn-default btn-small notification-btn review-btn sr">Review</button>
</div>
</div>
<div class="notification warning notification-save
is-hidden"
tabindex="-1">
<span class="icon fa fa-save" aria-hidden="true"></span>
<span class="notification-message" aria-describedby="checkpoint_w6_9-problem-title">None
</span>
<div class="notification-btn-wrapper">
<button type="button" class="btn btn-default btn-small notification-btn review-btn sr">Review</button>
</div>
</div>
<div class="notification general notification-show-answer
is-hidden"
tabindex="-1">
<span class="icon fa fa-info-circle" aria-hidden="true"></span>
<span class="notification-message" aria-describedby="checkpoint_w6_9-problem-title">Answers are displayed within the problem
</span>
<div class="notification-btn-wrapper">
<button type="button" class="btn btn-default btn-small notification-btn review-btn sr">Review</button>
</div>
</div>
</div>
"
data-graded="True">
<p class="loading-spinner">
<i class="fa fa-spinner fa-pulse fa-2x fa-fw"></i>
<span class="sr">Loading…</span>
</p>
</div>
</div>
</div>
</div>
</div>
<div class="xblock xblock-public_view xblock-public_view-vertical" data-usage-id="block-v1:MITx+8.02.2x+2T2018+type@vertical+block@vert-L15v03" data-graded="True" data-runtime-class="LmsRuntime" data-course-id="course-v1:MITx+8.02.2x+2T2018" data-block-type="vertical" data-request-token="a285686afe6b11ee8e28026cc65ec0d9" data-has-score="False" data-runtime-version="1" data-init="VerticalStudentView">
<h2 class="hd hd-2 unit-title">L15v3: Choosing Current Direction and Circulation Direction</h2>
<div class="vert-mod">
<div class="vert vert-0" data-id="block-v1:MITx+8.02.2x+2T2018+type@video+block@L15v03">
<div class="xblock xblock-public_view xblock-public_view-video xmodule_display xmodule_VideoBlock" data-usage-id="block-v1:MITx+8.02.2x+2T2018+type@video+block@L15v03" data-graded="True" data-runtime-class="LmsRuntime" data-course-id="course-v1:MITx+8.02.2x+2T2018" data-block-type="video" data-request-token="a285686afe6b11ee8e28026cc65ec0d9" data-has-score="False" data-runtime-version="1" data-init="XBlockToXModuleShim">
<script type="json/xblock-args" class="xblock-json-init-args">
{"xmodule-type": "Video"}
</script>
<h3 class="hd hd-2">L15v03: Choosing Current Direction and Circulation Direction</h3>
<div
id="video_L15v03"
class="video closed"
data-metadata='{"end": 0.0, "speed": null, "ytTestTimeout": 1500, "publishCompletionUrl": "/courses/course-v1:MITx+8.02.2x+2T2018/xblock/block-v1:MITx+8.02.2x+2T2018+type@video+block@L15v03/handler/publish_completion", "ytApiUrl": "https://www.youtube.com/iframe_api", "showCaptions": "true", "streams": "1.00:--hbP3mOwVo", "poster": null, "saveStateEnabled": false, "start": 0.0, "completionPercentage": 0.95, "transcriptAvailableTranslationsUrl": "/courses/course-v1:MITx+8.02.2x+2T2018/xblock/block-v1:MITx+8.02.2x+2T2018+type@video+block@L15v03/handler/transcript/available_translations", "autoplay": false, "transcriptLanguages": {"en": "English"}, "autohideHtml5": false, "transcriptTranslationUrl": "/courses/course-v1:MITx+8.02.2x+2T2018/xblock/block-v1:MITx+8.02.2x+2T2018+type@video+block@L15v03/handler/transcript/translation/__lang__", "ytMetadataEndpoint": "", "generalSpeed": 1.0, "lmsRootURL": "https://openlearninglibrary.mit.edu", "autoAdvance": false, "completionEnabled": false, "savedVideoPosition": 0.0, "saveStateUrl": "/courses/course-v1:MITx+8.02.2x+2T2018/xblock/block-v1:MITx+8.02.2x+2T2018+type@video+block@L15v03/handler/xmodule_handler/save_user_state", "captionDataDir": null, "sources": [], "transcriptLanguage": "en", "recordedYoutubeIsAvailable": true, "prioritizeHls": false, "duration": null}'
data-bumper-metadata='null'
data-autoadvance-enabled="False"
data-poster='null'
tabindex="-1"
>
<div class="focus_grabber first"></div>
<div class="tc-wrapper">
<div class="video-wrapper">
<span tabindex="0" class="spinner" aria-hidden="false" aria-label="Loading video player"></span>
<span tabindex="-1" class="btn-play fa fa-youtube-play fa-2x is-hidden" aria-hidden="true" aria-label="Play video"></span>
<div class="video-player-pre"></div>
<div class="video-player">
<div id="L15v03"></div>
<h4 class="hd hd-4 video-error is-hidden">No playable video sources found.</h4>
<h4 class="hd hd-4 video-hls-error is-hidden">
Your browser does not support this video format. Try using a different browser.
</h4>
</div>
<div class="video-player-post"></div>
<div class="closed-captions"></div>
<div class="video-controls is-hidden">
<div>
<div class="vcr"><div class="vidtime">0:00 / 0:00</div></div>
<div class="secondary-controls"></div>
</div>
</div>
</div>
</div>
<div class="focus_grabber last"></div>
<h3 class="hd hd-4 downloads-heading sr" id="video-download-transcripts_L15v03">Downloads and transcripts</h3>
<div class="wrapper-downloads" role="region" aria-labelledby="video-download-transcripts_L15v03">
<div class="wrapper-download-transcripts">
<h4 class="hd hd-5">Transcripts</h4>
<ul class="list-download-transcripts">
<li class="transcript-option">
<a class="btn btn-link" href="/courses/course-v1:MITx+8.02.2x+2T2018/xblock/block-v1:MITx+8.02.2x+2T2018+type@video+block@L15v03/handler/transcript/download" data-value="srt">Download SubRip (.srt) file</a>
</li>
<li class="transcript-option">
<a class="btn btn-link" href="/courses/course-v1:MITx+8.02.2x+2T2018/xblock/block-v1:MITx+8.02.2x+2T2018+type@video+block@L15v03/handler/transcript/download" data-value="txt">Download Text (.txt) file</a>
</li>
</ul>
</div>
</div>
</div>
</div>
</div>
</div>
</div>
<div class="xblock xblock-public_view xblock-public_view-vertical" data-usage-id="block-v1:MITx+8.02.2x+2T2018+type@vertical+block@vert-L15v04" data-graded="True" data-runtime-class="LmsRuntime" data-course-id="course-v1:MITx+8.02.2x+2T2018" data-block-type="vertical" data-request-token="a285686afe6b11ee8e28026cc65ec0d9" data-has-score="False" data-runtime-version="1" data-init="VerticalStudentView">
<h2 class="hd hd-2 unit-title">L15v4: Difference in Potential across a Battery and Resistor</h2>
<div class="vert-mod">
<div class="vert vert-0" data-id="block-v1:MITx+8.02.2x+2T2018+type@video+block@L15v04">
<div class="xblock xblock-public_view xblock-public_view-video xmodule_display xmodule_VideoBlock" data-usage-id="block-v1:MITx+8.02.2x+2T2018+type@video+block@L15v04" data-graded="True" data-runtime-class="LmsRuntime" data-course-id="course-v1:MITx+8.02.2x+2T2018" data-block-type="video" data-request-token="a285686afe6b11ee8e28026cc65ec0d9" data-has-score="False" data-runtime-version="1" data-init="XBlockToXModuleShim">
<script type="json/xblock-args" class="xblock-json-init-args">
{"xmodule-type": "Video"}
</script>
<h3 class="hd hd-2">L15v04: Difference in Potential across a Battery and Resistor</h3>
<div
id="video_L15v04"
class="video closed"
data-metadata='{"end": 0.0, "speed": null, "ytTestTimeout": 1500, "publishCompletionUrl": "/courses/course-v1:MITx+8.02.2x+2T2018/xblock/block-v1:MITx+8.02.2x+2T2018+type@video+block@L15v04/handler/publish_completion", "ytApiUrl": "https://www.youtube.com/iframe_api", "showCaptions": "true", "streams": "1.00:aegCSYOTO9I", "poster": null, "saveStateEnabled": false, "start": 0.0, "completionPercentage": 0.95, "transcriptAvailableTranslationsUrl": "/courses/course-v1:MITx+8.02.2x+2T2018/xblock/block-v1:MITx+8.02.2x+2T2018+type@video+block@L15v04/handler/transcript/available_translations", "autoplay": false, "transcriptLanguages": {"en": "English"}, "autohideHtml5": false, "transcriptTranslationUrl": "/courses/course-v1:MITx+8.02.2x+2T2018/xblock/block-v1:MITx+8.02.2x+2T2018+type@video+block@L15v04/handler/transcript/translation/__lang__", "ytMetadataEndpoint": "", "generalSpeed": 1.0, "lmsRootURL": "https://openlearninglibrary.mit.edu", "autoAdvance": false, "completionEnabled": false, "savedVideoPosition": 0.0, "saveStateUrl": "/courses/course-v1:MITx+8.02.2x+2T2018/xblock/block-v1:MITx+8.02.2x+2T2018+type@video+block@L15v04/handler/xmodule_handler/save_user_state", "captionDataDir": null, "sources": [], "transcriptLanguage": "en", "recordedYoutubeIsAvailable": true, "prioritizeHls": false, "duration": null}'
data-bumper-metadata='null'
data-autoadvance-enabled="False"
data-poster='null'
tabindex="-1"
>
<div class="focus_grabber first"></div>
<div class="tc-wrapper">
<div class="video-wrapper">
<span tabindex="0" class="spinner" aria-hidden="false" aria-label="Loading video player"></span>
<span tabindex="-1" class="btn-play fa fa-youtube-play fa-2x is-hidden" aria-hidden="true" aria-label="Play video"></span>
<div class="video-player-pre"></div>
<div class="video-player">
<div id="L15v04"></div>
<h4 class="hd hd-4 video-error is-hidden">No playable video sources found.</h4>
<h4 class="hd hd-4 video-hls-error is-hidden">
Your browser does not support this video format. Try using a different browser.
</h4>
</div>
<div class="video-player-post"></div>
<div class="closed-captions"></div>
<div class="video-controls is-hidden">
<div>
<div class="vcr"><div class="vidtime">0:00 / 0:00</div></div>
<div class="secondary-controls"></div>
</div>
</div>
</div>
</div>
<div class="focus_grabber last"></div>
<h3 class="hd hd-4 downloads-heading sr" id="video-download-transcripts_L15v04">Downloads and transcripts</h3>
<div class="wrapper-downloads" role="region" aria-labelledby="video-download-transcripts_L15v04">
<div class="wrapper-download-transcripts">
<h4 class="hd hd-5">Transcripts</h4>
<ul class="list-download-transcripts">
<li class="transcript-option">
<a class="btn btn-link" href="/courses/course-v1:MITx+8.02.2x+2T2018/xblock/block-v1:MITx+8.02.2x+2T2018+type@video+block@L15v04/handler/transcript/download" data-value="srt">Download SubRip (.srt) file</a>
</li>
<li class="transcript-option">
<a class="btn btn-link" href="/courses/course-v1:MITx+8.02.2x+2T2018/xblock/block-v1:MITx+8.02.2x+2T2018+type@video+block@L15v04/handler/transcript/download" data-value="txt">Download Text (.txt) file</a>
</li>
</ul>
</div>
</div>
</div>
</div>
</div>
</div>
</div>
<div class="xblock xblock-public_view xblock-public_view-vertical" data-usage-id="block-v1:MITx+8.02.2x+2T2018+type@vertical+block@vert-checkpoint_w6_10" data-graded="True" data-runtime-class="LmsRuntime" data-course-id="course-v1:MITx+8.02.2x+2T2018" data-block-type="vertical" data-request-token="a285686afe6b11ee8e28026cc65ec0d9" data-has-score="False" data-runtime-version="1" data-init="VerticalStudentView">
<h2 class="hd hd-2 unit-title">L15Q2: Example Loops</h2>
<div class="vert-mod">
<div class="vert vert-0" data-id="block-v1:MITx+8.02.2x+2T2018+type@problem+block@checkpoint_w6_10">
<div class="xblock xblock-public_view xblock-public_view-problem xmodule_display xmodule_ProblemBlock" data-usage-id="block-v1:MITx+8.02.2x+2T2018+type@problem+block@checkpoint_w6_10" data-graded="True" data-runtime-class="LmsRuntime" data-course-id="course-v1:MITx+8.02.2x+2T2018" data-block-type="problem" data-request-token="a285686afe6b11ee8e28026cc65ec0d9" data-has-score="True" data-runtime-version="1" data-init="XBlockToXModuleShim">
<script type="json/xblock-args" class="xblock-json-init-args">
{"xmodule-type": "Problem"}
</script>
<div id="problem_checkpoint_w6_10" class="problems-wrapper" role="group"
aria-labelledby="checkpoint_w6_10-problem-title"
data-problem-id="block-v1:MITx+8.02.2x+2T2018+type@problem+block@checkpoint_w6_10" data-url="/courses/course-v1:MITx+8.02.2x+2T2018/xblock/block-v1:MITx+8.02.2x+2T2018+type@problem+block@checkpoint_w6_10/handler/xmodule_handler"
data-problem-score="0.0"
data-problem-total-possible="1.0"
data-attempts-used="0"
data-content="
<h3 class="hd hd-3 problem-header" id="checkpoint_w6_10-problem-title" aria-describedby="block-v1:MITx+8.02.2x+2T2018+type@problem+block@checkpoint_w6_10-problem-progress" tabindex="-1">
Example Loops
</h3>
<div class="problem-progress" id="block-v1:MITx+8.02.2x+2T2018+type@problem+block@checkpoint_w6_10-problem-progress"></div>
<div class="problem">
<div>
<p>
The circuit shown consists of four different resistors and a battery. The current flowing through the battery, [mathjaxinline]I[/mathjaxinline], and the currents flowing through the four resistors, [mathjaxinline]I_1[/mathjaxinline], [mathjaxinline]I_2[/mathjaxinline], [mathjaxinline]I_3[/mathjaxinline], and [mathjaxinline]I_4[/mathjaxinline] are shown. </p>
<center>
<img src="/assets/courseware/v1/fe86a6c89dc864c96f83263198f54166/asset-v1:MITx+8.02.2x+2T2018+type@asset+block/images_checkpoint_w6_10.svg" width="330"/>
</center>
<p><b class="bfseries">(Part a)</b> Consider the closed loop formed by the battery, [mathjaxinline]R_1[/mathjaxinline] and [mathjaxinline]R_3[/mathjaxinline]. The closed loop is highlighted in the figure below. </p>
<center>
<img src="/assets/courseware/v1/41043bff9d44e14bfed505edaf1acd1b/asset-v1:MITx+8.02.2x+2T2018+type@asset+block/images_checkpoint_w6_10_a2.svg" width="330"/>
</center>
<p>
Write the [mathjaxinline]\sum \Delta V[/mathjaxinline] if the sense of circulation of the loop is counterclockwise. Express your answer in terms of emf for [mathjaxinline]{\cal E}[/mathjaxinline], [mathjaxinline]I[/mathjaxinline], I_1 for [mathjaxinline]I_1[/mathjaxinline], I_2 for [mathjaxinline]I_2[/mathjaxinline], I_3 for [mathjaxinline]I_3[/mathjaxinline], I_4 for [mathjaxinline]I_4[/mathjaxinline], R_1 for [mathjaxinline]R_1[/mathjaxinline], R_2 for [mathjaxinline]R_2[/mathjaxinline], R_3 for [mathjaxinline]R_3[/mathjaxinline], and R_4 for [mathjaxinline]R_4[/mathjaxinline], as needed. </p>
<p>
<p style="display:inline">[mathjaxinline]\sum \Delta V =[/mathjaxinline] </p>
<div class="inline" tabindex="-1" aria-label="Question 1" role="group"><div id="inputtype_checkpoint_w6_10_2_1" class="text-input-dynamath capa_inputtype inline textline">
<div class="unanswered inline">
<input type="text" name="input_checkpoint_w6_10_2_1" id="input_checkpoint_w6_10_2_1" aria-describedby="status_checkpoint_w6_10_2_1" value="" class="math" size="40"/>
<span class="trailing_text" id="trailing_text_checkpoint_w6_10_2_1"/>
<span class="status unanswered" id="status_checkpoint_w6_10_2_1" data-tooltip="Not yet answered.">
<span class="sr">unanswered</span><span class="status-icon" aria-hidden="true"/>
</span>
<p id="answer_checkpoint_w6_10_2_1" class="answer"/>
<div id="display_checkpoint_w6_10_2_1" class="equation">`{::}`</div>
<textarea style="display:none" id="input_checkpoint_w6_10_2_1_dynamath" name="input_checkpoint_w6_10_2_1_dynamath"/>
</div>
</div></div>
</p>
<p>
<div class="solution-span">
<span id="solution_checkpoint_w6_10_solution_1"/>
</div></p>
<p><b class="bfseries">(Part b)</b> Consider the closed loop formed by [mathjaxinline]R_1[/mathjaxinline], [mathjaxinline]R_3[/mathjaxinline] and [mathjaxinline]R_4[/mathjaxinline]. The closed loop is highlighted in the figure below. </p>
<center>
<img src="/assets/courseware/v1/a2fa99fcd04cca45dce8e89d274fa278/asset-v1:MITx+8.02.2x+2T2018+type@asset+block/images_checkpoint_w6_10_b2.svg" width="330"/>
</center>
<p>
Write the [mathjaxinline]\sum \Delta V[/mathjaxinline] if the sense of circulation along the closed loop is clockwise. Express your answer in terms of emf for [mathjaxinline]{\cal E}[/mathjaxinline], [mathjaxinline]I[/mathjaxinline], I_1 for [mathjaxinline]I_1[/mathjaxinline], I_2 for [mathjaxinline]I_2[/mathjaxinline], I_3 for [mathjaxinline]I_3[/mathjaxinline], I_4 for [mathjaxinline]I_4[/mathjaxinline], R_1 for [mathjaxinline]R_1[/mathjaxinline], R_2 for [mathjaxinline]R_2[/mathjaxinline], R_3 for [mathjaxinline]R_3[/mathjaxinline], and R_4 for [mathjaxinline]R_4[/mathjaxinline], as needed. </p>
<p>
<p style="display:inline">[mathjaxinline]\sum \Delta V =[/mathjaxinline] </p>
<div class="inline" tabindex="-1" aria-label="Question 2" role="group"><div id="inputtype_checkpoint_w6_10_3_1" class="text-input-dynamath capa_inputtype inline textline">
<div class="unanswered inline">
<input type="text" name="input_checkpoint_w6_10_3_1" id="input_checkpoint_w6_10_3_1" aria-describedby="status_checkpoint_w6_10_3_1" value="" class="math" size="40"/>
<span class="trailing_text" id="trailing_text_checkpoint_w6_10_3_1"/>
<span class="status unanswered" id="status_checkpoint_w6_10_3_1" data-tooltip="Not yet answered.">
<span class="sr">unanswered</span><span class="status-icon" aria-hidden="true"/>
</span>
<p id="answer_checkpoint_w6_10_3_1" class="answer"/>
<div id="display_checkpoint_w6_10_3_1" class="equation">`{::}`</div>
<textarea style="display:none" id="input_checkpoint_w6_10_3_1_dynamath" name="input_checkpoint_w6_10_3_1_dynamath"/>
</div>
</div></div>
</p>
<p>
<div class="solution-span">
<span id="solution_checkpoint_w6_10_solution_2"/>
</div></p>
</div>
<div class="action">
<input type="hidden" name="problem_id" value="Example Loops" />
<div class="submit-attempt-container">
<button type="button" class="submit btn-brand" data-submitting="Submitting" data-value="Submit" data-should-enable-submit-button="True" aria-describedby="submission_feedback_checkpoint_w6_10" >
<span class="submit-label">Submit</span>
</button>
<div class="submission-feedback" id="submission_feedback_checkpoint_w6_10">
<span class="sr">Some problems have options such as save, reset, hints, or show answer. These options follow the Submit button.</span>
</div>
</div>
<div class="problem-action-buttons-wrapper">
</div>
</div>
<div class="notification warning notification-gentle-alert
is-hidden"
tabindex="-1">
<span class="icon fa fa-exclamation-circle" aria-hidden="true"></span>
<span class="notification-message" aria-describedby="checkpoint_w6_10-problem-title">
</span>
<div class="notification-btn-wrapper">
<button type="button" class="btn btn-default btn-small notification-btn review-btn sr">Review</button>
</div>
</div>
<div class="notification warning notification-save
is-hidden"
tabindex="-1">
<span class="icon fa fa-save" aria-hidden="true"></span>
<span class="notification-message" aria-describedby="checkpoint_w6_10-problem-title">None
</span>
<div class="notification-btn-wrapper">
<button type="button" class="btn btn-default btn-small notification-btn review-btn sr">Review</button>
</div>
</div>
<div class="notification general notification-show-answer
is-hidden"
tabindex="-1">
<span class="icon fa fa-info-circle" aria-hidden="true"></span>
<span class="notification-message" aria-describedby="checkpoint_w6_10-problem-title">Answers are displayed within the problem
</span>
<div class="notification-btn-wrapper">
<button type="button" class="btn btn-default btn-small notification-btn review-btn sr">Review</button>
</div>
</div>
</div>
"
data-graded="True">
<p class="loading-spinner">
<i class="fa fa-spinner fa-pulse fa-2x fa-fw"></i>
<span class="sr">Loading…</span>
</p>
</div>
</div>
</div>
</div>
</div>
<div class="xblock xblock-public_view xblock-public_view-vertical" data-usage-id="block-v1:MITx+8.02.2x+2T2018+type@vertical+block@vert-L15v05" data-graded="True" data-runtime-class="LmsRuntime" data-course-id="course-v1:MITx+8.02.2x+2T2018" data-block-type="vertical" data-request-token="a285686afe6b11ee8e28026cc65ec0d9" data-has-score="False" data-runtime-version="1" data-init="VerticalStudentView">
<h2 class="hd hd-2 unit-title">L15v5: Worked Example - Simple Circuit</h2>
<div class="vert-mod">
<div class="vert vert-0" data-id="block-v1:MITx+8.02.2x+2T2018+type@problem+block@checkpoint_w6_11">
<div class="xblock xblock-public_view xblock-public_view-problem xmodule_display xmodule_ProblemBlock" data-usage-id="block-v1:MITx+8.02.2x+2T2018+type@problem+block@checkpoint_w6_11" data-graded="True" data-runtime-class="LmsRuntime" data-course-id="course-v1:MITx+8.02.2x+2T2018" data-block-type="problem" data-request-token="a285686afe6b11ee8e28026cc65ec0d9" data-has-score="True" data-runtime-version="1" data-init="XBlockToXModuleShim">
<script type="json/xblock-args" class="xblock-json-init-args">
{"xmodule-type": "Problem"}
</script>
<div id="problem_checkpoint_w6_11" class="problems-wrapper" role="group"
aria-labelledby="checkpoint_w6_11-problem-title"
data-problem-id="block-v1:MITx+8.02.2x+2T2018+type@problem+block@checkpoint_w6_11" data-url="/courses/course-v1:MITx+8.02.2x+2T2018/xblock/block-v1:MITx+8.02.2x+2T2018+type@problem+block@checkpoint_w6_11/handler/xmodule_handler"
data-problem-score="0"
data-problem-total-possible="0"
data-attempts-used="0"
data-content="
<h3 class="hd hd-3 problem-header" id="checkpoint_w6_11-problem-title" aria-describedby="block-v1:MITx+8.02.2x+2T2018+type@problem+block@checkpoint_w6_11-problem-progress" tabindex="-1">
Worked Example: Simple Circuit
</h3>
<div class="problem-progress" id="block-v1:MITx+8.02.2x+2T2018+type@problem+block@checkpoint_w6_11-problem-progress"></div>
<div class="problem">
<div>
<center>
<img src="/assets/courseware/v1/5076da82557779d8a062f2edaa94fde0/asset-v1:MITx+8.02.2x+2T2018+type@asset+block/images_checkpoint_w6_11.svg" width="330"/>
</center>
<p>
Consider the circuit in the figure. The emf of each battery and the resistance of each resistors are known. Assume the current [mathjaxinline]I[/mathjaxinline] circulates counterclockwise as shown. Calculate [mathjaxinline]I[/mathjaxinline] in terms of emf_1 for [mathjaxinline]{\cal E}_1[/mathjaxinline], emf_2 for [mathjaxinline]{\cal E}_2[/mathjaxinline], R_1 for [mathjaxinline]R_1[/mathjaxinline], and R_2 for [mathjaxinline]R_2[/mathjaxinline] as needed. </p>
<p>
<p style="display:inline">[mathjaxinline]I =[/mathjaxinline] </p>
<div class="inline" tabindex="-1" aria-label="Question 1" role="group"><div id="inputtype_checkpoint_w6_11_2_1" class="text-input-dynamath capa_inputtype inline textline">
<div class="unanswered inline">
<input type="text" name="input_checkpoint_w6_11_2_1" id="input_checkpoint_w6_11_2_1" aria-describedby="status_checkpoint_w6_11_2_1" value="" class="math" size="40"/>
<span class="trailing_text" id="trailing_text_checkpoint_w6_11_2_1"/>
<span class="status unanswered" id="status_checkpoint_w6_11_2_1" data-tooltip="Not yet answered.">
<span class="sr">unanswered</span><span class="status-icon" aria-hidden="true"/>
</span>
<p id="answer_checkpoint_w6_11_2_1" class="answer"/>
<div id="display_checkpoint_w6_11_2_1" class="equation">`{::}`</div>
<textarea style="display:none" id="input_checkpoint_w6_11_2_1_dynamath" name="input_checkpoint_w6_11_2_1_dynamath"/>
</div>
</div></div>
</p>
<p>
<div class="solution-span">
<span id="solution_checkpoint_w6_11_solution_1"/>
</div></p>
</div>
<div class="action">
<input type="hidden" name="problem_id" value="Worked Example: Simple Circuit" />
<div class="submit-attempt-container">
<button type="button" class="submit btn-brand" data-submitting="Submitting" data-value="Submit" data-should-enable-submit-button="True" aria-describedby="submission_feedback_checkpoint_w6_11" >
<span class="submit-label">Submit</span>
</button>
<div class="submission-feedback" id="submission_feedback_checkpoint_w6_11">
<span class="sr">Some problems have options such as save, reset, hints, or show answer. These options follow the Submit button.</span>
</div>
</div>
<div class="problem-action-buttons-wrapper">
</div>
</div>
<div class="notification warning notification-gentle-alert
is-hidden"
tabindex="-1">
<span class="icon fa fa-exclamation-circle" aria-hidden="true"></span>
<span class="notification-message" aria-describedby="checkpoint_w6_11-problem-title">
</span>
<div class="notification-btn-wrapper">
<button type="button" class="btn btn-default btn-small notification-btn review-btn sr">Review</button>
</div>
</div>
<div class="notification warning notification-save
is-hidden"
tabindex="-1">
<span class="icon fa fa-save" aria-hidden="true"></span>
<span class="notification-message" aria-describedby="checkpoint_w6_11-problem-title">None
</span>
<div class="notification-btn-wrapper">
<button type="button" class="btn btn-default btn-small notification-btn review-btn sr">Review</button>
</div>
</div>
<div class="notification general notification-show-answer
is-hidden"
tabindex="-1">
<span class="icon fa fa-info-circle" aria-hidden="true"></span>
<span class="notification-message" aria-describedby="checkpoint_w6_11-problem-title">Answers are displayed within the problem
</span>
<div class="notification-btn-wrapper">
<button type="button" class="btn btn-default btn-small notification-btn review-btn sr">Review</button>
</div>
</div>
</div>
"
data-graded="True">
<p class="loading-spinner">
<i class="fa fa-spinner fa-pulse fa-2x fa-fw"></i>
<span class="sr">Loading…</span>
</p>
</div>
</div>
</div>
<div class="vert vert-1" data-id="block-v1:MITx+8.02.2x+2T2018+type@video+block@L15v05">
<div class="xblock xblock-public_view xblock-public_view-video xmodule_display xmodule_VideoBlock" data-usage-id="block-v1:MITx+8.02.2x+2T2018+type@video+block@L15v05" data-graded="True" data-runtime-class="LmsRuntime" data-course-id="course-v1:MITx+8.02.2x+2T2018" data-block-type="video" data-request-token="a285686afe6b11ee8e28026cc65ec0d9" data-has-score="False" data-runtime-version="1" data-init="XBlockToXModuleShim">
<script type="json/xblock-args" class="xblock-json-init-args">
{"xmodule-type": "Video"}
</script>
<h3 class="hd hd-2">L15v05: Worked Example - Simple Circuit</h3>
<div
id="video_L15v05"
class="video closed"
data-metadata='{"end": 0.0, "speed": null, "ytTestTimeout": 1500, "publishCompletionUrl": "/courses/course-v1:MITx+8.02.2x+2T2018/xblock/block-v1:MITx+8.02.2x+2T2018+type@video+block@L15v05/handler/publish_completion", "ytApiUrl": "https://www.youtube.com/iframe_api", "showCaptions": "true", "streams": "1.00:dbaf6TxxnLk", "poster": null, "saveStateEnabled": false, "start": 0.0, "completionPercentage": 0.95, "transcriptAvailableTranslationsUrl": "/courses/course-v1:MITx+8.02.2x+2T2018/xblock/block-v1:MITx+8.02.2x+2T2018+type@video+block@L15v05/handler/transcript/available_translations", "autoplay": false, "transcriptLanguages": {"en": "English"}, "autohideHtml5": false, "transcriptTranslationUrl": "/courses/course-v1:MITx+8.02.2x+2T2018/xblock/block-v1:MITx+8.02.2x+2T2018+type@video+block@L15v05/handler/transcript/translation/__lang__", "ytMetadataEndpoint": "", "generalSpeed": 1.0, "lmsRootURL": "https://openlearninglibrary.mit.edu", "autoAdvance": false, "completionEnabled": false, "savedVideoPosition": 0.0, "saveStateUrl": "/courses/course-v1:MITx+8.02.2x+2T2018/xblock/block-v1:MITx+8.02.2x+2T2018+type@video+block@L15v05/handler/xmodule_handler/save_user_state", "captionDataDir": null, "sources": [], "transcriptLanguage": "en", "recordedYoutubeIsAvailable": true, "prioritizeHls": false, "duration": null}'
data-bumper-metadata='null'
data-autoadvance-enabled="False"
data-poster='null'
tabindex="-1"
>
<div class="focus_grabber first"></div>
<div class="tc-wrapper">
<div class="video-wrapper">
<span tabindex="0" class="spinner" aria-hidden="false" aria-label="Loading video player"></span>
<span tabindex="-1" class="btn-play fa fa-youtube-play fa-2x is-hidden" aria-hidden="true" aria-label="Play video"></span>
<div class="video-player-pre"></div>
<div class="video-player">
<div id="L15v05"></div>
<h4 class="hd hd-4 video-error is-hidden">No playable video sources found.</h4>
<h4 class="hd hd-4 video-hls-error is-hidden">
Your browser does not support this video format. Try using a different browser.
</h4>
</div>
<div class="video-player-post"></div>
<div class="closed-captions"></div>
<div class="video-controls is-hidden">
<div>
<div class="vcr"><div class="vidtime">0:00 / 0:00</div></div>
<div class="secondary-controls"></div>
</div>
</div>
</div>
</div>
<div class="focus_grabber last"></div>
<h3 class="hd hd-4 downloads-heading sr" id="video-download-transcripts_L15v05">Downloads and transcripts</h3>
<div class="wrapper-downloads" role="region" aria-labelledby="video-download-transcripts_L15v05">
<div class="wrapper-download-transcripts">
<h4 class="hd hd-5">Transcripts</h4>
<ul class="list-download-transcripts">
<li class="transcript-option">
<a class="btn btn-link" href="/courses/course-v1:MITx+8.02.2x+2T2018/xblock/block-v1:MITx+8.02.2x+2T2018+type@video+block@L15v05/handler/transcript/download" data-value="srt">Download SubRip (.srt) file</a>
</li>
<li class="transcript-option">
<a class="btn btn-link" href="/courses/course-v1:MITx+8.02.2x+2T2018/xblock/block-v1:MITx+8.02.2x+2T2018+type@video+block@L15v05/handler/transcript/download" data-value="txt">Download Text (.txt) file</a>
</li>
</ul>
</div>
</div>
</div>
</div>
</div>
</div>
</div>
<div class="xblock xblock-public_view xblock-public_view-vertical" data-usage-id="block-v1:MITx+8.02.2x+2T2018+type@vertical+block@vert-L15v06" data-graded="True" data-runtime-class="LmsRuntime" data-course-id="course-v1:MITx+8.02.2x+2T2018" data-block-type="vertical" data-request-token="a285686afe6b11ee8e28026cc65ec0d9" data-has-score="False" data-runtime-version="1" data-init="VerticalStudentView">
<h2 class="hd hd-2 unit-title">L15v6: Multiloop Circuits</h2>
<div class="vert-mod">
<div class="vert vert-0" data-id="block-v1:MITx+8.02.2x+2T2018+type@html+block@lesson15_04">
<div class="xblock xblock-public_view xblock-public_view-html xmodule_display xmodule_HtmlBlock" data-usage-id="block-v1:MITx+8.02.2x+2T2018+type@html+block@lesson15_04" data-graded="True" data-runtime-class="LmsRuntime" data-course-id="course-v1:MITx+8.02.2x+2T2018" data-block-type="html" data-request-token="a285686afe6b11ee8e28026cc65ec0d9" data-has-score="False" data-runtime-version="1" data-init="XBlockToXModuleShim">
<script type="json/xblock-args" class="xblock-json-init-args">
{"xmodule-type": "HTMLModule"}
</script>
<center><b>Multiloop Circuits</b></center><p> In a single-loop circuit there is only one unknown current, the Kirchhoff's Loop Rule, \(\sum_{\text{closed loop}} \Delta V = 0\), is enough to calculate the current. In a circuit of more than one loop like the one shown in the video, there is more than one current to determine. The <b>Kirchhoff's Loop Rule</b> together with the <b>Kirchhoff's Junction Rule</b> provide the set of independent equations needed to calculate the unknown currents in a multiloop circuit.</p><center><b>Kirchhoff's Junction Rule</b></center><p> The sum of the currents into a junction must be equal to the sum of the currents out of the junction:</p>
\[\sum I_{in} = \sum I_{out}\]
</div>
</div>
<div class="vert vert-1" data-id="block-v1:MITx+8.02.2x+2T2018+type@video+block@L15v06">
<div class="xblock xblock-public_view xblock-public_view-video xmodule_display xmodule_VideoBlock" data-usage-id="block-v1:MITx+8.02.2x+2T2018+type@video+block@L15v06" data-graded="True" data-runtime-class="LmsRuntime" data-course-id="course-v1:MITx+8.02.2x+2T2018" data-block-type="video" data-request-token="a285686afe6b11ee8e28026cc65ec0d9" data-has-score="False" data-runtime-version="1" data-init="XBlockToXModuleShim">
<script type="json/xblock-args" class="xblock-json-init-args">
{"xmodule-type": "Video"}
</script>
<h3 class="hd hd-2">L15v06: Multiloop Circuits</h3>
<div
id="video_L15v06"
class="video closed"
data-metadata='{"end": 0.0, "speed": null, "ytTestTimeout": 1500, "publishCompletionUrl": "/courses/course-v1:MITx+8.02.2x+2T2018/xblock/block-v1:MITx+8.02.2x+2T2018+type@video+block@L15v06/handler/publish_completion", "ytApiUrl": "https://www.youtube.com/iframe_api", "showCaptions": "true", "streams": "1.00:ysjWwfCOV_4", "poster": null, "saveStateEnabled": false, "start": 0.0, "completionPercentage": 0.95, "transcriptAvailableTranslationsUrl": "/courses/course-v1:MITx+8.02.2x+2T2018/xblock/block-v1:MITx+8.02.2x+2T2018+type@video+block@L15v06/handler/transcript/available_translations", "autoplay": false, "transcriptLanguages": {"en": "English"}, "autohideHtml5": false, "transcriptTranslationUrl": "/courses/course-v1:MITx+8.02.2x+2T2018/xblock/block-v1:MITx+8.02.2x+2T2018+type@video+block@L15v06/handler/transcript/translation/__lang__", "ytMetadataEndpoint": "", "generalSpeed": 1.0, "lmsRootURL": "https://openlearninglibrary.mit.edu", "autoAdvance": false, "completionEnabled": false, "savedVideoPosition": 0.0, "saveStateUrl": "/courses/course-v1:MITx+8.02.2x+2T2018/xblock/block-v1:MITx+8.02.2x+2T2018+type@video+block@L15v06/handler/xmodule_handler/save_user_state", "captionDataDir": null, "sources": [], "transcriptLanguage": "en", "recordedYoutubeIsAvailable": true, "prioritizeHls": false, "duration": null}'
data-bumper-metadata='null'
data-autoadvance-enabled="False"
data-poster='null'
tabindex="-1"
>
<div class="focus_grabber first"></div>
<div class="tc-wrapper">
<div class="video-wrapper">
<span tabindex="0" class="spinner" aria-hidden="false" aria-label="Loading video player"></span>
<span tabindex="-1" class="btn-play fa fa-youtube-play fa-2x is-hidden" aria-hidden="true" aria-label="Play video"></span>
<div class="video-player-pre"></div>
<div class="video-player">
<div id="L15v06"></div>
<h4 class="hd hd-4 video-error is-hidden">No playable video sources found.</h4>
<h4 class="hd hd-4 video-hls-error is-hidden">
Your browser does not support this video format. Try using a different browser.
</h4>
</div>
<div class="video-player-post"></div>
<div class="closed-captions"></div>
<div class="video-controls is-hidden">
<div>
<div class="vcr"><div class="vidtime">0:00 / 0:00</div></div>
<div class="secondary-controls"></div>
</div>
</div>
</div>
</div>
<div class="focus_grabber last"></div>
<h3 class="hd hd-4 downloads-heading sr" id="video-download-transcripts_L15v06">Downloads and transcripts</h3>
<div class="wrapper-downloads" role="region" aria-labelledby="video-download-transcripts_L15v06">
<div class="wrapper-download-transcripts">
<h4 class="hd hd-5">Transcripts</h4>
<ul class="list-download-transcripts">
<li class="transcript-option">
<a class="btn btn-link" href="/courses/course-v1:MITx+8.02.2x+2T2018/xblock/block-v1:MITx+8.02.2x+2T2018+type@video+block@L15v06/handler/transcript/download" data-value="srt">Download SubRip (.srt) file</a>
</li>
<li class="transcript-option">
<a class="btn btn-link" href="/courses/course-v1:MITx+8.02.2x+2T2018/xblock/block-v1:MITx+8.02.2x+2T2018+type@video+block@L15v06/handler/transcript/download" data-value="txt">Download Text (.txt) file</a>
</li>
</ul>
</div>
</div>
</div>
</div>
</div>
</div>
</div>
<div class="xblock xblock-public_view xblock-public_view-vertical" data-usage-id="block-v1:MITx+8.02.2x+2T2018+type@vertical+block@vert-L15v07" data-graded="True" data-runtime-class="LmsRuntime" data-course-id="course-v1:MITx+8.02.2x+2T2018" data-block-type="vertical" data-request-token="a285686afe6b11ee8e28026cc65ec0d9" data-has-score="False" data-runtime-version="1" data-init="VerticalStudentView">
<h2 class="hd hd-2 unit-title">L15v7: Resistors in Series and in Parallel</h2>
<div class="vert-mod">
<div class="vert vert-0" data-id="block-v1:MITx+8.02.2x+2T2018+type@video+block@L15v07">
<div class="xblock xblock-public_view xblock-public_view-video xmodule_display xmodule_VideoBlock" data-usage-id="block-v1:MITx+8.02.2x+2T2018+type@video+block@L15v07" data-graded="True" data-runtime-class="LmsRuntime" data-course-id="course-v1:MITx+8.02.2x+2T2018" data-block-type="video" data-request-token="a285686afe6b11ee8e28026cc65ec0d9" data-has-score="False" data-runtime-version="1" data-init="XBlockToXModuleShim">
<script type="json/xblock-args" class="xblock-json-init-args">
{"xmodule-type": "Video"}
</script>
<h3 class="hd hd-2">L15v07: Resistors in Series and in Parallel</h3>
<div
id="video_L15v07"
class="video closed"
data-metadata='{"end": 0.0, "speed": null, "ytTestTimeout": 1500, "publishCompletionUrl": "/courses/course-v1:MITx+8.02.2x+2T2018/xblock/block-v1:MITx+8.02.2x+2T2018+type@video+block@L15v07/handler/publish_completion", "ytApiUrl": "https://www.youtube.com/iframe_api", "showCaptions": "true", "streams": "1.00:u1FMVNJaSr0", "poster": null, "saveStateEnabled": false, "start": 0.0, "completionPercentage": 0.95, "transcriptAvailableTranslationsUrl": "/courses/course-v1:MITx+8.02.2x+2T2018/xblock/block-v1:MITx+8.02.2x+2T2018+type@video+block@L15v07/handler/transcript/available_translations", "autoplay": false, "transcriptLanguages": {"en": "English"}, "autohideHtml5": false, "transcriptTranslationUrl": "/courses/course-v1:MITx+8.02.2x+2T2018/xblock/block-v1:MITx+8.02.2x+2T2018+type@video+block@L15v07/handler/transcript/translation/__lang__", "ytMetadataEndpoint": "", "generalSpeed": 1.0, "lmsRootURL": "https://openlearninglibrary.mit.edu", "autoAdvance": false, "completionEnabled": false, "savedVideoPosition": 0.0, "saveStateUrl": "/courses/course-v1:MITx+8.02.2x+2T2018/xblock/block-v1:MITx+8.02.2x+2T2018+type@video+block@L15v07/handler/xmodule_handler/save_user_state", "captionDataDir": null, "sources": [], "transcriptLanguage": "en", "recordedYoutubeIsAvailable": true, "prioritizeHls": false, "duration": null}'
data-bumper-metadata='null'
data-autoadvance-enabled="False"
data-poster='null'
tabindex="-1"
>
<div class="focus_grabber first"></div>
<div class="tc-wrapper">
<div class="video-wrapper">
<span tabindex="0" class="spinner" aria-hidden="false" aria-label="Loading video player"></span>
<span tabindex="-1" class="btn-play fa fa-youtube-play fa-2x is-hidden" aria-hidden="true" aria-label="Play video"></span>
<div class="video-player-pre"></div>
<div class="video-player">
<div id="L15v07"></div>
<h4 class="hd hd-4 video-error is-hidden">No playable video sources found.</h4>
<h4 class="hd hd-4 video-hls-error is-hidden">
Your browser does not support this video format. Try using a different browser.
</h4>
</div>
<div class="video-player-post"></div>
<div class="closed-captions"></div>
<div class="video-controls is-hidden">
<div>
<div class="vcr"><div class="vidtime">0:00 / 0:00</div></div>
<div class="secondary-controls"></div>
</div>
</div>
</div>
</div>
<div class="focus_grabber last"></div>
<h3 class="hd hd-4 downloads-heading sr" id="video-download-transcripts_L15v07">Downloads and transcripts</h3>
<div class="wrapper-downloads" role="region" aria-labelledby="video-download-transcripts_L15v07">
<div class="wrapper-download-transcripts">
<h4 class="hd hd-5">Transcripts</h4>
<ul class="list-download-transcripts">
<li class="transcript-option">
<a class="btn btn-link" href="/courses/course-v1:MITx+8.02.2x+2T2018/xblock/block-v1:MITx+8.02.2x+2T2018+type@video+block@L15v07/handler/transcript/download" data-value="srt">Download SubRip (.srt) file</a>
</li>
<li class="transcript-option">
<a class="btn btn-link" href="/courses/course-v1:MITx+8.02.2x+2T2018/xblock/block-v1:MITx+8.02.2x+2T2018+type@video+block@L15v07/handler/transcript/download" data-value="txt">Download Text (.txt) file</a>
</li>
</ul>
</div>
</div>
</div>
</div>
</div>
</div>
</div>
<div class="xblock xblock-public_view xblock-public_view-vertical" data-usage-id="block-v1:MITx+8.02.2x+2T2018+type@vertical+block@vert-onlinepset10_1" data-graded="True" data-runtime-class="LmsRuntime" data-course-id="course-v1:MITx+8.02.2x+2T2018" data-block-type="vertical" data-request-token="a285686afe6b11ee8e28026cc65ec0d9" data-has-score="False" data-runtime-version="1" data-init="VerticalStudentView">
<h2 class="hd hd-2 unit-title">L15Q3: Connection in Series and Parallel</h2>
<div class="vert-mod">
<div class="vert vert-0" data-id="block-v1:MITx+8.02.2x+2T2018+type@problem+block@pcq_w10d1a1">
<div class="xblock xblock-public_view xblock-public_view-problem xmodule_display xmodule_ProblemBlock" data-usage-id="block-v1:MITx+8.02.2x+2T2018+type@problem+block@pcq_w10d1a1" data-graded="True" data-runtime-class="LmsRuntime" data-course-id="course-v1:MITx+8.02.2x+2T2018" data-block-type="problem" data-request-token="a285686afe6b11ee8e28026cc65ec0d9" data-has-score="True" data-runtime-version="1" data-init="XBlockToXModuleShim">
<script type="json/xblock-args" class="xblock-json-init-args">
{"xmodule-type": "Problem"}
</script>
<div id="problem_pcq_w10d1a1" class="problems-wrapper" role="group"
aria-labelledby="pcq_w10d1a1-problem-title"
data-problem-id="block-v1:MITx+8.02.2x+2T2018+type@problem+block@pcq_w10d1a1" data-url="/courses/course-v1:MITx+8.02.2x+2T2018/xblock/block-v1:MITx+8.02.2x+2T2018+type@problem+block@pcq_w10d1a1/handler/xmodule_handler"
data-problem-score="0.0"
data-problem-total-possible="1.0"
data-attempts-used="0"
data-content="
<h3 class="hd hd-3 problem-header" id="pcq_w10d1a1-problem-title" aria-describedby="block-v1:MITx+8.02.2x+2T2018+type@problem+block@pcq_w10d1a1-problem-progress" tabindex="-1">
Connection in series
</h3>
<div class="problem-progress" id="block-v1:MITx+8.02.2x+2T2018+type@problem+block@pcq_w10d1a1-problem-progress"></div>
<div class="problem">
<div>
<p>When two unlike resistors [mathjaxinline]R_1[/mathjaxinline] and
[mathjaxinline]R_2[/mathjaxinline] are connected in series, which of the following is the same for each resistor?</p>
<div class="wrapper-problem-response" tabindex="-1" aria-label="Question 1" role="group"><div class="inputtype option-input ">
<select name="input_pcq_w10d1a1_2_1" id="input_pcq_w10d1a1_2_1" aria-describedby="status_pcq_w10d1a1_2_1">
<option value="option_pcq_w10d1a1_2_1_dummy_default">Select an option</option>
<option value="Current"> Current</option>
<option value="Potential difference"> Potential difference</option>
<option value="Power"> Power</option>
</select>
<div class="indicator-container">
<span class="status unanswered" id="status_pcq_w10d1a1_2_1" data-tooltip="Not yet answered.">
<span class="sr">unanswered</span><span class="status-icon" aria-hidden="true"/>
</span>
</div>
<p class="answer" id="answer_pcq_w10d1a1_2_1"/>
</div></div>
<div class="solution-span">
<span id="solution_pcq_w10d1a1_solution_1"/>
</div></div>
<div class="action">
<input type="hidden" name="problem_id" value="Connection in series" />
<div class="submit-attempt-container">
<button type="button" class="submit btn-brand" data-submitting="Submitting" data-value="Submit" data-should-enable-submit-button="True" aria-describedby="submission_feedback_pcq_w10d1a1" >
<span class="submit-label">Submit</span>
</button>
<div class="submission-feedback" id="submission_feedback_pcq_w10d1a1">
<span class="sr">Some problems have options such as save, reset, hints, or show answer. These options follow the Submit button.</span>
</div>
</div>
<div class="problem-action-buttons-wrapper">
</div>
</div>
<div class="notification warning notification-gentle-alert
is-hidden"
tabindex="-1">
<span class="icon fa fa-exclamation-circle" aria-hidden="true"></span>
<span class="notification-message" aria-describedby="pcq_w10d1a1-problem-title">
</span>
<div class="notification-btn-wrapper">
<button type="button" class="btn btn-default btn-small notification-btn review-btn sr">Review</button>
</div>
</div>
<div class="notification warning notification-save
is-hidden"
tabindex="-1">
<span class="icon fa fa-save" aria-hidden="true"></span>
<span class="notification-message" aria-describedby="pcq_w10d1a1-problem-title">None
</span>
<div class="notification-btn-wrapper">
<button type="button" class="btn btn-default btn-small notification-btn review-btn sr">Review</button>
</div>
</div>
<div class="notification general notification-show-answer
is-hidden"
tabindex="-1">
<span class="icon fa fa-info-circle" aria-hidden="true"></span>
<span class="notification-message" aria-describedby="pcq_w10d1a1-problem-title">Answers are displayed within the problem
</span>
<div class="notification-btn-wrapper">
<button type="button" class="btn btn-default btn-small notification-btn review-btn sr">Review</button>
</div>
</div>
</div>
"
data-graded="True">
<p class="loading-spinner">
<i class="fa fa-spinner fa-pulse fa-2x fa-fw"></i>
<span class="sr">Loading…</span>
</p>
</div>
</div>
</div>
<div class="vert vert-1" data-id="block-v1:MITx+8.02.2x+2T2018+type@problem+block@pcq_w10d1a2">
<div class="xblock xblock-public_view xblock-public_view-problem xmodule_display xmodule_ProblemBlock" data-usage-id="block-v1:MITx+8.02.2x+2T2018+type@problem+block@pcq_w10d1a2" data-graded="True" data-runtime-class="LmsRuntime" data-course-id="course-v1:MITx+8.02.2x+2T2018" data-block-type="problem" data-request-token="a285686afe6b11ee8e28026cc65ec0d9" data-has-score="True" data-runtime-version="1" data-init="XBlockToXModuleShim">
<script type="json/xblock-args" class="xblock-json-init-args">
{"xmodule-type": "Problem"}
</script>
<div id="problem_pcq_w10d1a2" class="problems-wrapper" role="group"
aria-labelledby="pcq_w10d1a2-problem-title"
data-problem-id="block-v1:MITx+8.02.2x+2T2018+type@problem+block@pcq_w10d1a2" data-url="/courses/course-v1:MITx+8.02.2x+2T2018/xblock/block-v1:MITx+8.02.2x+2T2018+type@problem+block@pcq_w10d1a2/handler/xmodule_handler"
data-problem-score="0.0"
data-problem-total-possible="1.0"
data-attempts-used="0"
data-content="
<h3 class="hd hd-3 problem-header" id="pcq_w10d1a2-problem-title" aria-describedby="block-v1:MITx+8.02.2x+2T2018+type@problem+block@pcq_w10d1a2-problem-progress" tabindex="-1">
Connection in parallel
</h3>
<div class="problem-progress" id="block-v1:MITx+8.02.2x+2T2018+type@problem+block@pcq_w10d1a2-problem-progress"></div>
<div class="problem">
<div>
<p>When two unlike resistors [mathjaxinline]R_1[/mathjaxinline] and
[mathjaxinline]R_2[/mathjaxinline] are connected in parallel, which of the following is the same for each resistor?</p>
<div class="wrapper-problem-response" tabindex="-1" aria-label="Question 1" role="group"><div class="inputtype option-input ">
<select name="input_pcq_w10d1a2_2_1" id="input_pcq_w10d1a2_2_1" aria-describedby="status_pcq_w10d1a2_2_1">
<option value="option_pcq_w10d1a2_2_1_dummy_default">Select an option</option>
<option value="Current"> Current</option>
<option value="Potential difference"> Potential difference</option>
<option value="Power"> Power</option>
</select>
<div class="indicator-container">
<span class="status unanswered" id="status_pcq_w10d1a2_2_1" data-tooltip="Not yet answered.">
<span class="sr">unanswered</span><span class="status-icon" aria-hidden="true"/>
</span>
</div>
<p class="answer" id="answer_pcq_w10d1a2_2_1"/>
</div></div>
<div class="solution-span">
<span id="solution_pcq_w10d1a2_solution_1"/>
</div></div>
<div class="action">
<input type="hidden" name="problem_id" value="Connection in parallel" />
<div class="submit-attempt-container">
<button type="button" class="submit btn-brand" data-submitting="Submitting" data-value="Submit" data-should-enable-submit-button="True" aria-describedby="submission_feedback_pcq_w10d1a2" >
<span class="submit-label">Submit</span>
</button>
<div class="submission-feedback" id="submission_feedback_pcq_w10d1a2">
<span class="sr">Some problems have options such as save, reset, hints, or show answer. These options follow the Submit button.</span>
</div>
</div>
<div class="problem-action-buttons-wrapper">
</div>
</div>
<div class="notification warning notification-gentle-alert
is-hidden"
tabindex="-1">
<span class="icon fa fa-exclamation-circle" aria-hidden="true"></span>
<span class="notification-message" aria-describedby="pcq_w10d1a2-problem-title">
</span>
<div class="notification-btn-wrapper">
<button type="button" class="btn btn-default btn-small notification-btn review-btn sr">Review</button>
</div>
</div>
<div class="notification warning notification-save
is-hidden"
tabindex="-1">
<span class="icon fa fa-save" aria-hidden="true"></span>
<span class="notification-message" aria-describedby="pcq_w10d1a2-problem-title">None
</span>
<div class="notification-btn-wrapper">
<button type="button" class="btn btn-default btn-small notification-btn review-btn sr">Review</button>
</div>
</div>
<div class="notification general notification-show-answer
is-hidden"
tabindex="-1">
<span class="icon fa fa-info-circle" aria-hidden="true"></span>
<span class="notification-message" aria-describedby="pcq_w10d1a2-problem-title">Answers are displayed within the problem
</span>
<div class="notification-btn-wrapper">
<button type="button" class="btn btn-default btn-small notification-btn review-btn sr">Review</button>
</div>
</div>
</div>
"
data-graded="True">
<p class="loading-spinner">
<i class="fa fa-spinner fa-pulse fa-2x fa-fw"></i>
<span class="sr">Loading…</span>
</p>
</div>
</div>
</div>
</div>
</div>
<div class="xblock xblock-public_view xblock-public_view-vertical" data-usage-id="block-v1:MITx+8.02.2x+2T2018+type@vertical+block@vert-checkpoint_w6_14" data-graded="True" data-runtime-class="LmsRuntime" data-course-id="course-v1:MITx+8.02.2x+2T2018" data-block-type="vertical" data-request-token="a285686afe6b11ee8e28026cc65ec0d9" data-has-score="False" data-runtime-version="1" data-init="VerticalStudentView">
<h2 class="hd hd-2 unit-title">L15Q4: Three Resistors</h2>
<div class="vert-mod">
<div class="vert vert-0" data-id="block-v1:MITx+8.02.2x+2T2018+type@problem+block@checkpoint_w6_14">
<div class="xblock xblock-public_view xblock-public_view-problem xmodule_display xmodule_ProblemBlock" data-usage-id="block-v1:MITx+8.02.2x+2T2018+type@problem+block@checkpoint_w6_14" data-graded="True" data-runtime-class="LmsRuntime" data-course-id="course-v1:MITx+8.02.2x+2T2018" data-block-type="problem" data-request-token="a285686afe6b11ee8e28026cc65ec0d9" data-has-score="True" data-runtime-version="1" data-init="XBlockToXModuleShim">
<script type="json/xblock-args" class="xblock-json-init-args">
{"xmodule-type": "Problem"}
</script>
<div id="problem_checkpoint_w6_14" class="problems-wrapper" role="group"
aria-labelledby="checkpoint_w6_14-problem-title"
data-problem-id="block-v1:MITx+8.02.2x+2T2018+type@problem+block@checkpoint_w6_14" data-url="/courses/course-v1:MITx+8.02.2x+2T2018/xblock/block-v1:MITx+8.02.2x+2T2018+type@problem+block@checkpoint_w6_14/handler/xmodule_handler"
data-problem-score="0.0"
data-problem-total-possible="1.0"
data-attempts-used="0"
data-content="
<h3 class="hd hd-3 problem-header" id="checkpoint_w6_14-problem-title" aria-describedby="block-v1:MITx+8.02.2x+2T2018+type@problem+block@checkpoint_w6_14-problem-progress" tabindex="-1">
Three resistors
</h3>
<div class="problem-progress" id="block-v1:MITx+8.02.2x+2T2018+type@problem+block@checkpoint_w6_14-problem-progress"></div>
<div class="problem">
<div>
<center>
<img src="/assets/courseware/v1/6b5ff65d9a6ecd8f3cbcc744085e775c/asset-v1:MITx+8.02.2x+2T2018+type@asset+block/images_checkpoint_w6_14.svg" width="440"/>
</center>
<p>
Consider the circuit shown in the figure. The three resistors have the same resistance [mathjaxinline]R[/mathjaxinline]. Which of the following statements is (are) true? </p>
<p>
<div class="wrapper-problem-response" tabindex="-1" aria-label="Question 1" role="group"><div class="choicegroup capa_inputtype" id="inputtype_checkpoint_w6_14_2_1">
<fieldset aria-describedby="status_checkpoint_w6_14_2_1">
<div class="field">
<input type="checkbox" name="input_checkpoint_w6_14_2_1[]" id="input_checkpoint_w6_14_2_1_choice_0" class="field-input input-checkbox" value="choice_0"/><label id="checkpoint_w6_14_2_1-choice_0-label" for="input_checkpoint_w6_14_2_1_choice_0" class="response-label field-label label-inline" aria-describedby="status_checkpoint_w6_14_2_1">
<text>a. Resistors 2 and 3 are in series.</text>
</label>
</div>
<div class="field">
<input type="checkbox" name="input_checkpoint_w6_14_2_1[]" id="input_checkpoint_w6_14_2_1_choice_1" class="field-input input-checkbox" value="choice_1"/><label id="checkpoint_w6_14_2_1-choice_1-label" for="input_checkpoint_w6_14_2_1_choice_1" class="response-label field-label label-inline" aria-describedby="status_checkpoint_w6_14_2_1">
<text>b. Resistors 2 and 3 together are in parallel with resistor 1.</text>
</label>
</div>
<div class="field">
<input type="checkbox" name="input_checkpoint_w6_14_2_1[]" id="input_checkpoint_w6_14_2_1_choice_2" class="field-input input-checkbox" value="choice_2"/><label id="checkpoint_w6_14_2_1-choice_2-label" for="input_checkpoint_w6_14_2_1_choice_2" class="response-label field-label label-inline" aria-describedby="status_checkpoint_w6_14_2_1">
<text>c. The ratio of the resistance of the upper branch to the resistance of the lower branch is 0.5.</text>
</label>
</div>
<div class="field">
<input type="checkbox" name="input_checkpoint_w6_14_2_1[]" id="input_checkpoint_w6_14_2_1_choice_3" class="field-input input-checkbox" value="choice_3"/><label id="checkpoint_w6_14_2_1-choice_3-label" for="input_checkpoint_w6_14_2_1_choice_3" class="response-label field-label label-inline" aria-describedby="status_checkpoint_w6_14_2_1">
<text>d. The current through resistor 1 is twice the current through resistor 2.</text>
</label>
</div>
<span id="answer_checkpoint_w6_14_2_1"/>
</fieldset>
<div class="indicator-container">
<span class="status unanswered" id="status_checkpoint_w6_14_2_1" data-tooltip="Not yet answered.">
<span class="sr">unanswered</span><span class="status-icon" aria-hidden="true"/>
</span>
</div>
</div></div>
</p>
<p>
<div class="solution-span">
<span id="solution_checkpoint_w6_14_solution_1"/>
</div></p>
</div>
<div class="action">
<input type="hidden" name="problem_id" value="Three resistors" />
<div class="submit-attempt-container">
<button type="button" class="submit btn-brand" data-submitting="Submitting" data-value="Submit" data-should-enable-submit-button="True" aria-describedby="submission_feedback_checkpoint_w6_14" >
<span class="submit-label">Submit</span>
</button>
<div class="submission-feedback" id="submission_feedback_checkpoint_w6_14">
<span class="sr">Some problems have options such as save, reset, hints, or show answer. These options follow the Submit button.</span>
</div>
</div>
<div class="problem-action-buttons-wrapper">
</div>
</div>
<div class="notification warning notification-gentle-alert
is-hidden"
tabindex="-1">
<span class="icon fa fa-exclamation-circle" aria-hidden="true"></span>
<span class="notification-message" aria-describedby="checkpoint_w6_14-problem-title">
</span>
<div class="notification-btn-wrapper">
<button type="button" class="btn btn-default btn-small notification-btn review-btn sr">Review</button>
</div>
</div>
<div class="notification warning notification-save
is-hidden"
tabindex="-1">
<span class="icon fa fa-save" aria-hidden="true"></span>
<span class="notification-message" aria-describedby="checkpoint_w6_14-problem-title">None
</span>
<div class="notification-btn-wrapper">
<button type="button" class="btn btn-default btn-small notification-btn review-btn sr">Review</button>
</div>
</div>
<div class="notification general notification-show-answer
is-hidden"
tabindex="-1">
<span class="icon fa fa-info-circle" aria-hidden="true"></span>
<span class="notification-message" aria-describedby="checkpoint_w6_14-problem-title">Answers are displayed within the problem
</span>
<div class="notification-btn-wrapper">
<button type="button" class="btn btn-default btn-small notification-btn review-btn sr">Review</button>
</div>
</div>
</div>
"
data-graded="True">
<p class="loading-spinner">
<i class="fa fa-spinner fa-pulse fa-2x fa-fw"></i>
<span class="sr">Loading…</span>
</p>
</div>
</div>
</div>
</div>
</div>
<div class="xblock xblock-public_view xblock-public_view-vertical" data-usage-id="block-v1:MITx+8.02.2x+2T2018+type@vertical+block@vert-L15v08" data-graded="True" data-runtime-class="LmsRuntime" data-course-id="course-v1:MITx+8.02.2x+2T2018" data-block-type="vertical" data-request-token="a285686afe6b11ee8e28026cc65ec0d9" data-has-score="False" data-runtime-version="1" data-init="VerticalStudentView">
<h2 class="hd hd-2 unit-title">L15v8: Worked Example - Reducing a Circuit Diagram</h2>
<div class="vert-mod">
<div class="vert vert-0" data-id="block-v1:MITx+8.02.2x+2T2018+type@problem+block@checkpoint_w6_12">
<div class="xblock xblock-public_view xblock-public_view-problem xmodule_display xmodule_ProblemBlock" data-usage-id="block-v1:MITx+8.02.2x+2T2018+type@problem+block@checkpoint_w6_12" data-graded="True" data-runtime-class="LmsRuntime" data-course-id="course-v1:MITx+8.02.2x+2T2018" data-block-type="problem" data-request-token="a285686afe6b11ee8e28026cc65ec0d9" data-has-score="True" data-runtime-version="1" data-init="XBlockToXModuleShim">
<script type="json/xblock-args" class="xblock-json-init-args">
{"xmodule-type": "Problem"}
</script>
<div id="problem_checkpoint_w6_12" class="problems-wrapper" role="group"
aria-labelledby="checkpoint_w6_12-problem-title"
data-problem-id="block-v1:MITx+8.02.2x+2T2018+type@problem+block@checkpoint_w6_12" data-url="/courses/course-v1:MITx+8.02.2x+2T2018/xblock/block-v1:MITx+8.02.2x+2T2018+type@problem+block@checkpoint_w6_12/handler/xmodule_handler"
data-problem-score="0"
data-problem-total-possible="0"
data-attempts-used="0"
data-content="
<h3 class="hd hd-3 problem-header" id="checkpoint_w6_12-problem-title" aria-describedby="block-v1:MITx+8.02.2x+2T2018+type@problem+block@checkpoint_w6_12-problem-progress" tabindex="-1">
Worked Example: Reducing a circuit diagram
</h3>
<div class="problem-progress" id="block-v1:MITx+8.02.2x+2T2018+type@problem+block@checkpoint_w6_12-problem-progress"></div>
<div class="problem">
<div>
<center>
<img src="/assets/courseware/v1/2babe687eb64ac15e1713fb0367a0ebe/asset-v1:MITx+8.02.2x+2T2018+type@asset+block/images_checkpoint_w6_12.svg" width="770"/>
</center>
<p>
Consider the circuit in the left figure. The emf of each battery and the resistance of [mathjaxinline]R_1[/mathjaxinline], [mathjaxinline]R_2[/mathjaxinline], [mathjaxinline]R_3[/mathjaxinline] and [mathjaxinline]R_4[/mathjaxinline] are known. The circuit can be reduced to the circuit shown in the right figure. Calculate the value of the equivalent resistance [mathjaxinline]R_{e}[/mathjaxinline] shown in the middle of the right figure. Express your answer in terms of R_2 for [mathjaxinline]R_2[/mathjaxinline], and R_3 for [mathjaxinline]R_3[/mathjaxinline]. </p>
<p>
<p style="display:inline">[mathjaxinline]R_{e} =[/mathjaxinline] </p>
<div class="inline" tabindex="-1" aria-label="Question 1" role="group"><div id="inputtype_checkpoint_w6_12_2_1" class="text-input-dynamath capa_inputtype inline textline">
<div class="unanswered inline">
<input type="text" name="input_checkpoint_w6_12_2_1" id="input_checkpoint_w6_12_2_1" aria-describedby="status_checkpoint_w6_12_2_1" value="" class="math" size="40"/>
<span class="trailing_text" id="trailing_text_checkpoint_w6_12_2_1"/>
<span class="status unanswered" id="status_checkpoint_w6_12_2_1" data-tooltip="Not yet answered.">
<span class="sr">unanswered</span><span class="status-icon" aria-hidden="true"/>
</span>
<p id="answer_checkpoint_w6_12_2_1" class="answer"/>
<div id="display_checkpoint_w6_12_2_1" class="equation">`{::}`</div>
<textarea style="display:none" id="input_checkpoint_w6_12_2_1_dynamath" name="input_checkpoint_w6_12_2_1_dynamath"/>
</div>
</div></div>
</p>
<p>
<div class="solution-span">
<span id="solution_checkpoint_w6_12_solution_1"/>
</div></p>
</div>
<div class="action">
<input type="hidden" name="problem_id" value="Worked Example: Reducing a circuit diagram" />
<div class="submit-attempt-container">
<button type="button" class="submit btn-brand" data-submitting="Submitting" data-value="Submit" data-should-enable-submit-button="True" aria-describedby="submission_feedback_checkpoint_w6_12" >
<span class="submit-label">Submit</span>
</button>
<div class="submission-feedback" id="submission_feedback_checkpoint_w6_12">
<span class="sr">Some problems have options such as save, reset, hints, or show answer. These options follow the Submit button.</span>
</div>
</div>
<div class="problem-action-buttons-wrapper">
</div>
</div>
<div class="notification warning notification-gentle-alert
is-hidden"
tabindex="-1">
<span class="icon fa fa-exclamation-circle" aria-hidden="true"></span>
<span class="notification-message" aria-describedby="checkpoint_w6_12-problem-title">
</span>
<div class="notification-btn-wrapper">
<button type="button" class="btn btn-default btn-small notification-btn review-btn sr">Review</button>
</div>
</div>
<div class="notification warning notification-save
is-hidden"
tabindex="-1">
<span class="icon fa fa-save" aria-hidden="true"></span>
<span class="notification-message" aria-describedby="checkpoint_w6_12-problem-title">None
</span>
<div class="notification-btn-wrapper">
<button type="button" class="btn btn-default btn-small notification-btn review-btn sr">Review</button>
</div>
</div>
<div class="notification general notification-show-answer
is-hidden"
tabindex="-1">
<span class="icon fa fa-info-circle" aria-hidden="true"></span>
<span class="notification-message" aria-describedby="checkpoint_w6_12-problem-title">Answers are displayed within the problem
</span>
<div class="notification-btn-wrapper">
<button type="button" class="btn btn-default btn-small notification-btn review-btn sr">Review</button>
</div>
</div>
</div>
"
data-graded="True">
<p class="loading-spinner">
<i class="fa fa-spinner fa-pulse fa-2x fa-fw"></i>
<span class="sr">Loading…</span>
</p>
</div>
</div>
</div>
<div class="vert vert-1" data-id="block-v1:MITx+8.02.2x+2T2018+type@video+block@L15v08">
<div class="xblock xblock-public_view xblock-public_view-video xmodule_display xmodule_VideoBlock" data-usage-id="block-v1:MITx+8.02.2x+2T2018+type@video+block@L15v08" data-graded="True" data-runtime-class="LmsRuntime" data-course-id="course-v1:MITx+8.02.2x+2T2018" data-block-type="video" data-request-token="a285686afe6b11ee8e28026cc65ec0d9" data-has-score="False" data-runtime-version="1" data-init="XBlockToXModuleShim">
<script type="json/xblock-args" class="xblock-json-init-args">
{"xmodule-type": "Video"}
</script>
<h3 class="hd hd-2">L15v08: Worked Example: Reducing a Circuit Diagram</h3>
<div
id="video_L15v08"
class="video closed"
data-metadata='{"end": 0.0, "speed": null, "ytTestTimeout": 1500, "publishCompletionUrl": "/courses/course-v1:MITx+8.02.2x+2T2018/xblock/block-v1:MITx+8.02.2x+2T2018+type@video+block@L15v08/handler/publish_completion", "ytApiUrl": "https://www.youtube.com/iframe_api", "showCaptions": "true", "streams": "1.00:bT_7TUgTRA4", "poster": null, "saveStateEnabled": false, "start": 0.0, "completionPercentage": 0.95, "transcriptAvailableTranslationsUrl": "/courses/course-v1:MITx+8.02.2x+2T2018/xblock/block-v1:MITx+8.02.2x+2T2018+type@video+block@L15v08/handler/transcript/available_translations", "autoplay": false, "transcriptLanguages": {"en": "English"}, "autohideHtml5": false, "transcriptTranslationUrl": "/courses/course-v1:MITx+8.02.2x+2T2018/xblock/block-v1:MITx+8.02.2x+2T2018+type@video+block@L15v08/handler/transcript/translation/__lang__", "ytMetadataEndpoint": "", "generalSpeed": 1.0, "lmsRootURL": "https://openlearninglibrary.mit.edu", "autoAdvance": false, "completionEnabled": false, "savedVideoPosition": 0.0, "saveStateUrl": "/courses/course-v1:MITx+8.02.2x+2T2018/xblock/block-v1:MITx+8.02.2x+2T2018+type@video+block@L15v08/handler/xmodule_handler/save_user_state", "captionDataDir": null, "sources": [], "transcriptLanguage": "en", "recordedYoutubeIsAvailable": true, "prioritizeHls": false, "duration": null}'
data-bumper-metadata='null'
data-autoadvance-enabled="False"
data-poster='null'
tabindex="-1"
>
<div class="focus_grabber first"></div>
<div class="tc-wrapper">
<div class="video-wrapper">
<span tabindex="0" class="spinner" aria-hidden="false" aria-label="Loading video player"></span>
<span tabindex="-1" class="btn-play fa fa-youtube-play fa-2x is-hidden" aria-hidden="true" aria-label="Play video"></span>
<div class="video-player-pre"></div>
<div class="video-player">
<div id="L15v08"></div>
<h4 class="hd hd-4 video-error is-hidden">No playable video sources found.</h4>
<h4 class="hd hd-4 video-hls-error is-hidden">
Your browser does not support this video format. Try using a different browser.
</h4>
</div>
<div class="video-player-post"></div>
<div class="closed-captions"></div>
<div class="video-controls is-hidden">
<div>
<div class="vcr"><div class="vidtime">0:00 / 0:00</div></div>
<div class="secondary-controls"></div>
</div>
</div>
</div>
</div>
<div class="focus_grabber last"></div>
<h3 class="hd hd-4 downloads-heading sr" id="video-download-transcripts_L15v08">Downloads and transcripts</h3>
<div class="wrapper-downloads" role="region" aria-labelledby="video-download-transcripts_L15v08">
<div class="wrapper-download-transcripts">
<h4 class="hd hd-5">Transcripts</h4>
<ul class="list-download-transcripts">
<li class="transcript-option">
<a class="btn btn-link" href="/courses/course-v1:MITx+8.02.2x+2T2018/xblock/block-v1:MITx+8.02.2x+2T2018+type@video+block@L15v08/handler/transcript/download" data-value="srt">Download SubRip (.srt) file</a>
</li>
<li class="transcript-option">
<a class="btn btn-link" href="/courses/course-v1:MITx+8.02.2x+2T2018/xblock/block-v1:MITx+8.02.2x+2T2018+type@video+block@L15v08/handler/transcript/download" data-value="txt">Download Text (.txt) file</a>
</li>
</ul>
</div>
</div>
</div>
</div>
</div>
</div>
</div>
<div class="xblock xblock-public_view xblock-public_view-vertical" data-usage-id="block-v1:MITx+8.02.2x+2T2018+type@vertical+block@vert-onlinepset10_6" data-graded="True" data-runtime-class="LmsRuntime" data-course-id="course-v1:MITx+8.02.2x+2T2018" data-block-type="vertical" data-request-token="a285686afe6b11ee8e28026cc65ec0d9" data-has-score="False" data-runtime-version="1" data-init="VerticalStudentView">
<h2 class="hd hd-2 unit-title">L15Q5: Calculating Voltage Difference</h2>
<div class="vert-mod">
<div class="vert vert-0" data-id="block-v1:MITx+8.02.2x+2T2018+type@problem+block@pcq_w10d1f">
<div class="xblock xblock-public_view xblock-public_view-problem xmodule_display xmodule_ProblemBlock" data-usage-id="block-v1:MITx+8.02.2x+2T2018+type@problem+block@pcq_w10d1f" data-graded="True" data-runtime-class="LmsRuntime" data-course-id="course-v1:MITx+8.02.2x+2T2018" data-block-type="problem" data-request-token="a285686afe6b11ee8e28026cc65ec0d9" data-has-score="True" data-runtime-version="1" data-init="XBlockToXModuleShim">
<script type="json/xblock-args" class="xblock-json-init-args">
{"xmodule-type": "Problem"}
</script>
<div id="problem_pcq_w10d1f" class="problems-wrapper" role="group"
aria-labelledby="pcq_w10d1f-problem-title"
data-problem-id="block-v1:MITx+8.02.2x+2T2018+type@problem+block@pcq_w10d1f" data-url="/courses/course-v1:MITx+8.02.2x+2T2018/xblock/block-v1:MITx+8.02.2x+2T2018+type@problem+block@pcq_w10d1f/handler/xmodule_handler"
data-problem-score="0.0"
data-problem-total-possible="2.0"
data-attempts-used="0"
data-content="
<h3 class="hd hd-3 problem-header" id="pcq_w10d1f-problem-title" aria-describedby="block-v1:MITx+8.02.2x+2T2018+type@problem+block@pcq_w10d1f-problem-progress" tabindex="-1">
Calculating Voltage Difference
</h3>
<div class="problem-progress" id="block-v1:MITx+8.02.2x+2T2018+type@problem+block@pcq_w10d1f-problem-progress"></div>
<div class="problem">
<div>
<p>The figure shows a circuit that contains four identical resistors each with a resistance of
[mathjaxinline]1000 \, \Omega[/mathjaxinline]. The battery is applying a potential difference of [mathjaxinline]300 \, V[/mathjaxinline], and a current of [mathjaxinline]200 \, mA[/mathjaxinline] flows through the battery.</p>
<center>
<img src="/assets/courseware/v1/149617d3cf3a3c681d2f31a6087000db/asset-v1:MITx+8.02.2x+2T2018+type@asset+block/images_W06D1_4resistor.png" width="440"/>
</center>
<p><b>(Part a)</b> What is \(\Delta V_{R_2}\)the magnitude of the voltage difference across [mathjaxinline]R_2[/mathjaxinline]?</p>
<p style="display:inline">\(\Delta V_{R_2}\) = </p>
<div class="inline" tabindex="-1" aria-label="Question 1" role="group"><div id="inputtype_pcq_w10d1f_2_1" class=" capa_inputtype inline textline">
<div class="unanswered inline">
<input type="text" name="input_pcq_w10d1f_2_1" id="input_pcq_w10d1f_2_1" aria-describedby="status_pcq_w10d1f_2_1" value="" size="8"/>
<span class="trailing_text" id="trailing_text_pcq_w10d1f_2_1"/>
<span class="status unanswered" id="status_pcq_w10d1f_2_1" data-tooltip="Not yet answered.">
<span class="sr">unanswered</span><span class="status-icon" aria-hidden="true"/>
</span>
<p id="answer_pcq_w10d1f_2_1" class="answer"/>
</div>
</div></div>
<p style="display:inline"> (in [mathjaxinline] V [/mathjaxinline])</p>
<p><b>(Part b)</b> What is the \(\Delta V_{AB}\), the magnitude of the difference in voltage between points [mathjaxinline]A[/mathjaxinline] and [mathjaxinline]B[/mathjaxinline]?</p>
<p style="display:inline">\(\Delta V_{AB}\)= </p>
<div class="inline" tabindex="-1" aria-label="Question 2" role="group"><div id="inputtype_pcq_w10d1f_3_1" class=" capa_inputtype inline textline">
<div class="unanswered inline">
<input type="text" name="input_pcq_w10d1f_3_1" id="input_pcq_w10d1f_3_1" aria-describedby="status_pcq_w10d1f_3_1" value="" size="8"/>
<span class="trailing_text" id="trailing_text_pcq_w10d1f_3_1"/>
<span class="status unanswered" id="status_pcq_w10d1f_3_1" data-tooltip="Not yet answered.">
<span class="sr">unanswered</span><span class="status-icon" aria-hidden="true"/>
</span>
<p id="answer_pcq_w10d1f_3_1" class="answer"/>
</div>
</div></div>
<p style="display:inline"> (in [mathjaxinline] V [/mathjaxinline])</p>
<p><b>(Part c)</b> What is \(\Delta V_{ED}\), the magnitude of the voltage difference between points [mathjaxinline]E[/mathjaxinline] and[mathjaxinline]D[/mathjaxinline]?</p>
<p style="display:inline">\(\Delta V_{ED}\) = </p>
<div class="inline" tabindex="-1" aria-label="Question 3" role="group"><div id="inputtype_pcq_w10d1f_4_1" class=" capa_inputtype inline textline">
<div class="unanswered inline">
<input type="text" name="input_pcq_w10d1f_4_1" id="input_pcq_w10d1f_4_1" aria-describedby="status_pcq_w10d1f_4_1" value="" size="8"/>
<span class="trailing_text" id="trailing_text_pcq_w10d1f_4_1"/>
<span class="status unanswered" id="status_pcq_w10d1f_4_1" data-tooltip="Not yet answered.">
<span class="sr">unanswered</span><span class="status-icon" aria-hidden="true"/>
</span>
<p id="answer_pcq_w10d1f_4_1" class="answer"/>
</div>
</div></div>
<p style="display:inline"> (in [mathjaxinline] V [/mathjaxinline])</p>
<p><b>(Part d)</b> What is the current flowing through [mathjaxinline]R_3[/mathjaxinline]?</p>
<p style="display:inline">Current through [mathjaxinline]R_3[/mathjaxinline] = </p>
<div class="inline" tabindex="-1" aria-label="Question 4" role="group"><div id="inputtype_pcq_w10d1f_5_1" class=" capa_inputtype inline textline">
<div class="unanswered inline">
<input type="text" name="input_pcq_w10d1f_5_1" id="input_pcq_w10d1f_5_1" aria-describedby="status_pcq_w10d1f_5_1" value="" size="8"/>
<span class="trailing_text" id="trailing_text_pcq_w10d1f_5_1"/>
<span class="status unanswered" id="status_pcq_w10d1f_5_1" data-tooltip="Not yet answered.">
<span class="sr">unanswered</span><span class="status-icon" aria-hidden="true"/>
</span>
<p id="answer_pcq_w10d1f_5_1" class="answer"/>
</div>
</div></div>
<p style="display:inline"> (in [mathjaxinline] A [/mathjaxinline])</p>
<div class="solution-span">
<span id="solution_pcq_w10d1f_solution_1"/>
</div></div>
<div class="action">
<input type="hidden" name="problem_id" value="Calculating Voltage Difference" />
<div class="submit-attempt-container">
<button type="button" class="submit btn-brand" data-submitting="Submitting" data-value="Submit" data-should-enable-submit-button="True" aria-describedby="submission_feedback_pcq_w10d1f" >
<span class="submit-label">Submit</span>
</button>
<div class="submission-feedback" id="submission_feedback_pcq_w10d1f">
<span class="sr">Some problems have options such as save, reset, hints, or show answer. These options follow the Submit button.</span>
</div>
</div>
<div class="problem-action-buttons-wrapper">
</div>
</div>
<div class="notification warning notification-gentle-alert
is-hidden"
tabindex="-1">
<span class="icon fa fa-exclamation-circle" aria-hidden="true"></span>
<span class="notification-message" aria-describedby="pcq_w10d1f-problem-title">
</span>
<div class="notification-btn-wrapper">
<button type="button" class="btn btn-default btn-small notification-btn review-btn sr">Review</button>
</div>
</div>
<div class="notification warning notification-save
is-hidden"
tabindex="-1">
<span class="icon fa fa-save" aria-hidden="true"></span>
<span class="notification-message" aria-describedby="pcq_w10d1f-problem-title">None
</span>
<div class="notification-btn-wrapper">
<button type="button" class="btn btn-default btn-small notification-btn review-btn sr">Review</button>
</div>
</div>
<div class="notification general notification-show-answer
is-hidden"
tabindex="-1">
<span class="icon fa fa-info-circle" aria-hidden="true"></span>
<span class="notification-message" aria-describedby="pcq_w10d1f-problem-title">Answers are displayed within the problem
</span>
<div class="notification-btn-wrapper">
<button type="button" class="btn btn-default btn-small notification-btn review-btn sr">Review</button>
</div>
</div>
</div>
"
data-graded="True">
<p class="loading-spinner">
<i class="fa fa-spinner fa-pulse fa-2x fa-fw"></i>
<span class="sr">Loading…</span>
</p>
</div>
</div>
</div>
</div>
</div>
<div class="xblock xblock-public_view xblock-public_view-vertical" data-usage-id="block-v1:MITx+8.02.2x+2T2018+type@vertical+block@vert-L15v09" data-graded="True" data-runtime-class="LmsRuntime" data-course-id="course-v1:MITx+8.02.2x+2T2018" data-block-type="vertical" data-request-token="a285686afe6b11ee8e28026cc65ec0d9" data-has-score="False" data-runtime-version="1" data-init="VerticalStudentView">
<h2 class="hd hd-2 unit-title">L15v9: Power in a Circuit</h2>
<div class="vert-mod">
<div class="vert vert-0" data-id="block-v1:MITx+8.02.2x+2T2018+type@video+block@L15v09">
<div class="xblock xblock-public_view xblock-public_view-video xmodule_display xmodule_VideoBlock" data-usage-id="block-v1:MITx+8.02.2x+2T2018+type@video+block@L15v09" data-graded="True" data-runtime-class="LmsRuntime" data-course-id="course-v1:MITx+8.02.2x+2T2018" data-block-type="video" data-request-token="a285686afe6b11ee8e28026cc65ec0d9" data-has-score="False" data-runtime-version="1" data-init="XBlockToXModuleShim">
<script type="json/xblock-args" class="xblock-json-init-args">
{"xmodule-type": "Video"}
</script>
<h3 class="hd hd-2">L15v09: Power in a circuit</h3>
<div
id="video_L15v09"
class="video closed"
data-metadata='{"end": 0.0, "speed": null, "ytTestTimeout": 1500, "publishCompletionUrl": "/courses/course-v1:MITx+8.02.2x+2T2018/xblock/block-v1:MITx+8.02.2x+2T2018+type@video+block@L15v09/handler/publish_completion", "ytApiUrl": "https://www.youtube.com/iframe_api", "showCaptions": "true", "streams": "1.00:YM-m60S8DHM", "poster": null, "saveStateEnabled": false, "start": 0.0, "completionPercentage": 0.95, "transcriptAvailableTranslationsUrl": "/courses/course-v1:MITx+8.02.2x+2T2018/xblock/block-v1:MITx+8.02.2x+2T2018+type@video+block@L15v09/handler/transcript/available_translations", "autoplay": false, "transcriptLanguages": {"en": "English"}, "autohideHtml5": false, "transcriptTranslationUrl": "/courses/course-v1:MITx+8.02.2x+2T2018/xblock/block-v1:MITx+8.02.2x+2T2018+type@video+block@L15v09/handler/transcript/translation/__lang__", "ytMetadataEndpoint": "", "generalSpeed": 1.0, "lmsRootURL": "https://openlearninglibrary.mit.edu", "autoAdvance": false, "completionEnabled": false, "savedVideoPosition": 0.0, "saveStateUrl": "/courses/course-v1:MITx+8.02.2x+2T2018/xblock/block-v1:MITx+8.02.2x+2T2018+type@video+block@L15v09/handler/xmodule_handler/save_user_state", "captionDataDir": null, "sources": [], "transcriptLanguage": "en", "recordedYoutubeIsAvailable": true, "prioritizeHls": false, "duration": null}'
data-bumper-metadata='null'
data-autoadvance-enabled="False"
data-poster='null'
tabindex="-1"
>
<div class="focus_grabber first"></div>
<div class="tc-wrapper">
<div class="video-wrapper">
<span tabindex="0" class="spinner" aria-hidden="false" aria-label="Loading video player"></span>
<span tabindex="-1" class="btn-play fa fa-youtube-play fa-2x is-hidden" aria-hidden="true" aria-label="Play video"></span>
<div class="video-player-pre"></div>
<div class="video-player">
<div id="L15v09"></div>
<h4 class="hd hd-4 video-error is-hidden">No playable video sources found.</h4>
<h4 class="hd hd-4 video-hls-error is-hidden">
Your browser does not support this video format. Try using a different browser.
</h4>
</div>
<div class="video-player-post"></div>
<div class="closed-captions"></div>
<div class="video-controls is-hidden">
<div>
<div class="vcr"><div class="vidtime">0:00 / 0:00</div></div>
<div class="secondary-controls"></div>
</div>
</div>
</div>
</div>
<div class="focus_grabber last"></div>
<h3 class="hd hd-4 downloads-heading sr" id="video-download-transcripts_L15v09">Downloads and transcripts</h3>
<div class="wrapper-downloads" role="region" aria-labelledby="video-download-transcripts_L15v09">
<div class="wrapper-download-transcripts">
<h4 class="hd hd-5">Transcripts</h4>
<ul class="list-download-transcripts">
<li class="transcript-option">
<a class="btn btn-link" href="/courses/course-v1:MITx+8.02.2x+2T2018/xblock/block-v1:MITx+8.02.2x+2T2018+type@video+block@L15v09/handler/transcript/download" data-value="srt">Download SubRip (.srt) file</a>
</li>
<li class="transcript-option">
<a class="btn btn-link" href="/courses/course-v1:MITx+8.02.2x+2T2018/xblock/block-v1:MITx+8.02.2x+2T2018+type@video+block@L15v09/handler/transcript/download" data-value="txt">Download Text (.txt) file</a>
</li>
</ul>
</div>
</div>
</div>
</div>
</div>
</div>
</div>
<div class="xblock xblock-public_view xblock-public_view-vertical" data-usage-id="block-v1:MITx+8.02.2x+2T2018+type@vertical+block@vert-onlinepset10_7" data-graded="True" data-runtime-class="LmsRuntime" data-course-id="course-v1:MITx+8.02.2x+2T2018" data-block-type="vertical" data-request-token="a285686afe6b11ee8e28026cc65ec0d9" data-has-score="False" data-runtime-version="1" data-init="VerticalStudentView">
<h2 class="hd hd-2 unit-title">L15Q6: Two Light Bulbs in Series</h2>
<div class="vert-mod">
<div class="vert vert-0" data-id="block-v1:MITx+8.02.2x+2T2018+type@problem+block@checkpoint_w6_13">
<div class="xblock xblock-public_view xblock-public_view-problem xmodule_display xmodule_ProblemBlock" data-usage-id="block-v1:MITx+8.02.2x+2T2018+type@problem+block@checkpoint_w6_13" data-graded="True" data-runtime-class="LmsRuntime" data-course-id="course-v1:MITx+8.02.2x+2T2018" data-block-type="problem" data-request-token="a285686afe6b11ee8e28026cc65ec0d9" data-has-score="True" data-runtime-version="1" data-init="XBlockToXModuleShim">
<script type="json/xblock-args" class="xblock-json-init-args">
{"xmodule-type": "Problem"}
</script>
<div id="problem_checkpoint_w6_13" class="problems-wrapper" role="group"
aria-labelledby="checkpoint_w6_13-problem-title"
data-problem-id="block-v1:MITx+8.02.2x+2T2018+type@problem+block@checkpoint_w6_13" data-url="/courses/course-v1:MITx+8.02.2x+2T2018/xblock/block-v1:MITx+8.02.2x+2T2018+type@problem+block@checkpoint_w6_13/handler/xmodule_handler"
data-problem-score="0.0"
data-problem-total-possible="1.0"
data-attempts-used="0"
data-content="
<h3 class="hd hd-3 problem-header" id="checkpoint_w6_13-problem-title" aria-describedby="block-v1:MITx+8.02.2x+2T2018+type@problem+block@checkpoint_w6_13-problem-progress" tabindex="-1">
Two light bulb in series
</h3>
<div class="problem-progress" id="block-v1:MITx+8.02.2x+2T2018+type@problem+block@checkpoint_w6_13-problem-progress"></div>
<div class="problem">
<div>
<p>
Two bulbs are connected in series such that one has a power of 60 W and the other has a power of 100 W in a circuit. <div class="wrapper-problem-response" tabindex="-1" aria-label="Question 1" role="group"><div class="choicegroup capa_inputtype" id="inputtype_checkpoint_w6_13_2_1">
<fieldset aria-describedby="status_checkpoint_w6_13_2_1">
<div class="field">
<input type="radio" name="input_checkpoint_w6_13_2_1" id="input_checkpoint_w6_13_2_1_choice_1" class="field-input input-radio" value="choice_1"/><label id="checkpoint_w6_13_2_1-choice_1-label" for="input_checkpoint_w6_13_2_1_choice_1" class="response-label field-label label-inline" aria-describedby="status_checkpoint_w6_13_2_1"> <text> 1. The potential difference across the 60 W light bulb is greater.</text>
</label>
</div>
<div class="field">
<input type="radio" name="input_checkpoint_w6_13_2_1" id="input_checkpoint_w6_13_2_1_choice_2" class="field-input input-radio" value="choice_2"/><label id="checkpoint_w6_13_2_1-choice_2-label" for="input_checkpoint_w6_13_2_1_choice_2" class="response-label field-label label-inline" aria-describedby="status_checkpoint_w6_13_2_1"> <text> 2. The potential difference is the same across each bulb</text>
</label>
</div>
<div class="field">
<input type="radio" name="input_checkpoint_w6_13_2_1" id="input_checkpoint_w6_13_2_1_choice_3" class="field-input input-radio" value="choice_3"/><label id="checkpoint_w6_13_2_1-choice_3-label" for="input_checkpoint_w6_13_2_1_choice_3" class="response-label field-label label-inline" aria-describedby="status_checkpoint_w6_13_2_1"> <text> 3. The potential difference across the 60 W light bulb is smaller.</text>
</label>
</div>
<span id="answer_checkpoint_w6_13_2_1"/>
</fieldset>
<div class="indicator-container">
<span class="status unanswered" id="status_checkpoint_w6_13_2_1" data-tooltip="Not yet answered.">
<span class="sr">unanswered</span><span class="status-icon" aria-hidden="true"/>
</span>
</div>
</div></div> </p>
<p>
<div class="solution-span">
<span id="solution_checkpoint_w6_13_solution_1"/>
</div></p>
</div>
<div class="action">
<input type="hidden" name="problem_id" value="Two light bulb in series" />
<div class="submit-attempt-container">
<button type="button" class="submit btn-brand" data-submitting="Submitting" data-value="Submit" data-should-enable-submit-button="True" aria-describedby="submission_feedback_checkpoint_w6_13" >
<span class="submit-label">Submit</span>
</button>
<div class="submission-feedback" id="submission_feedback_checkpoint_w6_13">
<span class="sr">Some problems have options such as save, reset, hints, or show answer. These options follow the Submit button.</span>
</div>
</div>
<div class="problem-action-buttons-wrapper">
</div>
</div>
<div class="notification warning notification-gentle-alert
is-hidden"
tabindex="-1">
<span class="icon fa fa-exclamation-circle" aria-hidden="true"></span>
<span class="notification-message" aria-describedby="checkpoint_w6_13-problem-title">
</span>
<div class="notification-btn-wrapper">
<button type="button" class="btn btn-default btn-small notification-btn review-btn sr">Review</button>
</div>
</div>
<div class="notification warning notification-save
is-hidden"
tabindex="-1">
<span class="icon fa fa-save" aria-hidden="true"></span>
<span class="notification-message" aria-describedby="checkpoint_w6_13-problem-title">None
</span>
<div class="notification-btn-wrapper">
<button type="button" class="btn btn-default btn-small notification-btn review-btn sr">Review</button>
</div>
</div>
<div class="notification general notification-show-answer
is-hidden"
tabindex="-1">
<span class="icon fa fa-info-circle" aria-hidden="true"></span>
<span class="notification-message" aria-describedby="checkpoint_w6_13-problem-title">Answers are displayed within the problem
</span>
<div class="notification-btn-wrapper">
<button type="button" class="btn btn-default btn-small notification-btn review-btn sr">Review</button>
</div>
</div>
</div>
"
data-graded="True">
<p class="loading-spinner">
<i class="fa fa-spinner fa-pulse fa-2x fa-fw"></i>
<span class="sr">Loading…</span>
</p>
</div>
</div>
</div>
</div>
</div>
<div class="xblock xblock-public_view xblock-public_view-vertical" data-usage-id="block-v1:MITx+8.02.2x+2T2018+type@vertical+block@vert-onlinepset10_4" data-graded="True" data-runtime-class="LmsRuntime" data-course-id="course-v1:MITx+8.02.2x+2T2018" data-block-type="vertical" data-request-token="a285686afe6b11ee8e28026cc65ec0d9" data-has-score="False" data-runtime-version="1" data-init="VerticalStudentView">
<h2 class="hd hd-2 unit-title">L15Q7: Three Light Bulbs</h2>
<div class="vert-mod">
<div class="vert vert-0" data-id="block-v1:MITx+8.02.2x+2T2018+type@problem+block@pcq_w10d1d">
<div class="xblock xblock-public_view xblock-public_view-problem xmodule_display xmodule_ProblemBlock" data-usage-id="block-v1:MITx+8.02.2x+2T2018+type@problem+block@pcq_w10d1d" data-graded="True" data-runtime-class="LmsRuntime" data-course-id="course-v1:MITx+8.02.2x+2T2018" data-block-type="problem" data-request-token="a285686afe6b11ee8e28026cc65ec0d9" data-has-score="True" data-runtime-version="1" data-init="XBlockToXModuleShim">
<script type="json/xblock-args" class="xblock-json-init-args">
{"xmodule-type": "Problem"}
</script>
<div id="problem_pcq_w10d1d" class="problems-wrapper" role="group"
aria-labelledby="pcq_w10d1d-problem-title"
data-problem-id="block-v1:MITx+8.02.2x+2T2018+type@problem+block@pcq_w10d1d" data-url="/courses/course-v1:MITx+8.02.2x+2T2018/xblock/block-v1:MITx+8.02.2x+2T2018+type@problem+block@pcq_w10d1d/handler/xmodule_handler"
data-problem-score="0.0"
data-problem-total-possible="1.0"
data-attempts-used="0"
data-content="
<h3 class="hd hd-3 problem-header" id="pcq_w10d1d-problem-title" aria-describedby="block-v1:MITx+8.02.2x+2T2018+type@problem+block@pcq_w10d1d-problem-progress" tabindex="-1">
Three light Bulbs
</h3>
<div class="problem-progress" id="block-v1:MITx+8.02.2x+2T2018+type@problem+block@pcq_w10d1d-problem-progress"></div>
<div class="problem">
<div>
<center>
<img src="/assets/courseware/v1/76d733939e72b8e4c2c1cf1636349040/asset-v1:MITx+8.02.2x+2T2018+type@asset+block/images_W10D2_3_bulb_circuit.png" width="260"/>
</center>
<p>The picture shows a circuit containing three identical light bulbs A,B, and C, connected to a perfect battery (constant voltage, no
internal resistance). Bulb C is connected by the switch which can be open or closed.</p>
<p>Let [mathjaxinline]I_{\rm open}[/mathjaxinline] and [mathjaxinline]I_{\rm closed}[/mathjaxinline] be the current through the battery when the switch is opened or closed, respectively. Let [mathjaxinline]B_{\rm open}[/mathjaxinline] and [mathjaxinline]B_{\rm closed}[/mathjaxinline] be the brightness of bulb A when the switch is open or closed, respectively. A bulb can be thought of as a resistor whose light production (brightness) is proportional to the power dissipated in the resistor.</p>
<p>Which of the following set of inequalities correctly describes the current through the battery and the brightness of bulb A?</p>
<div class="wrapper-problem-response" tabindex="-1" aria-label="Question 1" role="group"><div class="choicegroup capa_inputtype" id="inputtype_pcq_w10d1d_2_1">
<fieldset aria-describedby="status_pcq_w10d1d_2_1">
<div class="field">
<input type="radio" name="input_pcq_w10d1d_2_1" id="input_pcq_w10d1d_2_1_choice_0" class="field-input input-radio" value="choice_0"/><label id="pcq_w10d1d_2_1-choice_0-label" for="input_pcq_w10d1d_2_1_choice_0" class="response-label field-label label-inline" aria-describedby="status_pcq_w10d1d_2_1"> (a) \(I_{\rm closed}\lt I_{\rm open}\) and \({\rm B}_{\rm closed} \lt {\rm B}_{\rm
open}\)
</label>
</div>
<div class="field">
<input type="radio" name="input_pcq_w10d1d_2_1" id="input_pcq_w10d1d_2_1_choice_1" class="field-input input-radio" value="choice_1"/><label id="pcq_w10d1d_2_1-choice_1-label" for="input_pcq_w10d1d_2_1_choice_1" class="response-label field-label label-inline" aria-describedby="status_pcq_w10d1d_2_1"> (b) \(I_{\rm closed}\gt I_{\rm open}\) and \({\rm B}_{\rm closed} \lt {\rm B}_{\rm
open}\)
</label>
</div>
<div class="field">
<input type="radio" name="input_pcq_w10d1d_2_1" id="input_pcq_w10d1d_2_1_choice_2" class="field-input input-radio" value="choice_2"/><label id="pcq_w10d1d_2_1-choice_2-label" for="input_pcq_w10d1d_2_1_choice_2" class="response-label field-label label-inline" aria-describedby="status_pcq_w10d1d_2_1"> (c) \(I_{\rm closed}\gt I_{\rm open}\) and \({\rm B}_{\rm closed} \gt {\rm B}_{\rm
open}\)
</label>
</div>
<div class="field">
<input type="radio" name="input_pcq_w10d1d_2_1" id="input_pcq_w10d1d_2_1_choice_3" class="field-input input-radio" value="choice_3"/><label id="pcq_w10d1d_2_1-choice_3-label" for="input_pcq_w10d1d_2_1_choice_3" class="response-label field-label label-inline" aria-describedby="status_pcq_w10d1d_2_1"> (d) \(I_{\rm closed}\lt I_{\rm open}\) and \({\rm B}_{\rm closed} \gt {\rm B}_{\rm
open}\)
</label>
</div>
<span id="answer_pcq_w10d1d_2_1"/>
</fieldset>
<div class="indicator-container">
<span class="status unanswered" id="status_pcq_w10d1d_2_1" data-tooltip="Not yet answered.">
<span class="sr">unanswered</span><span class="status-icon" aria-hidden="true"/>
</span>
</div>
</div></div>
<p> You can check your answer using the interactive simulation from the University of Colorado.</p>
<p>
<center>
<div style="position: relative; width: 300px; height: 200px;">
<a href="https://phet.colorado.edu/sims/html/circuit-construction-kit-dc/latest/circuit-construction-kit-dc_en.html" target="_blank" style="text-decoration: none;">
<img src="https://phet.colorado.edu/sims/html/circuit-construction-kit-dc/latest/circuit-construction-kit-dc-600.png" alt="Circuit Construction Kit: DC" style="border: none;" width="300" height="200"/>
<div style="position: absolute; width: 200px; height: 80px; left: 50px; top: 60px; background-color: #FFF; opacity: 0.6; filter: alpha(opacity = 60);"/>
<table style="position: absolute; width: 200px; height: 80px; left: 50px; top: 60px;">
<tr>
<td style="text-align: center; color: #000; font-size: 24px; font-family: Arial,sans-serif;">Click to Run</td>
</tr>
</table>
</a>
</div>
</center>
</p>
<div class="solution-span">
<span id="solution_pcq_w10d1d_solution_1"/>
</div></div>
<div class="action">
<input type="hidden" name="problem_id" value="Three light Bulbs" />
<div class="submit-attempt-container">
<button type="button" class="submit btn-brand" data-submitting="Submitting" data-value="Submit" data-should-enable-submit-button="True" aria-describedby="submission_feedback_pcq_w10d1d" >
<span class="submit-label">Submit</span>
</button>
<div class="submission-feedback" id="submission_feedback_pcq_w10d1d">
<span class="sr">Some problems have options such as save, reset, hints, or show answer. These options follow the Submit button.</span>
</div>
</div>
<div class="problem-action-buttons-wrapper">
</div>
</div>
<div class="notification warning notification-gentle-alert
is-hidden"
tabindex="-1">
<span class="icon fa fa-exclamation-circle" aria-hidden="true"></span>
<span class="notification-message" aria-describedby="pcq_w10d1d-problem-title">
</span>
<div class="notification-btn-wrapper">
<button type="button" class="btn btn-default btn-small notification-btn review-btn sr">Review</button>
</div>
</div>
<div class="notification warning notification-save
is-hidden"
tabindex="-1">
<span class="icon fa fa-save" aria-hidden="true"></span>
<span class="notification-message" aria-describedby="pcq_w10d1d-problem-title">None
</span>
<div class="notification-btn-wrapper">
<button type="button" class="btn btn-default btn-small notification-btn review-btn sr">Review</button>
</div>
</div>
<div class="notification general notification-show-answer
is-hidden"
tabindex="-1">
<span class="icon fa fa-info-circle" aria-hidden="true"></span>
<span class="notification-message" aria-describedby="pcq_w10d1d-problem-title">Answers are displayed within the problem
</span>
<div class="notification-btn-wrapper">
<button type="button" class="btn btn-default btn-small notification-btn review-btn sr">Review</button>
</div>
</div>
</div>
"
data-graded="True">
<p class="loading-spinner">
<i class="fa fa-spinner fa-pulse fa-2x fa-fw"></i>
<span class="sr">Loading…</span>
</p>
</div>
</div>
</div>
</div>
</div>
© All Rights Reserved