<div class="xblock xblock-public_view xblock-public_view-vertical" data-request-token="04a14dec05d811f0a17b0affe2bbc7c1" data-usage-id="block-v1:MITx+8.02.3x+1T2019+type@vertical+block@vert-Peter30" data-init="VerticalStudentView" data-block-type="vertical" data-runtime-class="LmsRuntime" data-course-id="course-v1:MITx+8.02.3x+1T2019" data-has-score="False" data-graded="False" data-runtime-version="1"> <h2 class="hd hd-2 unit-title">Adding Circuit Elements in Parallel</h2> <div class="vert-mod"> <div class="vert vert-0" data-id="block-v1:MITx+8.02.3x+1T2019+type@problem+block@fridayw12_6"> <div class="xblock xblock-public_view xblock-public_view-problem xmodule_display xmodule_ProblemBlock" data-request-token="04a14dec05d811f0a17b0affe2bbc7c1" data-usage-id="block-v1:MITx+8.02.3x+1T2019+type@problem+block@fridayw12_6" data-init="XBlockToXModuleShim" data-block-type="problem" data-runtime-class="LmsRuntime" data-course-id="course-v1:MITx+8.02.3x+1T2019" data-has-score="True" data-graded="False" data-runtime-version="1"> <script type="json/xblock-args" class="xblock-json-init-args"> {"xmodule-type": "Problem"} </script> <div id="problem_fridayw12_6" class="problems-wrapper" role="group" aria-labelledby="fridayw12_6-problem-title" data-problem-id="block-v1:MITx+8.02.3x+1T2019+type@problem+block@fridayw12_6" data-url="/courses/course-v1:MITx+8.02.3x+1T2019/xblock/block-v1:MITx+8.02.3x+1T2019+type@problem+block@fridayw12_6/handler/xmodule_handler" data-problem-score="0" data-problem-total-possible="0" data-attempts-used="0" data-content=" &lt;h3 class=&#34;hd hd-3 problem-header&#34; id=&#34;fridayw12_6-problem-title&#34; aria-describedby=&#34;block-v1:MITx+8.02.3x+1T2019+type@problem+block@fridayw12_6-problem-progress&#34; tabindex=&#34;-1&#34;&gt; Adding Circuit Elements in Parallel &lt;/h3&gt; &lt;div class=&#34;problem-progress&#34; id=&#34;block-v1:MITx+8.02.3x+1T2019+type@problem+block@fridayw12_6-problem-progress&#34;&gt;&lt;/div&gt; &lt;div class=&#34;problem&#34;&gt; &lt;div&gt; &lt;p&gt; We have a circuit with a driving EMF in parallel with each of a resistor, with resistance [mathjaxinline]R[/mathjaxinline], an inductor with inductance [mathjaxinline]L[/mathjaxinline], and a capacitor with capacitance, [mathjaxinline]C[/mathjaxinline]. If we are driving the circuit with a voltage [mathjaxinline]V = V_0 e^{i \omega t}[/mathjaxinline], find the amplitude and phase of the current response, [mathjaxinline]I_0 e^{i\omega t}e^{-i \phi }[/mathjaxinline]. &lt;/p&gt; &lt;p&gt; &lt;p style=&#34;display:inline&#34;&gt;[mathjaxinline]I_0[/mathjaxinline] = &lt;/p&gt; &lt;div class=&#34;inline&#34; tabindex=&#34;-1&#34; aria-label=&#34;Question 1&#34; role=&#34;group&#34;&gt;&lt;div id=&#34;inputtype_fridayw12_6_2_1&#34; class=&#34;text-input-dynamath capa_inputtype inline textline&#34;&gt; &lt;div class=&#34;unanswered inline&#34;&gt; &lt;input type=&#34;text&#34; name=&#34;input_fridayw12_6_2_1&#34; id=&#34;input_fridayw12_6_2_1&#34; aria-describedby=&#34;status_fridayw12_6_2_1&#34; value=&#34;&#34; class=&#34;math&#34; size=&#34;50&#34;/&gt; &lt;span class=&#34;trailing_text&#34; id=&#34;trailing_text_fridayw12_6_2_1&#34;/&gt; &lt;span class=&#34;status unanswered&#34; id=&#34;status_fridayw12_6_2_1&#34; data-tooltip=&#34;Not yet answered.&#34;&gt; &lt;span class=&#34;sr&#34;&gt;unanswered&lt;/span&gt;&lt;span class=&#34;status-icon&#34; aria-hidden=&#34;true&#34;/&gt; &lt;/span&gt; &lt;p id=&#34;answer_fridayw12_6_2_1&#34; class=&#34;answer&#34;/&gt; &lt;div id=&#34;display_fridayw12_6_2_1&#34; class=&#34;equation&#34;&gt;`{::}`&lt;/div&gt; &lt;textarea style=&#34;display:none&#34; id=&#34;input_fridayw12_6_2_1_dynamath&#34; name=&#34;input_fridayw12_6_2_1_dynamath&#34;/&gt; &lt;/div&gt; &lt;/div&gt;&lt;/div&gt; &lt;/p&gt; &lt;p&gt; &lt;p style=&#34;display:inline&#34;&gt;[mathjaxinline]\phi[/mathjaxinline] = &lt;/p&gt; &lt;div class=&#34;inline&#34; tabindex=&#34;-1&#34; aria-label=&#34;Question 2&#34; role=&#34;group&#34;&gt;&lt;div id=&#34;inputtype_fridayw12_6_3_1&#34; class=&#34;text-input-dynamath capa_inputtype inline textline&#34;&gt; &lt;div class=&#34;unanswered inline&#34;&gt; &lt;input type=&#34;text&#34; name=&#34;input_fridayw12_6_3_1&#34; id=&#34;input_fridayw12_6_3_1&#34; aria-describedby=&#34;status_fridayw12_6_3_1&#34; value=&#34;&#34; class=&#34;math&#34; size=&#34;50&#34;/&gt; &lt;span class=&#34;trailing_text&#34; id=&#34;trailing_text_fridayw12_6_3_1&#34;/&gt; &lt;span class=&#34;status unanswered&#34; id=&#34;status_fridayw12_6_3_1&#34; data-tooltip=&#34;Not yet answered.&#34;&gt; &lt;span class=&#34;sr&#34;&gt;unanswered&lt;/span&gt;&lt;span class=&#34;status-icon&#34; aria-hidden=&#34;true&#34;/&gt; &lt;/span&gt; &lt;p id=&#34;answer_fridayw12_6_3_1&#34; class=&#34;answer&#34;/&gt; &lt;div id=&#34;display_fridayw12_6_3_1&#34; class=&#34;equation&#34;&gt;`{::}`&lt;/div&gt; &lt;textarea style=&#34;display:none&#34; id=&#34;input_fridayw12_6_3_1_dynamath&#34; name=&#34;input_fridayw12_6_3_1_dynamath&#34;/&gt; &lt;/div&gt; &lt;/div&gt;&lt;/div&gt; &lt;/p&gt; &lt;p&gt; &lt;div class=&#34;solution-span&#34;&gt; &lt;span id=&#34;solution_fridayw12_6_solution_1&#34;/&gt; &lt;/div&gt;&lt;/p&gt; &lt;/div&gt; &lt;div class=&#34;action&#34;&gt; &lt;input type=&#34;hidden&#34; name=&#34;problem_id&#34; value=&#34;Adding Circuit Elements in Parallel&#34; /&gt; &lt;div class=&#34;submit-attempt-container&#34;&gt; &lt;button type=&#34;button&#34; class=&#34;submit btn-brand&#34; data-submitting=&#34;Submitting&#34; data-value=&#34;Submit&#34; data-should-enable-submit-button=&#34;True&#34; aria-describedby=&#34;submission_feedback_fridayw12_6&#34; &gt; &lt;span class=&#34;submit-label&#34;&gt;Submit&lt;/span&gt; &lt;/button&gt; &lt;div class=&#34;submission-feedback&#34; id=&#34;submission_feedback_fridayw12_6&#34;&gt; &lt;span class=&#34;sr&#34;&gt;Some problems have options such as save, reset, hints, or show answer. 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<div class="xblock xblock-public_view xblock-public_view-vertical" data-request-token="04a14dec05d811f0a17b0affe2bbc7c1" data-usage-id="block-v1:MITx+8.02.3x+1T2019+type@vertical+block@vert-w12d3-q1" data-init="VerticalStudentView" data-block-type="vertical" data-runtime-class="LmsRuntime" data-course-id="course-v1:MITx+8.02.3x+1T2019" data-has-score="False" data-graded="False" data-runtime-version="1"> <h2 class="hd hd-2 unit-title">Low Pass Filter</h2> <div class="vert-mod"> <div class="vert vert-0" data-id="block-v1:MITx+8.02.3x+1T2019+type@problem+block@fridayw12_1a"> <div class="xblock xblock-public_view xblock-public_view-problem xmodule_display xmodule_ProblemBlock" data-request-token="04a14dec05d811f0a17b0affe2bbc7c1" data-usage-id="block-v1:MITx+8.02.3x+1T2019+type@problem+block@fridayw12_1a" data-init="XBlockToXModuleShim" data-block-type="problem" data-runtime-class="LmsRuntime" data-course-id="course-v1:MITx+8.02.3x+1T2019" data-has-score="True" data-graded="False" data-runtime-version="1"> <script type="json/xblock-args" class="xblock-json-init-args"> {"xmodule-type": "Problem"} </script> <div id="problem_fridayw12_1a" class="problems-wrapper" role="group" aria-labelledby="fridayw12_1a-problem-title" data-problem-id="block-v1:MITx+8.02.3x+1T2019+type@problem+block@fridayw12_1a" data-url="/courses/course-v1:MITx+8.02.3x+1T2019/xblock/block-v1:MITx+8.02.3x+1T2019+type@problem+block@fridayw12_1a/handler/xmodule_handler" data-problem-score="0" data-problem-total-possible="0" data-attempts-used="0" data-content=" &lt;h3 class=&#34;hd hd-3 problem-header&#34; id=&#34;fridayw12_1a-problem-title&#34; aria-describedby=&#34;block-v1:MITx+8.02.3x+1T2019+type@problem+block@fridayw12_1a-problem-progress&#34; tabindex=&#34;-1&#34;&gt; Low Pass Filter &lt;/h3&gt; &lt;div class=&#34;problem-progress&#34; id=&#34;block-v1:MITx+8.02.3x+1T2019+type@problem+block@fridayw12_1a-problem-progress&#34;&gt;&lt;/div&gt; &lt;div class=&#34;problem&#34;&gt; &lt;div&gt; &lt;p&gt; Consider an AC voltage source, [mathjaxinline]V_{in} = V_{in,0} e^{i \omega t}[/mathjaxinline], connected in series to a resistor with resistance [mathjaxinline]R[/mathjaxinline] and a capacitor with capacitance [mathjaxinline]C[/mathjaxinline] as shown in the figure below. The output voltage, [mathjaxinline]V_ C \equiv V_{out} = V_{out, 0} e^{i(\omega t - \delta )}[/mathjaxinline], is the voltage across the capacitor. In this problem, we shall solve for the ratio [mathjaxinline]V_{out, 0} / V_{in, 0}[/mathjaxinline] and identify the range of frequencies which are blocked by this filter. &lt;/p&gt; &lt;p&gt; &lt;center&gt; &lt;img src=&#34;/assets/courseware/v1/60cc6362e30f1ffad20b2fe2bc93d53a/asset-v1:MITx+8.02.3x+1T2019+type@asset+block/images_Friday_W12d3_1-001.jpg&#34; width=&#34;440&#34;/&gt; &lt;/center&gt; &lt;/p&gt; &lt;p&gt; Remember that inverse trigonometric functions are entered in the edX as arcsin(), arccos(), arctan(), arccot(), etc. You may also enter [mathjaxinline]i[/mathjaxinline] in your answers here, where [mathjaxinline]i = \sqrt {-1}[/mathjaxinline]. &lt;/p&gt; &lt;p&gt; Discussions of all of these questions can be found in the video linked below. &lt;/p&gt; &lt;p&gt;&lt;b class=&#34;bfseries&#34;&gt;(Part a)&lt;/b&gt; What is the equivalent impedance of this circuit? Express your answer using R, C, V_0 for [mathjaxinline]V_{in,0}[/mathjaxinline], and omega for [mathjaxinline]\omega[/mathjaxinline] as needed. &lt;/p&gt; &lt;p&gt; &lt;p style=&#34;display:inline&#34;&gt;[mathjaxinline]Z_{eq} =[/mathjaxinline] &lt;/p&gt; &lt;div class=&#34;inline&#34; tabindex=&#34;-1&#34; aria-label=&#34;Question 1&#34; role=&#34;group&#34;&gt;&lt;div id=&#34;inputtype_fridayw12_1a_2_1&#34; class=&#34;text-input-dynamath capa_inputtype inline textline&#34;&gt; &lt;div class=&#34;unanswered inline&#34;&gt; &lt;input type=&#34;text&#34; name=&#34;input_fridayw12_1a_2_1&#34; id=&#34;input_fridayw12_1a_2_1&#34; aria-describedby=&#34;status_fridayw12_1a_2_1&#34; value=&#34;&#34; class=&#34;math&#34; size=&#34;60&#34;/&gt; &lt;span class=&#34;trailing_text&#34; id=&#34;trailing_text_fridayw12_1a_2_1&#34;/&gt; &lt;span class=&#34;status unanswered&#34; id=&#34;status_fridayw12_1a_2_1&#34; data-tooltip=&#34;Not yet answered.&#34;&gt; &lt;span class=&#34;sr&#34;&gt;unanswered&lt;/span&gt;&lt;span class=&#34;status-icon&#34; aria-hidden=&#34;true&#34;/&gt; &lt;/span&gt; &lt;p id=&#34;answer_fridayw12_1a_2_1&#34; class=&#34;answer&#34;/&gt; &lt;div id=&#34;display_fridayw12_1a_2_1&#34; class=&#34;equation&#34;&gt;`{::}`&lt;/div&gt; &lt;textarea style=&#34;display:none&#34; id=&#34;input_fridayw12_1a_2_1_dynamath&#34; name=&#34;input_fridayw12_1a_2_1_dynamath&#34;/&gt; &lt;/div&gt; &lt;/div&gt;&lt;/div&gt; &lt;/p&gt; &lt;/div&gt; &lt;div class=&#34;action&#34;&gt; &lt;input type=&#34;hidden&#34; name=&#34;problem_id&#34; value=&#34;Low Pass Filter&#34; /&gt; &lt;div class=&#34;submit-attempt-container&#34;&gt; &lt;button type=&#34;button&#34; class=&#34;submit btn-brand&#34; data-submitting=&#34;Submitting&#34; data-value=&#34;Submit&#34; data-should-enable-submit-button=&#34;True&#34; aria-describedby=&#34;submission_feedback_fridayw12_1a&#34; &gt; &lt;span class=&#34;submit-label&#34;&gt;Submit&lt;/span&gt; &lt;/button&gt; &lt;div class=&#34;submission-feedback&#34; id=&#34;submission_feedback_fridayw12_1a&#34;&gt; &lt;span class=&#34;sr&#34;&gt;Some problems have options such as save, reset, hints, or show answer. These options follow the Submit button.&lt;/span&gt; &lt;/div&gt; &lt;/div&gt; &lt;div class=&#34;problem-action-buttons-wrapper&#34;&gt; &lt;/div&gt; &lt;/div&gt; &lt;div class=&#34;notification warning notification-gentle-alert is-hidden&#34; tabindex=&#34;-1&#34;&gt; &lt;span class=&#34;icon fa fa-exclamation-circle&#34; aria-hidden=&#34;true&#34;&gt;&lt;/span&gt; &lt;span class=&#34;notification-message&#34; aria-describedby=&#34;fridayw12_1a-problem-title&#34;&gt; &lt;/span&gt; &lt;div class=&#34;notification-btn-wrapper&#34;&gt; &lt;button type=&#34;button&#34; class=&#34;btn btn-default btn-small notification-btn review-btn sr&#34;&gt;Review&lt;/button&gt; &lt;/div&gt; &lt;/div&gt; &lt;div class=&#34;notification warning notification-save is-hidden&#34; tabindex=&#34;-1&#34;&gt; &lt;span class=&#34;icon fa fa-save&#34; aria-hidden=&#34;true&#34;&gt;&lt;/span&gt; &lt;span class=&#34;notification-message&#34; aria-describedby=&#34;fridayw12_1a-problem-title&#34;&gt;None &lt;/span&gt; &lt;div class=&#34;notification-btn-wrapper&#34;&gt; &lt;button type=&#34;button&#34; class=&#34;btn btn-default btn-small notification-btn review-btn sr&#34;&gt;Review&lt;/button&gt; &lt;/div&gt; &lt;/div&gt; &lt;div class=&#34;notification general notification-show-answer is-hidden&#34; tabindex=&#34;-1&#34;&gt; &lt;span class=&#34;icon fa fa-info-circle&#34; aria-hidden=&#34;true&#34;&gt;&lt;/span&gt; &lt;span class=&#34;notification-message&#34; aria-describedby=&#34;fridayw12_1a-problem-title&#34;&gt;Answers are displayed within the problem &lt;/span&gt; &lt;div class=&#34;notification-btn-wrapper&#34;&gt; &lt;button type=&#34;button&#34; class=&#34;btn btn-default btn-small notification-btn review-btn sr&#34;&gt;Review&lt;/button&gt; &lt;/div&gt; &lt;/div&gt; &lt;/div&gt; " data-graded="False"> <p class="loading-spinner"> <i class="fa fa-spinner fa-pulse fa-2x fa-fw"></i> <span class="sr">Loading&hellip;</span> </p> </div> </div> </div> <div class="vert vert-1" data-id="block-v1:MITx+8.02.3x+1T2019+type@problem+block@fridayw12_1b"> <div class="xblock xblock-public_view xblock-public_view-problem xmodule_display xmodule_ProblemBlock" data-request-token="04a14dec05d811f0a17b0affe2bbc7c1" data-usage-id="block-v1:MITx+8.02.3x+1T2019+type@problem+block@fridayw12_1b" data-init="XBlockToXModuleShim" data-block-type="problem" data-runtime-class="LmsRuntime" data-course-id="course-v1:MITx+8.02.3x+1T2019" data-has-score="True" data-graded="False" data-runtime-version="1"> <script type="json/xblock-args" class="xblock-json-init-args"> {"xmodule-type": "Problem"} </script> <div id="problem_fridayw12_1b" class="problems-wrapper" role="group" aria-labelledby="fridayw12_1b-problem-title" data-problem-id="block-v1:MITx+8.02.3x+1T2019+type@problem+block@fridayw12_1b" data-url="/courses/course-v1:MITx+8.02.3x+1T2019/xblock/block-v1:MITx+8.02.3x+1T2019+type@problem+block@fridayw12_1b/handler/xmodule_handler" data-problem-score="0" data-problem-total-possible="0" data-attempts-used="0" data-content=" &lt;h3 class=&#34;hd hd-3 problem-header&#34; id=&#34;fridayw12_1b-problem-title&#34; aria-describedby=&#34;block-v1:MITx+8.02.3x+1T2019+type@problem+block@fridayw12_1b-problem-progress&#34; tabindex=&#34;-1&#34;&gt; Impedance Modulus &lt;/h3&gt; &lt;div class=&#34;problem-progress&#34; id=&#34;block-v1:MITx+8.02.3x+1T2019+type@problem+block@fridayw12_1b-problem-progress&#34;&gt;&lt;/div&gt; &lt;div class=&#34;problem&#34;&gt; &lt;div&gt; &lt;p&gt;&lt;b class=&#34;bfseries&#34;&gt;(Part b)&lt;/b&gt; What is the modulus of the equivalent impedance? Express your answer using R, C, V_0 for [mathjaxinline]V_{in,0}[/mathjaxinline], and omega for [mathjaxinline]\omega[/mathjaxinline] as needed. &lt;/p&gt; &lt;p&gt; &lt;p style=&#34;display:inline&#34;&gt;[mathjaxinline]|Z_{eq}| =[/mathjaxinline] &lt;/p&gt; &lt;div class=&#34;inline&#34; tabindex=&#34;-1&#34; aria-label=&#34;Question 1&#34; role=&#34;group&#34;&gt;&lt;div id=&#34;inputtype_fridayw12_1b_2_1&#34; class=&#34;text-input-dynamath capa_inputtype inline textline&#34;&gt; &lt;div class=&#34;unanswered inline&#34;&gt; &lt;input type=&#34;text&#34; name=&#34;input_fridayw12_1b_2_1&#34; id=&#34;input_fridayw12_1b_2_1&#34; aria-describedby=&#34;status_fridayw12_1b_2_1&#34; value=&#34;&#34; class=&#34;math&#34; size=&#34;60&#34;/&gt; &lt;span class=&#34;trailing_text&#34; id=&#34;trailing_text_fridayw12_1b_2_1&#34;/&gt; &lt;span class=&#34;status unanswered&#34; id=&#34;status_fridayw12_1b_2_1&#34; data-tooltip=&#34;Not yet answered.&#34;&gt; &lt;span class=&#34;sr&#34;&gt;unanswered&lt;/span&gt;&lt;span class=&#34;status-icon&#34; aria-hidden=&#34;true&#34;/&gt; &lt;/span&gt; &lt;p id=&#34;answer_fridayw12_1b_2_1&#34; class=&#34;answer&#34;/&gt; &lt;div id=&#34;display_fridayw12_1b_2_1&#34; class=&#34;equation&#34;&gt;`{::}`&lt;/div&gt; &lt;textarea style=&#34;display:none&#34; id=&#34;input_fridayw12_1b_2_1_dynamath&#34; name=&#34;input_fridayw12_1b_2_1_dynamath&#34;/&gt; &lt;/div&gt; &lt;/div&gt;&lt;/div&gt; &lt;/p&gt; &lt;/div&gt; &lt;div class=&#34;action&#34;&gt; &lt;input type=&#34;hidden&#34; name=&#34;problem_id&#34; value=&#34;Impedance Modulus&#34; /&gt; &lt;div class=&#34;submit-attempt-container&#34;&gt; &lt;button type=&#34;button&#34; class=&#34;submit btn-brand&#34; data-submitting=&#34;Submitting&#34; data-value=&#34;Submit&#34; data-should-enable-submit-button=&#34;True&#34; aria-describedby=&#34;submission_feedback_fridayw12_1b&#34; &gt; &lt;span class=&#34;submit-label&#34;&gt;Submit&lt;/span&gt; &lt;/button&gt; &lt;div class=&#34;submission-feedback&#34; id=&#34;submission_feedback_fridayw12_1b&#34;&gt; &lt;span class=&#34;sr&#34;&gt;Some problems have options such as save, reset, hints, or show answer. These options follow the Submit button.&lt;/span&gt; &lt;/div&gt; &lt;/div&gt; &lt;div class=&#34;problem-action-buttons-wrapper&#34;&gt; &lt;/div&gt; &lt;/div&gt; &lt;div class=&#34;notification warning notification-gentle-alert is-hidden&#34; tabindex=&#34;-1&#34;&gt; &lt;span class=&#34;icon fa fa-exclamation-circle&#34; aria-hidden=&#34;true&#34;&gt;&lt;/span&gt; &lt;span class=&#34;notification-message&#34; aria-describedby=&#34;fridayw12_1b-problem-title&#34;&gt; &lt;/span&gt; &lt;div class=&#34;notification-btn-wrapper&#34;&gt; &lt;button type=&#34;button&#34; class=&#34;btn btn-default btn-small notification-btn review-btn sr&#34;&gt;Review&lt;/button&gt; &lt;/div&gt; &lt;/div&gt; &lt;div class=&#34;notification warning notification-save is-hidden&#34; tabindex=&#34;-1&#34;&gt; &lt;span class=&#34;icon fa fa-save&#34; aria-hidden=&#34;true&#34;&gt;&lt;/span&gt; &lt;span class=&#34;notification-message&#34; aria-describedby=&#34;fridayw12_1b-problem-title&#34;&gt;None &lt;/span&gt; &lt;div class=&#34;notification-btn-wrapper&#34;&gt; &lt;button type=&#34;button&#34; class=&#34;btn btn-default btn-small notification-btn review-btn sr&#34;&gt;Review&lt;/button&gt; &lt;/div&gt; &lt;/div&gt; &lt;div class=&#34;notification general notification-show-answer is-hidden&#34; tabindex=&#34;-1&#34;&gt; &lt;span class=&#34;icon fa fa-info-circle&#34; aria-hidden=&#34;true&#34;&gt;&lt;/span&gt; &lt;span class=&#34;notification-message&#34; aria-describedby=&#34;fridayw12_1b-problem-title&#34;&gt;Answers are displayed within the problem &lt;/span&gt; &lt;div class=&#34;notification-btn-wrapper&#34;&gt; &lt;button type=&#34;button&#34; class=&#34;btn btn-default btn-small notification-btn review-btn sr&#34;&gt;Review&lt;/button&gt; &lt;/div&gt; &lt;/div&gt; &lt;/div&gt; " data-graded="False"> <p class="loading-spinner"> <i class="fa fa-spinner fa-pulse fa-2x fa-fw"></i> <span class="sr">Loading&hellip;</span> </p> </div> </div> </div> <div class="vert vert-2" data-id="block-v1:MITx+8.02.3x+1T2019+type@problem+block@fridayw12_1c"> <div class="xblock xblock-public_view xblock-public_view-problem xmodule_display xmodule_ProblemBlock" data-request-token="04a14dec05d811f0a17b0affe2bbc7c1" data-usage-id="block-v1:MITx+8.02.3x+1T2019+type@problem+block@fridayw12_1c" data-init="XBlockToXModuleShim" data-block-type="problem" data-runtime-class="LmsRuntime" data-course-id="course-v1:MITx+8.02.3x+1T2019" data-has-score="True" data-graded="False" data-runtime-version="1"> <script type="json/xblock-args" class="xblock-json-init-args"> {"xmodule-type": "Problem"} </script> <div id="problem_fridayw12_1c" class="problems-wrapper" role="group" aria-labelledby="fridayw12_1c-problem-title" data-problem-id="block-v1:MITx+8.02.3x+1T2019+type@problem+block@fridayw12_1c" data-url="/courses/course-v1:MITx+8.02.3x+1T2019/xblock/block-v1:MITx+8.02.3x+1T2019+type@problem+block@fridayw12_1c/handler/xmodule_handler" data-problem-score="0" data-problem-total-possible="0" data-attempts-used="0" data-content=" &lt;h3 class=&#34;hd hd-3 problem-header&#34; id=&#34;fridayw12_1c-problem-title&#34; aria-describedby=&#34;block-v1:MITx+8.02.3x+1T2019+type@problem+block@fridayw12_1c-problem-progress&#34; tabindex=&#34;-1&#34;&gt; Current Amplitude &lt;/h3&gt; &lt;div class=&#34;problem-progress&#34; id=&#34;block-v1:MITx+8.02.3x+1T2019+type@problem+block@fridayw12_1c-problem-progress&#34;&gt;&lt;/div&gt; &lt;div class=&#34;problem&#34;&gt; &lt;div&gt; &lt;p&gt;&lt;b class=&#34;bfseries&#34;&gt;(Part c)&lt;/b&gt; What is the amplitude of the current? Express your answer using R, C, V_0 for [mathjaxinline]V_{in,0}[/mathjaxinline], and omega for [mathjaxinline]\omega[/mathjaxinline] as needed. &lt;/p&gt; &lt;p&gt; &lt;p style=&#34;display:inline&#34;&gt;[mathjaxinline]I_0 =[/mathjaxinline] &lt;/p&gt; &lt;div class=&#34;inline&#34; tabindex=&#34;-1&#34; aria-label=&#34;Question 1&#34; role=&#34;group&#34;&gt;&lt;div id=&#34;inputtype_fridayw12_1c_2_1&#34; class=&#34;text-input-dynamath capa_inputtype inline textline&#34;&gt; &lt;div class=&#34;unanswered inline&#34;&gt; &lt;input type=&#34;text&#34; name=&#34;input_fridayw12_1c_2_1&#34; id=&#34;input_fridayw12_1c_2_1&#34; aria-describedby=&#34;status_fridayw12_1c_2_1&#34; value=&#34;&#34; class=&#34;math&#34; size=&#34;60&#34;/&gt; &lt;span class=&#34;trailing_text&#34; id=&#34;trailing_text_fridayw12_1c_2_1&#34;/&gt; &lt;span class=&#34;status unanswered&#34; id=&#34;status_fridayw12_1c_2_1&#34; data-tooltip=&#34;Not yet answered.&#34;&gt; &lt;span class=&#34;sr&#34;&gt;unanswered&lt;/span&gt;&lt;span class=&#34;status-icon&#34; aria-hidden=&#34;true&#34;/&gt; &lt;/span&gt; &lt;p id=&#34;answer_fridayw12_1c_2_1&#34; class=&#34;answer&#34;/&gt; &lt;div id=&#34;display_fridayw12_1c_2_1&#34; class=&#34;equation&#34;&gt;`{::}`&lt;/div&gt; &lt;textarea style=&#34;display:none&#34; id=&#34;input_fridayw12_1c_2_1_dynamath&#34; name=&#34;input_fridayw12_1c_2_1_dynamath&#34;/&gt; &lt;/div&gt; &lt;/div&gt;&lt;/div&gt; &lt;/p&gt; &lt;/div&gt; &lt;div class=&#34;action&#34;&gt; &lt;input type=&#34;hidden&#34; name=&#34;problem_id&#34; value=&#34;Current Amplitude&#34; /&gt; &lt;div class=&#34;submit-attempt-container&#34;&gt; &lt;button type=&#34;button&#34; class=&#34;submit btn-brand&#34; data-submitting=&#34;Submitting&#34; data-value=&#34;Submit&#34; data-should-enable-submit-button=&#34;True&#34; aria-describedby=&#34;submission_feedback_fridayw12_1c&#34; &gt; &lt;span class=&#34;submit-label&#34;&gt;Submit&lt;/span&gt; &lt;/button&gt; &lt;div class=&#34;submission-feedback&#34; id=&#34;submission_feedback_fridayw12_1c&#34;&gt; &lt;span class=&#34;sr&#34;&gt;Some problems have options such as save, reset, hints, or show answer. These options follow the Submit button.&lt;/span&gt; &lt;/div&gt; &lt;/div&gt; &lt;div class=&#34;problem-action-buttons-wrapper&#34;&gt; &lt;/div&gt; &lt;/div&gt; &lt;div class=&#34;notification warning notification-gentle-alert is-hidden&#34; tabindex=&#34;-1&#34;&gt; &lt;span class=&#34;icon fa fa-exclamation-circle&#34; aria-hidden=&#34;true&#34;&gt;&lt;/span&gt; &lt;span class=&#34;notification-message&#34; aria-describedby=&#34;fridayw12_1c-problem-title&#34;&gt; &lt;/span&gt; &lt;div class=&#34;notification-btn-wrapper&#34;&gt; &lt;button type=&#34;button&#34; class=&#34;btn btn-default btn-small notification-btn review-btn sr&#34;&gt;Review&lt;/button&gt; &lt;/div&gt; &lt;/div&gt; &lt;div class=&#34;notification warning notification-save is-hidden&#34; tabindex=&#34;-1&#34;&gt; &lt;span class=&#34;icon fa fa-save&#34; aria-hidden=&#34;true&#34;&gt;&lt;/span&gt; &lt;span class=&#34;notification-message&#34; aria-describedby=&#34;fridayw12_1c-problem-title&#34;&gt;None &lt;/span&gt; &lt;div class=&#34;notification-btn-wrapper&#34;&gt; &lt;button type=&#34;button&#34; class=&#34;btn btn-default btn-small notification-btn review-btn sr&#34;&gt;Review&lt;/button&gt; &lt;/div&gt; &lt;/div&gt; &lt;div class=&#34;notification general notification-show-answer is-hidden&#34; tabindex=&#34;-1&#34;&gt; &lt;span class=&#34;icon fa fa-info-circle&#34; aria-hidden=&#34;true&#34;&gt;&lt;/span&gt; &lt;span class=&#34;notification-message&#34; aria-describedby=&#34;fridayw12_1c-problem-title&#34;&gt;Answers are displayed within the problem &lt;/span&gt; &lt;div class=&#34;notification-btn-wrapper&#34;&gt; &lt;button type=&#34;button&#34; class=&#34;btn btn-default btn-small notification-btn review-btn sr&#34;&gt;Review&lt;/button&gt; &lt;/div&gt; &lt;/div&gt; &lt;/div&gt; " data-graded="False"> <p class="loading-spinner"> <i class="fa fa-spinner fa-pulse fa-2x fa-fw"></i> <span class="sr">Loading&hellip;</span> </p> </div> </div> </div> <div class="vert vert-3" data-id="block-v1:MITx+8.02.3x+1T2019+type@problem+block@fridayw12_1d"> <div class="xblock xblock-public_view xblock-public_view-problem xmodule_display xmodule_ProblemBlock" data-request-token="04a14dec05d811f0a17b0affe2bbc7c1" data-usage-id="block-v1:MITx+8.02.3x+1T2019+type@problem+block@fridayw12_1d" data-init="XBlockToXModuleShim" data-block-type="problem" data-runtime-class="LmsRuntime" data-course-id="course-v1:MITx+8.02.3x+1T2019" data-has-score="True" data-graded="False" data-runtime-version="1"> <script type="json/xblock-args" class="xblock-json-init-args"> {"xmodule-type": "Problem"} </script> <div id="problem_fridayw12_1d" class="problems-wrapper" role="group" aria-labelledby="fridayw12_1d-problem-title" data-problem-id="block-v1:MITx+8.02.3x+1T2019+type@problem+block@fridayw12_1d" data-url="/courses/course-v1:MITx+8.02.3x+1T2019/xblock/block-v1:MITx+8.02.3x+1T2019+type@problem+block@fridayw12_1d/handler/xmodule_handler" data-problem-score="0" data-problem-total-possible="0" data-attempts-used="0" data-content=" &lt;h3 class=&#34;hd hd-3 problem-header&#34; id=&#34;fridayw12_1d-problem-title&#34; aria-describedby=&#34;block-v1:MITx+8.02.3x+1T2019+type@problem+block@fridayw12_1d-problem-progress&#34; tabindex=&#34;-1&#34;&gt; Current Phase &lt;/h3&gt; &lt;div class=&#34;problem-progress&#34; id=&#34;block-v1:MITx+8.02.3x+1T2019+type@problem+block@fridayw12_1d-problem-progress&#34;&gt;&lt;/div&gt; &lt;div class=&#34;problem&#34;&gt; &lt;div&gt; &lt;p&gt;&lt;b class=&#34;bfseries&#34;&gt;(Part d)&lt;/b&gt; What is the phase constant for the current? Express your answer using R, C, V_0 for [mathjaxinline]V_{in,0}[/mathjaxinline], and omega for [mathjaxinline]\omega[/mathjaxinline] as needed. &lt;/p&gt; &lt;p&gt; &lt;p style=&#34;display:inline&#34;&gt;[mathjaxinline]\phi =[/mathjaxinline] &lt;/p&gt; &lt;div class=&#34;inline&#34; tabindex=&#34;-1&#34; aria-label=&#34;Question 1&#34; role=&#34;group&#34;&gt;&lt;div id=&#34;inputtype_fridayw12_1d_2_1&#34; class=&#34;text-input-dynamath capa_inputtype inline textline&#34;&gt; &lt;div class=&#34;unanswered inline&#34;&gt; &lt;input type=&#34;text&#34; name=&#34;input_fridayw12_1d_2_1&#34; id=&#34;input_fridayw12_1d_2_1&#34; aria-describedby=&#34;status_fridayw12_1d_2_1&#34; value=&#34;&#34; class=&#34;math&#34; size=&#34;60&#34;/&gt; &lt;span class=&#34;trailing_text&#34; id=&#34;trailing_text_fridayw12_1d_2_1&#34;/&gt; &lt;span class=&#34;status unanswered&#34; id=&#34;status_fridayw12_1d_2_1&#34; data-tooltip=&#34;Not yet answered.&#34;&gt; &lt;span class=&#34;sr&#34;&gt;unanswered&lt;/span&gt;&lt;span class=&#34;status-icon&#34; aria-hidden=&#34;true&#34;/&gt; &lt;/span&gt; &lt;p id=&#34;answer_fridayw12_1d_2_1&#34; class=&#34;answer&#34;/&gt; &lt;div id=&#34;display_fridayw12_1d_2_1&#34; class=&#34;equation&#34;&gt;`{::}`&lt;/div&gt; &lt;textarea style=&#34;display:none&#34; id=&#34;input_fridayw12_1d_2_1_dynamath&#34; name=&#34;input_fridayw12_1d_2_1_dynamath&#34;/&gt; &lt;/div&gt; &lt;/div&gt;&lt;/div&gt; &lt;/p&gt; &lt;/div&gt; &lt;div class=&#34;action&#34;&gt; &lt;input type=&#34;hidden&#34; name=&#34;problem_id&#34; value=&#34;Current Phase&#34; /&gt; &lt;div class=&#34;submit-attempt-container&#34;&gt; &lt;button type=&#34;button&#34; class=&#34;submit btn-brand&#34; data-submitting=&#34;Submitting&#34; data-value=&#34;Submit&#34; data-should-enable-submit-button=&#34;True&#34; aria-describedby=&#34;submission_feedback_fridayw12_1d&#34; &gt; &lt;span class=&#34;submit-label&#34;&gt;Submit&lt;/span&gt; &lt;/button&gt; &lt;div class=&#34;submission-feedback&#34; id=&#34;submission_feedback_fridayw12_1d&#34;&gt; &lt;span class=&#34;sr&#34;&gt;Some problems have options such as save, reset, hints, or show answer. These options follow the Submit button.&lt;/span&gt; &lt;/div&gt; &lt;/div&gt; &lt;div class=&#34;problem-action-buttons-wrapper&#34;&gt; &lt;/div&gt; &lt;/div&gt; &lt;div class=&#34;notification warning notification-gentle-alert is-hidden&#34; tabindex=&#34;-1&#34;&gt; &lt;span class=&#34;icon fa fa-exclamation-circle&#34; aria-hidden=&#34;true&#34;&gt;&lt;/span&gt; &lt;span class=&#34;notification-message&#34; aria-describedby=&#34;fridayw12_1d-problem-title&#34;&gt; &lt;/span&gt; &lt;div class=&#34;notification-btn-wrapper&#34;&gt; &lt;button type=&#34;button&#34; class=&#34;btn btn-default btn-small notification-btn review-btn sr&#34;&gt;Review&lt;/button&gt; &lt;/div&gt; &lt;/div&gt; &lt;div class=&#34;notification warning notification-save is-hidden&#34; tabindex=&#34;-1&#34;&gt; &lt;span class=&#34;icon fa fa-save&#34; aria-hidden=&#34;true&#34;&gt;&lt;/span&gt; &lt;span class=&#34;notification-message&#34; aria-describedby=&#34;fridayw12_1d-problem-title&#34;&gt;None &lt;/span&gt; &lt;div class=&#34;notification-btn-wrapper&#34;&gt; &lt;button type=&#34;button&#34; class=&#34;btn btn-default btn-small notification-btn review-btn sr&#34;&gt;Review&lt;/button&gt; &lt;/div&gt; &lt;/div&gt; &lt;div class=&#34;notification general notification-show-answer is-hidden&#34; tabindex=&#34;-1&#34;&gt; &lt;span class=&#34;icon fa fa-info-circle&#34; aria-hidden=&#34;true&#34;&gt;&lt;/span&gt; &lt;span class=&#34;notification-message&#34; aria-describedby=&#34;fridayw12_1d-problem-title&#34;&gt;Answers are displayed within the problem &lt;/span&gt; &lt;div class=&#34;notification-btn-wrapper&#34;&gt; &lt;button type=&#34;button&#34; class=&#34;btn btn-default btn-small notification-btn review-btn sr&#34;&gt;Review&lt;/button&gt; &lt;/div&gt; &lt;/div&gt; &lt;/div&gt; " data-graded="False"> <p class="loading-spinner"> <i class="fa fa-spinner fa-pulse fa-2x fa-fw"></i> <span class="sr">Loading&hellip;</span> </p> </div> </div> </div> <div class="vert vert-4" data-id="block-v1:MITx+8.02.3x+1T2019+type@problem+block@fridayw12_1e"> <div class="xblock xblock-public_view xblock-public_view-problem xmodule_display xmodule_ProblemBlock" data-request-token="04a14dec05d811f0a17b0affe2bbc7c1" data-usage-id="block-v1:MITx+8.02.3x+1T2019+type@problem+block@fridayw12_1e" data-init="XBlockToXModuleShim" data-block-type="problem" data-runtime-class="LmsRuntime" data-course-id="course-v1:MITx+8.02.3x+1T2019" data-has-score="True" data-graded="False" data-runtime-version="1"> <script type="json/xblock-args" class="xblock-json-init-args"> {"xmodule-type": "Problem"} </script> <div id="problem_fridayw12_1e" class="problems-wrapper" role="group" aria-labelledby="fridayw12_1e-problem-title" data-problem-id="block-v1:MITx+8.02.3x+1T2019+type@problem+block@fridayw12_1e" data-url="/courses/course-v1:MITx+8.02.3x+1T2019/xblock/block-v1:MITx+8.02.3x+1T2019+type@problem+block@fridayw12_1e/handler/xmodule_handler" data-problem-score="0" data-problem-total-possible="0" data-attempts-used="0" data-content=" &lt;h3 class=&#34;hd hd-3 problem-header&#34; id=&#34;fridayw12_1e-problem-title&#34; aria-describedby=&#34;block-v1:MITx+8.02.3x+1T2019+type@problem+block@fridayw12_1e-problem-progress&#34; tabindex=&#34;-1&#34;&gt; Capacitor Voltage Time Dependence &lt;/h3&gt; &lt;div class=&#34;problem-progress&#34; id=&#34;block-v1:MITx+8.02.3x+1T2019+type@problem+block@fridayw12_1e-problem-progress&#34;&gt;&lt;/div&gt; &lt;div class=&#34;problem&#34;&gt; &lt;div&gt; &lt;p&gt;&lt;b class=&#34;bfseries&#34;&gt;(Part e)&lt;/b&gt; What is the voltage across the capacitor as a function of time? Please use [mathjaxinline]I_0[/mathjaxinline] and [mathjaxinline]\phi[/mathjaxinline], and do not expand them. Express your answer using C, t, I_0 for [mathjaxinline]I_0[/mathjaxinline], omega for [mathjaxinline]\omega[/mathjaxinline], and phi for [mathjaxinline]\phi[/mathjaxinline]. &lt;/p&gt; &lt;p&gt; &lt;p style=&#34;display:inline&#34;&gt;[mathjaxinline]V_{out} =[/mathjaxinline] &lt;/p&gt; &lt;div class=&#34;inline&#34; tabindex=&#34;-1&#34; aria-label=&#34;Question 1&#34; role=&#34;group&#34;&gt;&lt;div id=&#34;inputtype_fridayw12_1e_2_1&#34; class=&#34;text-input-dynamath capa_inputtype inline textline&#34;&gt; &lt;div class=&#34;unanswered inline&#34;&gt; &lt;input type=&#34;text&#34; name=&#34;input_fridayw12_1e_2_1&#34; id=&#34;input_fridayw12_1e_2_1&#34; aria-describedby=&#34;status_fridayw12_1e_2_1&#34; value=&#34;&#34; class=&#34;math&#34; size=&#34;60&#34;/&gt; &lt;span class=&#34;trailing_text&#34; id=&#34;trailing_text_fridayw12_1e_2_1&#34;/&gt; &lt;span class=&#34;status unanswered&#34; id=&#34;status_fridayw12_1e_2_1&#34; data-tooltip=&#34;Not yet answered.&#34;&gt; &lt;span class=&#34;sr&#34;&gt;unanswered&lt;/span&gt;&lt;span class=&#34;status-icon&#34; aria-hidden=&#34;true&#34;/&gt; &lt;/span&gt; &lt;p id=&#34;answer_fridayw12_1e_2_1&#34; class=&#34;answer&#34;/&gt; &lt;div id=&#34;display_fridayw12_1e_2_1&#34; class=&#34;equation&#34;&gt;`{::}`&lt;/div&gt; &lt;textarea style=&#34;display:none&#34; id=&#34;input_fridayw12_1e_2_1_dynamath&#34; name=&#34;input_fridayw12_1e_2_1_dynamath&#34;/&gt; &lt;/div&gt; &lt;/div&gt;&lt;/div&gt; &lt;/p&gt; &lt;/div&gt; &lt;div class=&#34;action&#34;&gt; &lt;input type=&#34;hidden&#34; name=&#34;problem_id&#34; value=&#34;Capacitor Voltage Time Dependence&#34; /&gt; &lt;div class=&#34;submit-attempt-container&#34;&gt; &lt;button type=&#34;button&#34; class=&#34;submit btn-brand&#34; data-submitting=&#34;Submitting&#34; data-value=&#34;Submit&#34; data-should-enable-submit-button=&#34;True&#34; aria-describedby=&#34;submission_feedback_fridayw12_1e&#34; &gt; &lt;span class=&#34;submit-label&#34;&gt;Submit&lt;/span&gt; &lt;/button&gt; &lt;div class=&#34;submission-feedback&#34; id=&#34;submission_feedback_fridayw12_1e&#34;&gt; &lt;span class=&#34;sr&#34;&gt;Some problems have options such as save, reset, hints, or show answer. These options follow the Submit button.&lt;/span&gt; &lt;/div&gt; &lt;/div&gt; &lt;div class=&#34;problem-action-buttons-wrapper&#34;&gt; &lt;/div&gt; &lt;/div&gt; &lt;div class=&#34;notification warning notification-gentle-alert is-hidden&#34; tabindex=&#34;-1&#34;&gt; &lt;span class=&#34;icon fa fa-exclamation-circle&#34; aria-hidden=&#34;true&#34;&gt;&lt;/span&gt; &lt;span class=&#34;notification-message&#34; aria-describedby=&#34;fridayw12_1e-problem-title&#34;&gt; &lt;/span&gt; &lt;div class=&#34;notification-btn-wrapper&#34;&gt; &lt;button type=&#34;button&#34; class=&#34;btn btn-default btn-small notification-btn review-btn sr&#34;&gt;Review&lt;/button&gt; &lt;/div&gt; &lt;/div&gt; &lt;div class=&#34;notification warning notification-save is-hidden&#34; tabindex=&#34;-1&#34;&gt; &lt;span class=&#34;icon fa fa-save&#34; aria-hidden=&#34;true&#34;&gt;&lt;/span&gt; &lt;span class=&#34;notification-message&#34; aria-describedby=&#34;fridayw12_1e-problem-title&#34;&gt;None &lt;/span&gt; &lt;div class=&#34;notification-btn-wrapper&#34;&gt; &lt;button type=&#34;button&#34; class=&#34;btn btn-default btn-small notification-btn review-btn sr&#34;&gt;Review&lt;/button&gt; &lt;/div&gt; &lt;/div&gt; &lt;div class=&#34;notification general notification-show-answer is-hidden&#34; tabindex=&#34;-1&#34;&gt; &lt;span class=&#34;icon fa fa-info-circle&#34; aria-hidden=&#34;true&#34;&gt;&lt;/span&gt; &lt;span class=&#34;notification-message&#34; aria-describedby=&#34;fridayw12_1e-problem-title&#34;&gt;Answers are displayed within the problem &lt;/span&gt; &lt;div class=&#34;notification-btn-wrapper&#34;&gt; &lt;button type=&#34;button&#34; class=&#34;btn btn-default btn-small notification-btn review-btn sr&#34;&gt;Review&lt;/button&gt; &lt;/div&gt; &lt;/div&gt; &lt;/div&gt; " data-graded="False"> <p class="loading-spinner"> <i class="fa fa-spinner fa-pulse fa-2x fa-fw"></i> <span class="sr">Loading&hellip;</span> </p> </div> </div> </div> <div class="vert vert-5" data-id="block-v1:MITx+8.02.3x+1T2019+type@problem+block@fridayw12_1f"> <div class="xblock xblock-public_view xblock-public_view-problem xmodule_display xmodule_ProblemBlock" data-request-token="04a14dec05d811f0a17b0affe2bbc7c1" data-usage-id="block-v1:MITx+8.02.3x+1T2019+type@problem+block@fridayw12_1f" data-init="XBlockToXModuleShim" data-block-type="problem" data-runtime-class="LmsRuntime" data-course-id="course-v1:MITx+8.02.3x+1T2019" data-has-score="True" data-graded="False" data-runtime-version="1"> <script type="json/xblock-args" class="xblock-json-init-args"> {"xmodule-type": "Problem"} </script> <div id="problem_fridayw12_1f" class="problems-wrapper" role="group" aria-labelledby="fridayw12_1f-problem-title" data-problem-id="block-v1:MITx+8.02.3x+1T2019+type@problem+block@fridayw12_1f" data-url="/courses/course-v1:MITx+8.02.3x+1T2019/xblock/block-v1:MITx+8.02.3x+1T2019+type@problem+block@fridayw12_1f/handler/xmodule_handler" data-problem-score="0" data-problem-total-possible="0" data-attempts-used="0" data-content=" &lt;h3 class=&#34;hd hd-3 problem-header&#34; id=&#34;fridayw12_1f-problem-title&#34; aria-describedby=&#34;block-v1:MITx+8.02.3x+1T2019+type@problem+block@fridayw12_1f-problem-progress&#34; tabindex=&#34;-1&#34;&gt; Capacitor Voltage Amplitude &lt;/h3&gt; &lt;div class=&#34;problem-progress&#34; id=&#34;block-v1:MITx+8.02.3x+1T2019+type@problem+block@fridayw12_1f-problem-progress&#34;&gt;&lt;/div&gt; &lt;div class=&#34;problem&#34;&gt; &lt;div&gt; &lt;p&gt;&lt;b class=&#34;bfseries&#34;&gt;(Part f)&lt;/b&gt; What is the amplitude of the voltage across the capacitor? Express your answer using R, C, V_0 for [mathjaxinline]V_{in,0}[/mathjaxinline], and omega for [mathjaxinline]\omega[/mathjaxinline] as needed. &lt;/p&gt; &lt;p&gt; &lt;p style=&#34;display:inline&#34;&gt;[mathjaxinline]V_{out,0} =[/mathjaxinline] &lt;/p&gt; &lt;div class=&#34;inline&#34; tabindex=&#34;-1&#34; aria-label=&#34;Question 1&#34; role=&#34;group&#34;&gt;&lt;div id=&#34;inputtype_fridayw12_1f_2_1&#34; class=&#34;text-input-dynamath capa_inputtype inline textline&#34;&gt; &lt;div class=&#34;unanswered inline&#34;&gt; &lt;input type=&#34;text&#34; name=&#34;input_fridayw12_1f_2_1&#34; id=&#34;input_fridayw12_1f_2_1&#34; aria-describedby=&#34;status_fridayw12_1f_2_1&#34; value=&#34;&#34; class=&#34;math&#34; size=&#34;60&#34;/&gt; &lt;span class=&#34;trailing_text&#34; id=&#34;trailing_text_fridayw12_1f_2_1&#34;/&gt; &lt;span class=&#34;status unanswered&#34; id=&#34;status_fridayw12_1f_2_1&#34; data-tooltip=&#34;Not yet answered.&#34;&gt; &lt;span class=&#34;sr&#34;&gt;unanswered&lt;/span&gt;&lt;span class=&#34;status-icon&#34; aria-hidden=&#34;true&#34;/&gt; &lt;/span&gt; &lt;p id=&#34;answer_fridayw12_1f_2_1&#34; class=&#34;answer&#34;/&gt; &lt;div id=&#34;display_fridayw12_1f_2_1&#34; class=&#34;equation&#34;&gt;`{::}`&lt;/div&gt; &lt;textarea style=&#34;display:none&#34; id=&#34;input_fridayw12_1f_2_1_dynamath&#34; name=&#34;input_fridayw12_1f_2_1_dynamath&#34;/&gt; &lt;/div&gt; &lt;/div&gt;&lt;/div&gt; &lt;/p&gt; &lt;/div&gt; &lt;div class=&#34;action&#34;&gt; &lt;input type=&#34;hidden&#34; name=&#34;problem_id&#34; value=&#34;Capacitor Voltage Amplitude&#34; /&gt; &lt;div class=&#34;submit-attempt-container&#34;&gt; &lt;button type=&#34;button&#34; class=&#34;submit btn-brand&#34; data-submitting=&#34;Submitting&#34; data-value=&#34;Submit&#34; data-should-enable-submit-button=&#34;True&#34; aria-describedby=&#34;submission_feedback_fridayw12_1f&#34; &gt; &lt;span class=&#34;submit-label&#34;&gt;Submit&lt;/span&gt; &lt;/button&gt; &lt;div class=&#34;submission-feedback&#34; id=&#34;submission_feedback_fridayw12_1f&#34;&gt; &lt;span class=&#34;sr&#34;&gt;Some problems have options such as save, reset, hints, or show answer. These options follow the Submit button.&lt;/span&gt; &lt;/div&gt; &lt;/div&gt; &lt;div class=&#34;problem-action-buttons-wrapper&#34;&gt; &lt;/div&gt; &lt;/div&gt; &lt;div class=&#34;notification warning notification-gentle-alert is-hidden&#34; tabindex=&#34;-1&#34;&gt; &lt;span class=&#34;icon fa fa-exclamation-circle&#34; aria-hidden=&#34;true&#34;&gt;&lt;/span&gt; &lt;span class=&#34;notification-message&#34; aria-describedby=&#34;fridayw12_1f-problem-title&#34;&gt; &lt;/span&gt; &lt;div class=&#34;notification-btn-wrapper&#34;&gt; &lt;button type=&#34;button&#34; class=&#34;btn btn-default btn-small notification-btn review-btn sr&#34;&gt;Review&lt;/button&gt; &lt;/div&gt; &lt;/div&gt; &lt;div class=&#34;notification warning notification-save is-hidden&#34; tabindex=&#34;-1&#34;&gt; &lt;span class=&#34;icon fa fa-save&#34; aria-hidden=&#34;true&#34;&gt;&lt;/span&gt; &lt;span class=&#34;notification-message&#34; aria-describedby=&#34;fridayw12_1f-problem-title&#34;&gt;None &lt;/span&gt; &lt;div class=&#34;notification-btn-wrapper&#34;&gt; &lt;button type=&#34;button&#34; class=&#34;btn btn-default btn-small notification-btn review-btn sr&#34;&gt;Review&lt;/button&gt; &lt;/div&gt; &lt;/div&gt; &lt;div class=&#34;notification general notification-show-answer is-hidden&#34; tabindex=&#34;-1&#34;&gt; &lt;span class=&#34;icon fa fa-info-circle&#34; aria-hidden=&#34;true&#34;&gt;&lt;/span&gt; &lt;span class=&#34;notification-message&#34; aria-describedby=&#34;fridayw12_1f-problem-title&#34;&gt;Answers are displayed within the problem &lt;/span&gt; &lt;div class=&#34;notification-btn-wrapper&#34;&gt; &lt;button type=&#34;button&#34; class=&#34;btn btn-default btn-small notification-btn review-btn sr&#34;&gt;Review&lt;/button&gt; &lt;/div&gt; &lt;/div&gt; &lt;/div&gt; " data-graded="False"> <p class="loading-spinner"> <i class="fa fa-spinner fa-pulse fa-2x fa-fw"></i> <span class="sr">Loading&hellip;</span> </p> </div> </div> </div> <div class="vert vert-6" data-id="block-v1:MITx+8.02.3x+1T2019+type@problem+block@fridayw12_1g"> <div class="xblock xblock-public_view xblock-public_view-problem xmodule_display xmodule_ProblemBlock" data-request-token="04a14dec05d811f0a17b0affe2bbc7c1" data-usage-id="block-v1:MITx+8.02.3x+1T2019+type@problem+block@fridayw12_1g" data-init="XBlockToXModuleShim" data-block-type="problem" data-runtime-class="LmsRuntime" data-course-id="course-v1:MITx+8.02.3x+1T2019" data-has-score="True" data-graded="False" data-runtime-version="1"> <script type="json/xblock-args" class="xblock-json-init-args"> {"xmodule-type": "Problem"} </script> <div id="problem_fridayw12_1g" class="problems-wrapper" role="group" aria-labelledby="fridayw12_1g-problem-title" data-problem-id="block-v1:MITx+8.02.3x+1T2019+type@problem+block@fridayw12_1g" data-url="/courses/course-v1:MITx+8.02.3x+1T2019/xblock/block-v1:MITx+8.02.3x+1T2019+type@problem+block@fridayw12_1g/handler/xmodule_handler" data-problem-score="0" data-problem-total-possible="0" data-attempts-used="0" data-content=" &lt;h3 class=&#34;hd hd-3 problem-header&#34; id=&#34;fridayw12_1g-problem-title&#34; aria-describedby=&#34;block-v1:MITx+8.02.3x+1T2019+type@problem+block@fridayw12_1g-problem-progress&#34; tabindex=&#34;-1&#34;&gt; Output/Input Voltage Ratio &lt;/h3&gt; &lt;div class=&#34;problem-progress&#34; id=&#34;block-v1:MITx+8.02.3x+1T2019+type@problem+block@fridayw12_1g-problem-progress&#34;&gt;&lt;/div&gt; &lt;div class=&#34;problem&#34;&gt; &lt;div&gt; &lt;p&gt;&lt;b class=&#34;bfseries&#34;&gt;(Part g)&lt;/b&gt; What is the ratio of the amplitude of the voltage across the capacitor to the amplitude of the AC voltage source, [mathjaxinline]V_{out,0} / V_{in,0}[/mathjaxinline]? Express your answer using R, C and omega for [mathjaxinline]\omega[/mathjaxinline]. &lt;/p&gt; &lt;p&gt; &lt;p style=&#34;display:inline&#34;&gt;[mathjaxinline]V_{out,0} / V_{in,0} =[/mathjaxinline] &lt;/p&gt; &lt;div class=&#34;inline&#34; tabindex=&#34;-1&#34; aria-label=&#34;Question 1&#34; role=&#34;group&#34;&gt;&lt;div id=&#34;inputtype_fridayw12_1g_2_1&#34; class=&#34;text-input-dynamath capa_inputtype inline textline&#34;&gt; &lt;div class=&#34;unanswered inline&#34;&gt; &lt;input type=&#34;text&#34; name=&#34;input_fridayw12_1g_2_1&#34; id=&#34;input_fridayw12_1g_2_1&#34; aria-describedby=&#34;status_fridayw12_1g_2_1&#34; value=&#34;&#34; class=&#34;math&#34; size=&#34;60&#34;/&gt; &lt;span class=&#34;trailing_text&#34; id=&#34;trailing_text_fridayw12_1g_2_1&#34;/&gt; &lt;span class=&#34;status unanswered&#34; id=&#34;status_fridayw12_1g_2_1&#34; data-tooltip=&#34;Not yet answered.&#34;&gt; &lt;span class=&#34;sr&#34;&gt;unanswered&lt;/span&gt;&lt;span class=&#34;status-icon&#34; aria-hidden=&#34;true&#34;/&gt; &lt;/span&gt; &lt;p id=&#34;answer_fridayw12_1g_2_1&#34; class=&#34;answer&#34;/&gt; &lt;div id=&#34;display_fridayw12_1g_2_1&#34; class=&#34;equation&#34;&gt;`{::}`&lt;/div&gt; &lt;textarea style=&#34;display:none&#34; id=&#34;input_fridayw12_1g_2_1_dynamath&#34; name=&#34;input_fridayw12_1g_2_1_dynamath&#34;/&gt; &lt;/div&gt; &lt;/div&gt;&lt;/div&gt; &lt;/p&gt; &lt;/div&gt; &lt;div class=&#34;action&#34;&gt; &lt;input type=&#34;hidden&#34; name=&#34;problem_id&#34; value=&#34;Output/Input Voltage Ratio&#34; /&gt; &lt;div class=&#34;submit-attempt-container&#34;&gt; &lt;button type=&#34;button&#34; class=&#34;submit btn-brand&#34; data-submitting=&#34;Submitting&#34; data-value=&#34;Submit&#34; data-should-enable-submit-button=&#34;True&#34; aria-describedby=&#34;submission_feedback_fridayw12_1g&#34; &gt; &lt;span class=&#34;submit-label&#34;&gt;Submit&lt;/span&gt; &lt;/button&gt; &lt;div class=&#34;submission-feedback&#34; id=&#34;submission_feedback_fridayw12_1g&#34;&gt; &lt;span class=&#34;sr&#34;&gt;Some problems have options such as save, reset, hints, or show answer. These options follow the Submit button.&lt;/span&gt; &lt;/div&gt; &lt;/div&gt; &lt;div class=&#34;problem-action-buttons-wrapper&#34;&gt; &lt;/div&gt; &lt;/div&gt; &lt;div class=&#34;notification warning notification-gentle-alert is-hidden&#34; tabindex=&#34;-1&#34;&gt; &lt;span class=&#34;icon fa fa-exclamation-circle&#34; aria-hidden=&#34;true&#34;&gt;&lt;/span&gt; &lt;span class=&#34;notification-message&#34; aria-describedby=&#34;fridayw12_1g-problem-title&#34;&gt; &lt;/span&gt; &lt;div class=&#34;notification-btn-wrapper&#34;&gt; &lt;button type=&#34;button&#34; class=&#34;btn btn-default btn-small notification-btn review-btn sr&#34;&gt;Review&lt;/button&gt; &lt;/div&gt; &lt;/div&gt; &lt;div class=&#34;notification warning notification-save is-hidden&#34; tabindex=&#34;-1&#34;&gt; &lt;span class=&#34;icon fa fa-save&#34; aria-hidden=&#34;true&#34;&gt;&lt;/span&gt; &lt;span class=&#34;notification-message&#34; aria-describedby=&#34;fridayw12_1g-problem-title&#34;&gt;None &lt;/span&gt; &lt;div class=&#34;notification-btn-wrapper&#34;&gt; &lt;button type=&#34;button&#34; class=&#34;btn btn-default btn-small notification-btn review-btn sr&#34;&gt;Review&lt;/button&gt; &lt;/div&gt; &lt;/div&gt; &lt;div class=&#34;notification general notification-show-answer is-hidden&#34; tabindex=&#34;-1&#34;&gt; &lt;span class=&#34;icon fa fa-info-circle&#34; aria-hidden=&#34;true&#34;&gt;&lt;/span&gt; &lt;span class=&#34;notification-message&#34; aria-describedby=&#34;fridayw12_1g-problem-title&#34;&gt;Answers are displayed within the problem &lt;/span&gt; &lt;div class=&#34;notification-btn-wrapper&#34;&gt; &lt;button type=&#34;button&#34; class=&#34;btn btn-default btn-small notification-btn review-btn sr&#34;&gt;Review&lt;/button&gt; &lt;/div&gt; &lt;/div&gt; &lt;/div&gt; " data-graded="False"> <p class="loading-spinner"> <i class="fa fa-spinner fa-pulse fa-2x fa-fw"></i> <span class="sr">Loading&hellip;</span> </p> </div> </div> </div> <div class="vert vert-7" data-id="block-v1:MITx+8.02.3x+1T2019+type@problem+block@fridayw12_1h"> <div class="xblock xblock-public_view xblock-public_view-problem xmodule_display xmodule_ProblemBlock" data-request-token="04a14dec05d811f0a17b0affe2bbc7c1" data-usage-id="block-v1:MITx+8.02.3x+1T2019+type@problem+block@fridayw12_1h" data-init="XBlockToXModuleShim" data-block-type="problem" data-runtime-class="LmsRuntime" data-course-id="course-v1:MITx+8.02.3x+1T2019" data-has-score="True" data-graded="False" data-runtime-version="1"> <script type="json/xblock-args" class="xblock-json-init-args"> {"xmodule-type": "Problem"} </script> <div id="problem_fridayw12_1h" class="problems-wrapper" role="group" aria-labelledby="fridayw12_1h-problem-title" data-problem-id="block-v1:MITx+8.02.3x+1T2019+type@problem+block@fridayw12_1h" data-url="/courses/course-v1:MITx+8.02.3x+1T2019/xblock/block-v1:MITx+8.02.3x+1T2019+type@problem+block@fridayw12_1h/handler/xmodule_handler" data-problem-score="0" data-problem-total-possible="0" data-attempts-used="0" data-content=" &lt;h3 class=&#34;hd hd-3 problem-header&#34; id=&#34;fridayw12_1h-problem-title&#34; aria-describedby=&#34;block-v1:MITx+8.02.3x+1T2019+type@problem+block@fridayw12_1h-problem-progress&#34; tabindex=&#34;-1&#34;&gt; Voltage Ratio at High Frequencies &lt;/h3&gt; &lt;div class=&#34;problem-progress&#34; id=&#34;block-v1:MITx+8.02.3x+1T2019+type@problem+block@fridayw12_1h-problem-progress&#34;&gt;&lt;/div&gt; &lt;div class=&#34;problem&#34;&gt; &lt;div&gt; &lt;p&gt;&lt;b class=&#34;bfseries&#34;&gt;(Part h)&lt;/b&gt; What is the limit of your answer to Part (g) when [mathjaxinline]\omega CR \gg 1[/mathjaxinline]? Expand your answer to the first non-zero term, do not include further terms. &lt;/p&gt; &lt;p&gt; &lt;p style=&#34;display:inline&#34;&gt;[mathjaxinline]V_{out,0} / V_{in,0} =[/mathjaxinline] &lt;/p&gt; &lt;div class=&#34;inline&#34; tabindex=&#34;-1&#34; aria-label=&#34;Question 1&#34; role=&#34;group&#34;&gt;&lt;div id=&#34;inputtype_fridayw12_1h_2_1&#34; class=&#34;text-input-dynamath capa_inputtype inline textline&#34;&gt; &lt;div class=&#34;unanswered inline&#34;&gt; &lt;input type=&#34;text&#34; name=&#34;input_fridayw12_1h_2_1&#34; id=&#34;input_fridayw12_1h_2_1&#34; aria-describedby=&#34;status_fridayw12_1h_2_1&#34; value=&#34;&#34; class=&#34;math&#34; size=&#34;60&#34;/&gt; &lt;span class=&#34;trailing_text&#34; id=&#34;trailing_text_fridayw12_1h_2_1&#34;/&gt; &lt;span class=&#34;status unanswered&#34; id=&#34;status_fridayw12_1h_2_1&#34; data-tooltip=&#34;Not yet answered.&#34;&gt; &lt;span class=&#34;sr&#34;&gt;unanswered&lt;/span&gt;&lt;span class=&#34;status-icon&#34; aria-hidden=&#34;true&#34;/&gt; &lt;/span&gt; &lt;p id=&#34;answer_fridayw12_1h_2_1&#34; class=&#34;answer&#34;/&gt; &lt;div id=&#34;display_fridayw12_1h_2_1&#34; class=&#34;equation&#34;&gt;`{::}`&lt;/div&gt; &lt;textarea style=&#34;display:none&#34; id=&#34;input_fridayw12_1h_2_1_dynamath&#34; name=&#34;input_fridayw12_1h_2_1_dynamath&#34;/&gt; &lt;/div&gt; &lt;/div&gt;&lt;/div&gt; &lt;/p&gt; &lt;/div&gt; &lt;div class=&#34;action&#34;&gt; &lt;input type=&#34;hidden&#34; name=&#34;problem_id&#34; value=&#34;Voltage Ratio at High Frequencies&#34; /&gt; &lt;div class=&#34;submit-attempt-container&#34;&gt; &lt;button type=&#34;button&#34; class=&#34;submit btn-brand&#34; data-submitting=&#34;Submitting&#34; data-value=&#34;Submit&#34; data-should-enable-submit-button=&#34;True&#34; aria-describedby=&#34;submission_feedback_fridayw12_1h&#34; &gt; &lt;span class=&#34;submit-label&#34;&gt;Submit&lt;/span&gt; &lt;/button&gt; &lt;div class=&#34;submission-feedback&#34; id=&#34;submission_feedback_fridayw12_1h&#34;&gt; &lt;span class=&#34;sr&#34;&gt;Some problems have options such as save, reset, hints, or show answer. These options follow the Submit button.&lt;/span&gt; &lt;/div&gt; &lt;/div&gt; &lt;div class=&#34;problem-action-buttons-wrapper&#34;&gt; &lt;/div&gt; &lt;/div&gt; &lt;div class=&#34;notification warning notification-gentle-alert is-hidden&#34; tabindex=&#34;-1&#34;&gt; &lt;span class=&#34;icon fa fa-exclamation-circle&#34; aria-hidden=&#34;true&#34;&gt;&lt;/span&gt; &lt;span class=&#34;notification-message&#34; aria-describedby=&#34;fridayw12_1h-problem-title&#34;&gt; &lt;/span&gt; &lt;div class=&#34;notification-btn-wrapper&#34;&gt; &lt;button type=&#34;button&#34; class=&#34;btn btn-default btn-small notification-btn review-btn sr&#34;&gt;Review&lt;/button&gt; &lt;/div&gt; &lt;/div&gt; &lt;div class=&#34;notification warning notification-save is-hidden&#34; tabindex=&#34;-1&#34;&gt; &lt;span class=&#34;icon fa fa-save&#34; aria-hidden=&#34;true&#34;&gt;&lt;/span&gt; &lt;span class=&#34;notification-message&#34; aria-describedby=&#34;fridayw12_1h-problem-title&#34;&gt;None &lt;/span&gt; &lt;div class=&#34;notification-btn-wrapper&#34;&gt; &lt;button type=&#34;button&#34; class=&#34;btn btn-default btn-small notification-btn review-btn sr&#34;&gt;Review&lt;/button&gt; &lt;/div&gt; &lt;/div&gt; &lt;div class=&#34;notification general notification-show-answer is-hidden&#34; tabindex=&#34;-1&#34;&gt; &lt;span class=&#34;icon fa fa-info-circle&#34; aria-hidden=&#34;true&#34;&gt;&lt;/span&gt; &lt;span class=&#34;notification-message&#34; aria-describedby=&#34;fridayw12_1h-problem-title&#34;&gt;Answers are displayed within the problem &lt;/span&gt; &lt;div class=&#34;notification-btn-wrapper&#34;&gt; &lt;button type=&#34;button&#34; class=&#34;btn btn-default btn-small notification-btn review-btn sr&#34;&gt;Review&lt;/button&gt; &lt;/div&gt; &lt;/div&gt; &lt;/div&gt; " data-graded="False"> <p class="loading-spinner"> <i class="fa fa-spinner fa-pulse fa-2x fa-fw"></i> <span class="sr">Loading&hellip;</span> </p> </div> </div> </div> <div class="vert vert-8" data-id="block-v1:MITx+8.02.3x+1T2019+type@problem+block@fridayw12_1i"> <div class="xblock xblock-public_view xblock-public_view-problem xmodule_display xmodule_ProblemBlock" data-request-token="04a14dec05d811f0a17b0affe2bbc7c1" data-usage-id="block-v1:MITx+8.02.3x+1T2019+type@problem+block@fridayw12_1i" data-init="XBlockToXModuleShim" data-block-type="problem" data-runtime-class="LmsRuntime" data-course-id="course-v1:MITx+8.02.3x+1T2019" data-has-score="True" data-graded="False" data-runtime-version="1"> <script type="json/xblock-args" class="xblock-json-init-args"> {"xmodule-type": "Problem"} </script> <div id="problem_fridayw12_1i" class="problems-wrapper" role="group" aria-labelledby="fridayw12_1i-problem-title" data-problem-id="block-v1:MITx+8.02.3x+1T2019+type@problem+block@fridayw12_1i" data-url="/courses/course-v1:MITx+8.02.3x+1T2019/xblock/block-v1:MITx+8.02.3x+1T2019+type@problem+block@fridayw12_1i/handler/xmodule_handler" data-problem-score="0" data-problem-total-possible="0" data-attempts-used="0" data-content=" &lt;h3 class=&#34;hd hd-3 problem-header&#34; id=&#34;fridayw12_1i-problem-title&#34; aria-describedby=&#34;block-v1:MITx+8.02.3x+1T2019+type@problem+block@fridayw12_1i-problem-progress&#34; tabindex=&#34;-1&#34;&gt; Low Pass Filter? &lt;/h3&gt; &lt;div class=&#34;problem-progress&#34; id=&#34;block-v1:MITx+8.02.3x+1T2019+type@problem+block@fridayw12_1i-problem-progress&#34;&gt;&lt;/div&gt; &lt;div class=&#34;problem&#34;&gt; &lt;div&gt; &lt;p&gt;&lt;b class=&#34;bfseries&#34;&gt;(Part i)&lt;/b&gt; Why is this type of filter called a low pass filter? &lt;/p&gt; &lt;p&gt; &lt;b class=&#34;bfseries&#34;&gt;This question cannot be checked online.&lt;/b&gt; &lt;/p&gt; &lt;/div&gt; &lt;div class=&#34;action&#34;&gt; &lt;input type=&#34;hidden&#34; name=&#34;problem_id&#34; value=&#34;Low Pass Filter?&#34; /&gt; &lt;div class=&#34;submit-attempt-container&#34;&gt; &lt;button type=&#34;button&#34; class=&#34;submit btn-brand&#34; data-submitting=&#34;Submitting&#34; data-value=&#34;Submit&#34; data-should-enable-submit-button=&#34;True&#34; aria-describedby=&#34;submission_feedback_fridayw12_1i&#34; &gt; &lt;span class=&#34;submit-label&#34;&gt;Submit&lt;/span&gt; &lt;/button&gt; &lt;div class=&#34;submission-feedback&#34; id=&#34;submission_feedback_fridayw12_1i&#34;&gt; &lt;span class=&#34;sr&#34;&gt;Some problems have options such as save, reset, hints, or show answer. These options follow the Submit button.&lt;/span&gt; &lt;/div&gt; &lt;/div&gt; &lt;div class=&#34;problem-action-buttons-wrapper&#34;&gt; &lt;/div&gt; &lt;/div&gt; &lt;div class=&#34;notification warning notification-gentle-alert is-hidden&#34; tabindex=&#34;-1&#34;&gt; &lt;span class=&#34;icon fa fa-exclamation-circle&#34; aria-hidden=&#34;true&#34;&gt;&lt;/span&gt; &lt;span class=&#34;notification-message&#34; aria-describedby=&#34;fridayw12_1i-problem-title&#34;&gt; &lt;/span&gt; &lt;div class=&#34;notification-btn-wrapper&#34;&gt; &lt;button type=&#34;button&#34; class=&#34;btn btn-default btn-small notification-btn review-btn sr&#34;&gt;Review&lt;/button&gt; &lt;/div&gt; &lt;/div&gt; &lt;div class=&#34;notification warning notification-save is-hidden&#34; tabindex=&#34;-1&#34;&gt; &lt;span class=&#34;icon fa fa-save&#34; aria-hidden=&#34;true&#34;&gt;&lt;/span&gt; &lt;span class=&#34;notification-message&#34; aria-describedby=&#34;fridayw12_1i-problem-title&#34;&gt;None &lt;/span&gt; &lt;div class=&#34;notification-btn-wrapper&#34;&gt; &lt;button type=&#34;button&#34; class=&#34;btn btn-default btn-small notification-btn review-btn sr&#34;&gt;Review&lt;/button&gt; &lt;/div&gt; &lt;/div&gt; &lt;div class=&#34;notification general notification-show-answer is-hidden&#34; tabindex=&#34;-1&#34;&gt; &lt;span class=&#34;icon fa fa-info-circle&#34; aria-hidden=&#34;true&#34;&gt;&lt;/span&gt; &lt;span class=&#34;notification-message&#34; aria-describedby=&#34;fridayw12_1i-problem-title&#34;&gt;Answers are displayed within the problem &lt;/span&gt; &lt;div class=&#34;notification-btn-wrapper&#34;&gt; &lt;button type=&#34;button&#34; class=&#34;btn btn-default btn-small notification-btn review-btn sr&#34;&gt;Review&lt;/button&gt; &lt;/div&gt; &lt;/div&gt; &lt;/div&gt; " data-graded="False"> <p class="loading-spinner"> <i class="fa fa-spinner fa-pulse fa-2x fa-fw"></i> <span class="sr">Loading&hellip;</span> </p> </div> </div> </div> <div class="vert vert-9" data-id="block-v1:MITx+8.02.3x+1T2019+type@video+block@W12PS02"> <div class="xblock xblock-public_view xblock-public_view-video xmodule_display xmodule_VideoBlock" data-request-token="04a14dec05d811f0a17b0affe2bbc7c1" data-usage-id="block-v1:MITx+8.02.3x+1T2019+type@video+block@W12PS02" data-init="XBlockToXModuleShim" data-block-type="video" data-runtime-class="LmsRuntime" data-course-id="course-v1:MITx+8.02.3x+1T2019" data-has-score="False" data-graded="False" data-runtime-version="1"> <script type="json/xblock-args" class="xblock-json-init-args"> {"xmodule-type": "Video"} </script> <h3 class="hd hd-2">W12PS2: Worked Example - Low Pass Filter</h3> <div id="video_W12PS02" class="video closed" data-metadata='{&#34;autoAdvance&#34;: false, &#34;prioritizeHls&#34;: false, &#34;recordedYoutubeIsAvailable&#34;: true, &#34;ytTestTimeout&#34;: 1500, &#34;poster&#34;: null, &#34;streams&#34;: &#34;1.00:OR4fd-bQdpw&#34;, &#34;saveStateEnabled&#34;: false, &#34;end&#34;: 0.0, &#34;speed&#34;: null, &#34;completionPercentage&#34;: 0.95, &#34;start&#34;: 0.0, &#34;publishCompletionUrl&#34;: &#34;/courses/course-v1:MITx+8.02.3x+1T2019/xblock/block-v1:MITx+8.02.3x+1T2019+type@video+block@W12PS02/handler/publish_completion&#34;, &#34;duration&#34;: null, &#34;autoplay&#34;: false, &#34;savedVideoPosition&#34;: 0.0, &#34;generalSpeed&#34;: 1.0, &#34;autohideHtml5&#34;: false, &#34;ytMetadataEndpoint&#34;: &#34;&#34;, &#34;transcriptTranslationUrl&#34;: &#34;/courses/course-v1:MITx+8.02.3x+1T2019/xblock/block-v1:MITx+8.02.3x+1T2019+type@video+block@W12PS02/handler/transcript/translation/__lang__&#34;, &#34;showCaptions&#34;: &#34;true&#34;, &#34;completionEnabled&#34;: false, &#34;captionDataDir&#34;: null, &#34;ytApiUrl&#34;: &#34;https://www.youtube.com/iframe_api&#34;, &#34;saveStateUrl&#34;: &#34;/courses/course-v1:MITx+8.02.3x+1T2019/xblock/block-v1:MITx+8.02.3x+1T2019+type@video+block@W12PS02/handler/xmodule_handler/save_user_state&#34;, &#34;transcriptAvailableTranslationsUrl&#34;: &#34;/courses/course-v1:MITx+8.02.3x+1T2019/xblock/block-v1:MITx+8.02.3x+1T2019+type@video+block@W12PS02/handler/transcript/available_translations&#34;, &#34;sources&#34;: [], &#34;transcriptLanguages&#34;: {&#34;en&#34;: &#34;English&#34;}, &#34;transcriptLanguage&#34;: &#34;en&#34;, &#34;lmsRootURL&#34;: &#34;https://openlearninglibrary.mit.edu&#34;}' 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="W12PS02"></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_W12PS02">Downloads and transcripts</h3> <div class="wrapper-downloads" role="region" aria-labelledby="video-download-transcripts_W12PS02"> <div class="wrapper-download-transcripts"> <h4 class="hd hd-5">Transcripts</h4> <a class="btn-link external-track" href="/assets/courseware/v1/e9818f7b42a863e4abcda6f90884dc5b/asset-v1:MITx+8.02.3x+1T2019+type@asset+block/subs_W12PS02.srt">Download transcript</a> </div> </div> </div> </div> </div> </div> </div>

<div class="xblock xblock-public_view xblock-public_view-vertical" data-request-token="04a14dec05d811f0a17b0affe2bbc7c1" data-usage-id="block-v1:MITx+8.02.3x+1T2019+type@vertical+block@vert-pset10.3" data-init="VerticalStudentView" data-block-type="vertical" data-runtime-class="LmsRuntime" data-course-id="course-v1:MITx+8.02.3x+1T2019" data-has-score="False" data-graded="False" data-runtime-version="1"> <h2 class="hd hd-2 unit-title">Impedance Mismatching</h2> <div class="vert-mod"> <div class="vert vert-0" data-id="block-v1:MITx+8.02.3x+1T2019+type@problem+block@pset10_3"> <div class="xblock xblock-public_view xblock-public_view-problem xmodule_display xmodule_ProblemBlock" data-request-token="04a14dec05d811f0a17b0affe2bbc7c1" data-usage-id="block-v1:MITx+8.02.3x+1T2019+type@problem+block@pset10_3" data-init="XBlockToXModuleShim" data-block-type="problem" data-runtime-class="LmsRuntime" data-course-id="course-v1:MITx+8.02.3x+1T2019" data-has-score="True" data-graded="False" data-runtime-version="1"> <script type="json/xblock-args" class="xblock-json-init-args"> {"xmodule-type": "Problem"} </script> <div id="problem_pset10_3" class="problems-wrapper" role="group" aria-labelledby="pset10_3-problem-title" data-problem-id="block-v1:MITx+8.02.3x+1T2019+type@problem+block@pset10_3" data-url="/courses/course-v1:MITx+8.02.3x+1T2019/xblock/block-v1:MITx+8.02.3x+1T2019+type@problem+block@pset10_3/handler/xmodule_handler" data-problem-score="0" data-problem-total-possible="0" data-attempts-used="0" data-content=" &lt;h3 class=&#34;hd hd-3 problem-header&#34; id=&#34;pset10_3-problem-title&#34; aria-describedby=&#34;block-v1:MITx+8.02.3x+1T2019+type@problem+block@pset10_3-problem-progress&#34; tabindex=&#34;-1&#34;&gt; Impedance Mismatching &lt;/h3&gt; &lt;div class=&#34;problem-progress&#34; id=&#34;block-v1:MITx+8.02.3x+1T2019+type@problem+block@pset10_3-problem-progress&#34;&gt;&lt;/div&gt; &lt;div class=&#34;problem&#34;&gt; &lt;div&gt; &lt;p&gt; You have a car stereo amplifier which you can think of as an AC voltage generator in series with a resistance internal to the amplifier. The EMF of the amplifier is [mathjaxinline]\mathcal{E}(t)=\mathcal{E}_0\cos (\omega t)[/mathjaxinline] where the amplitude [mathjaxinline]\mathcal{E}_0=18\, V[/mathjaxinline], and the internal resistance [mathjaxinline]R_{amplifier}=0.5\, \Omega[/mathjaxinline]. We say that the amplifier has an output impedance of half an ohm. &lt;/p&gt; &lt;p&gt; With this amplifier you want to drive a [mathjaxinline]75\, W[/mathjaxinline] monitor speaker, which you can think of as an [mathjaxinline]R_{speaker}=16\, \Omega[/mathjaxinline] resistor that can take up to a maximum of [mathjaxinline]75\, W[/mathjaxinline] of power (of course, the more power you dump in it the more sound you get out). &lt;/p&gt; &lt;p&gt; If you just connect your amplifier to the speaker, what is the average power that you will deliver to the speaker? (Hint: In order to time average a function, you need to integrate the function over one period, then divide by the period.) &lt;/p&gt; &lt;p&gt; &lt;p style=&#34;display:inline&#34;&gt;[mathjaxinline]P_{avg}=[/mathjaxinline] &lt;/p&gt; &lt;div class=&#34;inline&#34; tabindex=&#34;-1&#34; aria-label=&#34;Question 1&#34; role=&#34;group&#34;&gt;&lt;div id=&#34;inputtype_pset10_3_2_1&#34; class=&#34; capa_inputtype inline textline&#34;&gt; &lt;div class=&#34;unanswered inline&#34;&gt; &lt;input type=&#34;text&#34; name=&#34;input_pset10_3_2_1&#34; id=&#34;input_pset10_3_2_1&#34; aria-describedby=&#34;status_pset10_3_2_1&#34; value=&#34;&#34; size=&#34;30&#34;/&gt; &lt;span class=&#34;trailing_text&#34; id=&#34;trailing_text_pset10_3_2_1&#34;/&gt; &lt;span class=&#34;status unanswered&#34; id=&#34;status_pset10_3_2_1&#34; data-tooltip=&#34;Not yet answered.&#34;&gt; &lt;span class=&#34;sr&#34;&gt;unanswered&lt;/span&gt;&lt;span class=&#34;status-icon&#34; aria-hidden=&#34;true&#34;/&gt; &lt;/span&gt; &lt;p id=&#34;answer_pset10_3_2_1&#34; class=&#34;answer&#34;/&gt; &lt;/div&gt; &lt;/div&gt;&lt;/div&gt; &lt;p style=&#34;display:inline&#34;&gt; (in [mathjaxinline]W[/mathjaxinline])&lt;/p&gt; &lt;/p&gt; &lt;p&gt; &lt;div class=&#34;solution-span&#34;&gt; &lt;span id=&#34;solution_pset10_3_solution_1&#34;/&gt; &lt;/div&gt;&lt;/p&gt; &lt;/div&gt; &lt;div class=&#34;action&#34;&gt; &lt;input type=&#34;hidden&#34; name=&#34;problem_id&#34; value=&#34;Impedance Mismatching&#34; /&gt; &lt;div class=&#34;submit-attempt-container&#34;&gt; &lt;button type=&#34;button&#34; class=&#34;submit btn-brand&#34; data-submitting=&#34;Submitting&#34; data-value=&#34;Submit&#34; data-should-enable-submit-button=&#34;True&#34; aria-describedby=&#34;submission_feedback_pset10_3&#34; &gt; &lt;span class=&#34;submit-label&#34;&gt;Submit&lt;/span&gt; &lt;/button&gt; &lt;div class=&#34;submission-feedback&#34; id=&#34;submission_feedback_pset10_3&#34;&gt; &lt;span class=&#34;sr&#34;&gt;Some problems have options such as save, reset, hints, or show answer. These options follow the Submit button.&lt;/span&gt; &lt;/div&gt; &lt;/div&gt; &lt;div class=&#34;problem-action-buttons-wrapper&#34;&gt; &lt;/div&gt; &lt;/div&gt; &lt;div class=&#34;notification warning notification-gentle-alert is-hidden&#34; tabindex=&#34;-1&#34;&gt; &lt;span class=&#34;icon fa fa-exclamation-circle&#34; aria-hidden=&#34;true&#34;&gt;&lt;/span&gt; &lt;span class=&#34;notification-message&#34; aria-describedby=&#34;pset10_3-problem-title&#34;&gt; &lt;/span&gt; &lt;div class=&#34;notification-btn-wrapper&#34;&gt; &lt;button type=&#34;button&#34; class=&#34;btn btn-default btn-small notification-btn review-btn sr&#34;&gt;Review&lt;/button&gt; &lt;/div&gt; &lt;/div&gt; &lt;div class=&#34;notification warning notification-save is-hidden&#34; tabindex=&#34;-1&#34;&gt; &lt;span class=&#34;icon fa fa-save&#34; aria-hidden=&#34;true&#34;&gt;&lt;/span&gt; &lt;span class=&#34;notification-message&#34; aria-describedby=&#34;pset10_3-problem-title&#34;&gt;None &lt;/span&gt; &lt;div class=&#34;notification-btn-wrapper&#34;&gt; &lt;button type=&#34;button&#34; class=&#34;btn btn-default btn-small notification-btn review-btn sr&#34;&gt;Review&lt;/button&gt; &lt;/div&gt; &lt;/div&gt; &lt;div class=&#34;notification general notification-show-answer is-hidden&#34; tabindex=&#34;-1&#34;&gt; &lt;span class=&#34;icon fa fa-info-circle&#34; aria-hidden=&#34;true&#34;&gt;&lt;/span&gt; &lt;span class=&#34;notification-message&#34; aria-describedby=&#34;pset10_3-problem-title&#34;&gt;Answers are displayed within the problem &lt;/span&gt; &lt;div class=&#34;notification-btn-wrapper&#34;&gt; &lt;button type=&#34;button&#34; class=&#34;btn btn-default btn-small notification-btn review-btn sr&#34;&gt;Review&lt;/button&gt; &lt;/div&gt; &lt;/div&gt; &lt;/div&gt; " data-graded="False"> <p class="loading-spinner"> <i class="fa fa-spinner fa-pulse fa-2x fa-fw"></i> <span class="sr">Loading&hellip;</span> </p> </div> </div> </div> </div> </div>

<div class="xblock xblock-public_view xblock-public_view-vertical" data-request-token="04a14dec05d811f0a17b0affe2bbc7c1" data-usage-id="block-v1:MITx+8.02.3x+1T2019+type@vertical+block@vert-W12D2-7" data-init="VerticalStudentView" data-block-type="vertical" data-runtime-class="LmsRuntime" data-course-id="course-v1:MITx+8.02.3x+1T2019" data-has-score="False" data-graded="False" data-runtime-version="1"> <h2 class="hd hd-2 unit-title">Unknown Circuit Element</h2> <div class="vert-mod"> <div class="vert vert-0" data-id="block-v1:MITx+8.02.3x+1T2019+type@problem+block@finalexam-problem17"> <div class="xblock xblock-public_view xblock-public_view-problem xmodule_display xmodule_ProblemBlock" data-request-token="04a14dec05d811f0a17b0affe2bbc7c1" data-usage-id="block-v1:MITx+8.02.3x+1T2019+type@problem+block@finalexam-problem17" data-init="XBlockToXModuleShim" data-block-type="problem" data-runtime-class="LmsRuntime" data-course-id="course-v1:MITx+8.02.3x+1T2019" data-has-score="True" data-graded="False" data-runtime-version="1"> <script type="json/xblock-args" class="xblock-json-init-args"> {"xmodule-type": "Problem"} </script> <div id="problem_finalexam-problem17" class="problems-wrapper" role="group" aria-labelledby="finalexam-problem17-problem-title" data-problem-id="block-v1:MITx+8.02.3x+1T2019+type@problem+block@finalexam-problem17" data-url="/courses/course-v1:MITx+8.02.3x+1T2019/xblock/block-v1:MITx+8.02.3x+1T2019+type@problem+block@finalexam-problem17/handler/xmodule_handler" data-problem-score="0" data-problem-total-possible="0" data-attempts-used="0" data-content=" &lt;h3 class=&#34;hd hd-3 problem-header&#34; id=&#34;finalexam-problem17-problem-title&#34; aria-describedby=&#34;block-v1:MITx+8.02.3x+1T2019+type@problem+block@finalexam-problem17-problem-progress&#34; tabindex=&#34;-1&#34;&gt; Circuit Element(s) in a Driven Circuit &lt;/h3&gt; &lt;div class=&#34;problem-progress&#34; id=&#34;block-v1:MITx+8.02.3x+1T2019+type@problem+block@finalexam-problem17-problem-progress&#34;&gt;&lt;/div&gt; &lt;div class=&#34;problem&#34;&gt; &lt;div&gt; &lt;center&gt; &lt;img src=&#34;/assets/courseware/v1/7c2e19abe4ec7bb6fab1f60d5c269f55/asset-v1:MITx+8.02.3x+1T2019+type@asset+block/images_finalexam-problem17_fig1.png&#34; width=&#34;330&#34;/&gt; &lt;/center&gt; &lt;p&gt; The circuit shown above contains an AC generator with [mathjaxinline]V(t) = V_0 \sin \omega t[/mathjaxinline], a resistor with resistance [mathjaxinline]R=\sqrt {3} \rm {\Omega }[/mathjaxinline], and a &#34;black box&#34;, which contains &lt;b class=&#34;bfseries&#34;&gt;either an inductor, or a capacitor, or both an inductor and capacitor connected in series&lt;/b&gt;. In general, the current in the circuit is given by [mathjaxinline]I(t) = I_0 \sin (\omega t - \phi )[/mathjaxinline], where &lt;/p&gt; &lt;table id=&#34;a0000000002&#34; cellpadding=&#34;7&#34; width=&#34;100%&#34; cellspacing=&#34;0&#34; class=&#34;eqnarray&#34; style=&#34;table-layout:auto&#34;&gt; &lt;tr id=&#34;a0000000003&#34;&gt; &lt;td style=&#34;width:40%; border:none&#34;&gt;&amp;#160;&lt;/td&gt; &lt;td style=&#34;vertical-align:middle; text-align:right; border:none&#34;&gt; [mathjaxinline]\displaystyle I_0 = \frac{V_0}{(R^2 + (\omega L - 1/\omega C)^2)^{1/2}}[/mathjaxinline] &lt;/td&gt; &lt;td style=&#34;width:40%; border:none&#34;&gt;&amp;#160;&lt;/td&gt; &lt;td style=&#34;width:20%; border:none&#34; class=&#34;eqnnum&#34;&gt; &lt;span&gt;(&lt;span&gt;1&lt;/span&gt;)&lt;/span&gt; &lt;/td&gt; &lt;/tr&gt; &lt;/table&gt; &lt;p&gt; and &lt;/p&gt; &lt;table id=&#34;a0000000004&#34; cellpadding=&#34;7&#34; width=&#34;100%&#34; cellspacing=&#34;0&#34; class=&#34;eqnarray&#34; style=&#34;table-layout:auto&#34;&gt; &lt;tr id=&#34;a0000000005&#34;&gt; &lt;td style=&#34;width:40%; border:none&#34;&gt;&amp;#160;&lt;/td&gt; &lt;td style=&#34;vertical-align:middle; text-align:right; border:none&#34;&gt; [mathjaxinline]\displaystyle \tan \phi = \frac{\omega L - 1/\omega C}{R}[/mathjaxinline] &lt;/td&gt; &lt;td style=&#34;width:40%; border:none&#34;&gt;&amp;#160;&lt;/td&gt; &lt;td style=&#34;width:20%; border:none&#34; class=&#34;eqnnum&#34;&gt; &lt;span&gt;(&lt;span&gt;2&lt;/span&gt;)&lt;/span&gt; &lt;/td&gt; &lt;/tr&gt; &lt;/table&gt; &lt;p&gt; In the above equations: &lt;/p&gt; &lt;p&gt; 1. If there is no capacitor in the circuit, set [mathjaxinline]C = \infty[/mathjaxinline], then [mathjaxinline]1/C = 0[/mathjaxinline], (note that infinite capacitance means that the capacitor can be treated like a resistanceless wire); &lt;/p&gt; &lt;p&gt; 2. If there is no inductor in the circuit, set [mathjaxinline]L = 0[/mathjaxinline]. &lt;/p&gt; &lt;p&gt; We first measure the current in the circuit at an angular frequency [mathjaxinline]\omega _1 = 2\, \rm {rad \cdot s^{-1}}[/mathjaxinline] and find that the current leads the voltage source by exactly [mathjaxinline]\pi /6[/mathjaxinline] radians. We then measure the current in the circuit at an angular frequency [mathjaxinline]\omega _2 = 6\, \rm {rad \cdot s^{-1}}[/mathjaxinline] and find that the current lags the driving emf by exactly [mathjaxinline]\pi /6[/mathjaxinline] radians. [Note: [mathjaxinline](\pi /6) \rm { rad} = 30^{\circ }[/mathjaxinline], and [mathjaxinline]\tan (\pi /6) = 1/ \sqrt {3}[/mathjaxinline]]. &lt;/p&gt; &lt;p&gt;&lt;b class=&#34;bfseries&#34;&gt;(Part a)&lt;/b&gt; What is inside the black box? &lt;/p&gt; &lt;p&gt; &lt;div class=&#34;wrapper-problem-response&#34; tabindex=&#34;-1&#34; aria-label=&#34;Question 1&#34; role=&#34;group&#34;&gt;&lt;div class=&#34;choicegroup capa_inputtype&#34; id=&#34;inputtype_finalexam-problem17_2_1&#34;&gt; &lt;fieldset aria-describedby=&#34;status_finalexam-problem17_2_1&#34;&gt; &lt;div class=&#34;field&#34;&gt; &lt;input type=&#34;radio&#34; name=&#34;input_finalexam-problem17_2_1&#34; id=&#34;input_finalexam-problem17_2_1_choice_1&#34; class=&#34;field-input input-radio&#34; value=&#34;choice_1&#34;/&gt;&lt;label id=&#34;finalexam-problem17_2_1-choice_1-label&#34; for=&#34;input_finalexam-problem17_2_1_choice_1&#34; class=&#34;response-label field-label label-inline&#34; aria-describedby=&#34;status_finalexam-problem17_2_1&#34;&gt; &lt;text&gt; Only L.&lt;/text&gt; &lt;/label&gt; &lt;/div&gt; &lt;div class=&#34;field&#34;&gt; &lt;input type=&#34;radio&#34; name=&#34;input_finalexam-problem17_2_1&#34; id=&#34;input_finalexam-problem17_2_1_choice_2&#34; class=&#34;field-input input-radio&#34; value=&#34;choice_2&#34;/&gt;&lt;label id=&#34;finalexam-problem17_2_1-choice_2-label&#34; for=&#34;input_finalexam-problem17_2_1_choice_2&#34; class=&#34;response-label field-label label-inline&#34; aria-describedby=&#34;status_finalexam-problem17_2_1&#34;&gt; &lt;text&gt; Only C.&lt;/text&gt; &lt;/label&gt; &lt;/div&gt; &lt;div class=&#34;field&#34;&gt; &lt;input type=&#34;radio&#34; name=&#34;input_finalexam-problem17_2_1&#34; id=&#34;input_finalexam-problem17_2_1_choice_3&#34; class=&#34;field-input input-radio&#34; value=&#34;choice_3&#34;/&gt;&lt;label id=&#34;finalexam-problem17_2_1-choice_3-label&#34; for=&#34;input_finalexam-problem17_2_1_choice_3&#34; class=&#34;response-label field-label label-inline&#34; aria-describedby=&#34;status_finalexam-problem17_2_1&#34;&gt; &lt;text&gt; Both L &amp;amp; C.&lt;/text&gt; &lt;/label&gt; &lt;/div&gt; &lt;span id=&#34;answer_finalexam-problem17_2_1&#34;/&gt; &lt;/fieldset&gt; &lt;div class=&#34;indicator-container&#34;&gt; &lt;span class=&#34;status unanswered&#34; id=&#34;status_finalexam-problem17_2_1&#34; data-tooltip=&#34;Not yet answered.&#34;&gt; &lt;span class=&#34;sr&#34;&gt;unanswered&lt;/span&gt;&lt;span class=&#34;status-icon&#34; aria-hidden=&#34;true&#34;/&gt; &lt;/span&gt; &lt;/div&gt; &lt;/div&gt;&lt;/div&gt; &lt;/p&gt; &lt;p&gt; &lt;div class=&#34;solution-span&#34;&gt; &lt;span id=&#34;solution_finalexam-problem17_solution_1&#34;/&gt; &lt;/div&gt;&lt;/p&gt; &lt;p&gt; &lt;br/&gt; &lt;/p&gt; &lt;p&gt;&lt;b class=&#34;bfseries&#34;&gt;(Part b)&lt;/b&gt; What is (are) the value(s) of the inductance or (and) capacitance? &lt;/p&gt; &lt;p&gt; &lt;p style=&#34;display:inline&#34;&gt;[mathjaxinline]L =[/mathjaxinline]&lt;/p&gt; &lt;div class=&#34;inline&#34; tabindex=&#34;-1&#34; aria-label=&#34;Question 2&#34; role=&#34;group&#34;&gt;&lt;div id=&#34;inputtype_finalexam-problem17_3_1&#34; class=&#34; capa_inputtype inline textline&#34;&gt; &lt;div class=&#34;unanswered inline&#34;&gt; &lt;input type=&#34;text&#34; name=&#34;input_finalexam-problem17_3_1&#34; id=&#34;input_finalexam-problem17_3_1&#34; aria-describedby=&#34;status_finalexam-problem17_3_1&#34; value=&#34;&#34; size=&#34;25&#34;/&gt; &lt;span class=&#34;trailing_text&#34; id=&#34;trailing_text_finalexam-problem17_3_1&#34;/&gt; &lt;span class=&#34;status unanswered&#34; id=&#34;status_finalexam-problem17_3_1&#34; data-tooltip=&#34;Not yet answered.&#34;&gt; &lt;span class=&#34;sr&#34;&gt;unanswered&lt;/span&gt;&lt;span class=&#34;status-icon&#34; aria-hidden=&#34;true&#34;/&gt; &lt;/span&gt; &lt;p id=&#34;answer_finalexam-problem17_3_1&#34; class=&#34;answer&#34;/&gt; &lt;/div&gt; &lt;/div&gt;&lt;/div&gt; &lt;p style=&#34;display:inline&#34;&gt;H&lt;/p&gt; &lt;br/&gt; &lt;/p&gt; &lt;p&gt; &lt;p style=&#34;display:inline&#34;&gt;[mathjaxinline]C =[/mathjaxinline]&lt;/p&gt; &lt;div class=&#34;inline&#34; tabindex=&#34;-1&#34; aria-label=&#34;Question 3&#34; role=&#34;group&#34;&gt;&lt;div id=&#34;inputtype_finalexam-problem17_4_1&#34; class=&#34; capa_inputtype inline textline&#34;&gt; &lt;div class=&#34;unanswered inline&#34;&gt; &lt;input type=&#34;text&#34; name=&#34;input_finalexam-problem17_4_1&#34; id=&#34;input_finalexam-problem17_4_1&#34; aria-describedby=&#34;status_finalexam-problem17_4_1&#34; value=&#34;&#34; size=&#34;25&#34;/&gt; &lt;span class=&#34;trailing_text&#34; id=&#34;trailing_text_finalexam-problem17_4_1&#34;/&gt; &lt;span class=&#34;status unanswered&#34; id=&#34;status_finalexam-problem17_4_1&#34; data-tooltip=&#34;Not yet answered.&#34;&gt; &lt;span class=&#34;sr&#34;&gt;unanswered&lt;/span&gt;&lt;span class=&#34;status-icon&#34; aria-hidden=&#34;true&#34;/&gt; &lt;/span&gt; &lt;p id=&#34;answer_finalexam-problem17_4_1&#34; class=&#34;answer&#34;/&gt; &lt;/div&gt; &lt;/div&gt;&lt;/div&gt; &lt;p style=&#34;display:inline&#34;&gt;F&lt;/p&gt; &lt;/p&gt; &lt;p&gt; &lt;div class=&#34;solution-span&#34;&gt; &lt;span id=&#34;solution_finalexam-problem17_solution_2&#34;/&gt; &lt;/div&gt;&lt;/p&gt; &lt;p&gt; &lt;br/&gt; &lt;/p&gt; &lt;p&gt;&lt;b class=&#34;bfseries&#34;&gt;(Part c)&lt;/b&gt; Will the circuit resonate? If so, at what angular frequency? &lt;/p&gt; &lt;p&gt; &lt;p style=&#34;display:inline&#34;&gt;[mathjaxinline]\omega _0 =[/mathjaxinline]&lt;/p&gt; &lt;div class=&#34;inline&#34; tabindex=&#34;-1&#34; aria-label=&#34;Question 4&#34; role=&#34;group&#34;&gt;&lt;div id=&#34;inputtype_finalexam-problem17_5_1&#34; class=&#34; capa_inputtype inline textline&#34;&gt; &lt;div class=&#34;unanswered inline&#34;&gt; &lt;input type=&#34;text&#34; name=&#34;input_finalexam-problem17_5_1&#34; id=&#34;input_finalexam-problem17_5_1&#34; aria-describedby=&#34;status_finalexam-problem17_5_1&#34; value=&#34;&#34; size=&#34;25&#34;/&gt; &lt;span class=&#34;trailing_text&#34; id=&#34;trailing_text_finalexam-problem17_5_1&#34;/&gt; &lt;span class=&#34;status unanswered&#34; id=&#34;status_finalexam-problem17_5_1&#34; data-tooltip=&#34;Not yet answered.&#34;&gt; &lt;span class=&#34;sr&#34;&gt;unanswered&lt;/span&gt;&lt;span class=&#34;status-icon&#34; aria-hidden=&#34;true&#34;/&gt; &lt;/span&gt; &lt;p id=&#34;answer_finalexam-problem17_5_1&#34; class=&#34;answer&#34;/&gt; &lt;/div&gt; &lt;/div&gt;&lt;/div&gt; &lt;p style=&#34;display:inline&#34;&gt;[mathjaxinline]\rm {rad \cdot s^{-1}}[/mathjaxinline]&lt;/p&gt; &lt;br/&gt; &lt;/p&gt; &lt;p&gt; &lt;div class=&#34;solution-span&#34;&gt; &lt;span id=&#34;solution_finalexam-problem17_solution_3&#34;/&gt; &lt;/div&gt;&lt;/p&gt; &lt;/div&gt; &lt;div class=&#34;action&#34;&gt; &lt;input type=&#34;hidden&#34; name=&#34;problem_id&#34; value=&#34;Circuit Element(s) in a Driven Circuit&#34; /&gt; &lt;div class=&#34;submit-attempt-container&#34;&gt; &lt;button type=&#34;button&#34; class=&#34;submit btn-brand&#34; data-submitting=&#34;Submitting&#34; data-value=&#34;Submit&#34; data-should-enable-submit-button=&#34;True&#34; aria-describedby=&#34;submission_feedback_finalexam-problem17&#34; &gt; &lt;span class=&#34;submit-label&#34;&gt;Submit&lt;/span&gt; &lt;/button&gt; &lt;div class=&#34;submission-feedback&#34; id=&#34;submission_feedback_finalexam-problem17&#34;&gt; &lt;span class=&#34;sr&#34;&gt;Some problems have options such as save, reset, hints, or show answer. 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<div class="xblock xblock-public_view xblock-public_view-vertical" data-request-token="04a14dec05d811f0a17b0affe2bbc7c1" data-usage-id="block-v1:MITx+8.02.3x+1T2019+type@vertical+block@vert-checkpoint_w13_31" data-init="VerticalStudentView" data-block-type="vertical" data-runtime-class="LmsRuntime" data-course-id="course-v1:MITx+8.02.3x+1T2019" data-has-score="False" data-graded="False" data-runtime-version="1"> <h2 class="hd hd-2 unit-title">Power in a Driven RLC Circuit</h2> <div class="vert-mod"> <div class="vert vert-0" data-id="block-v1:MITx+8.02.3x+1T2019+type@problem+block@checkpoint_w13_31"> <div class="xblock xblock-public_view xblock-public_view-problem xmodule_display xmodule_ProblemBlock" data-request-token="04a14dec05d811f0a17b0affe2bbc7c1" data-usage-id="block-v1:MITx+8.02.3x+1T2019+type@problem+block@checkpoint_w13_31" data-init="XBlockToXModuleShim" data-block-type="problem" data-runtime-class="LmsRuntime" data-course-id="course-v1:MITx+8.02.3x+1T2019" data-has-score="True" data-graded="False" data-runtime-version="1"> <script type="json/xblock-args" class="xblock-json-init-args"> {"xmodule-type": "Problem"} </script> <div id="problem_checkpoint_w13_31" class="problems-wrapper" role="group" aria-labelledby="checkpoint_w13_31-problem-title" data-problem-id="block-v1:MITx+8.02.3x+1T2019+type@problem+block@checkpoint_w13_31" data-url="/courses/course-v1:MITx+8.02.3x+1T2019/xblock/block-v1:MITx+8.02.3x+1T2019+type@problem+block@checkpoint_w13_31/handler/xmodule_handler" data-problem-score="0" data-problem-total-possible="0" data-attempts-used="0" data-content=" &lt;h3 class=&#34;hd hd-3 problem-header&#34; id=&#34;checkpoint_w13_31-problem-title&#34; aria-describedby=&#34;block-v1:MITx+8.02.3x+1T2019+type@problem+block@checkpoint_w13_31-problem-progress&#34; tabindex=&#34;-1&#34;&gt; Maximum Power in a Driven RLC Circuit &lt;/h3&gt; &lt;div class=&#34;problem-progress&#34; id=&#34;block-v1:MITx+8.02.3x+1T2019+type@problem+block@checkpoint_w13_31-problem-progress&#34;&gt;&lt;/div&gt; &lt;div class=&#34;problem&#34;&gt; &lt;div&gt; &lt;center&gt; &lt;img src=&#34;/assets/courseware/v1/c441efff170a0554807c4a96fa3026b3/asset-v1:MITx+8.02.3x+1T2019+type@asset+block/images_checkpoint_w13_24.svg&#34; width=&#34;495&#34;/&gt; &lt;/center&gt; &lt;p&gt; Consider the RLC circuit in the figure above. The driving voltage is given by [mathjaxinline]V(t) = V_0\sin (\omega t)[/mathjaxinline] and the current in the circuit is [mathjaxinline]I(t) = I_0\sin (\omega t - \phi )[/mathjaxinline]. The amplitude of the current as a function of [mathjaxinline]\omega[/mathjaxinline] is given by: &lt;/p&gt; &lt;table id=&#34;a0000000002&#34; cellpadding=&#34;7&#34; width=&#34;100%&#34; cellspacing=&#34;0&#34; class=&#34;eqnarray&#34; style=&#34;table-layout:auto&#34;&gt; &lt;tr id=&#34;a0000000003&#34;&gt; &lt;td style=&#34;width:40%; border:none&#34;&gt;&amp;#160;&lt;/td&gt; &lt;td style=&#34;vertical-align:middle; text-align:right; border:none&#34;&gt; [mathjaxinline]\displaystyle I_0=\dfrac {V_0}{\sqrt {R^2+(\omega L - 1/\omega C)^2}}[/mathjaxinline] &lt;/td&gt; &lt;td style=&#34;width:40%; border:none&#34;&gt;&amp;#160;&lt;/td&gt; &lt;td style=&#34;width:20%; border:none&#34; class=&#34;eqnnum&#34;&gt; &lt;span&gt;(&lt;span&gt;1&lt;/span&gt;)&lt;/span&gt; &lt;/td&gt; &lt;/tr&gt; &lt;/table&gt; &lt;p&gt; and its phase shift with respect to the voltage source as a function of [mathjaxinline]\omega[/mathjaxinline] is: &lt;/p&gt; &lt;table id=&#34;a0000000004&#34; cellpadding=&#34;7&#34; width=&#34;100%&#34; cellspacing=&#34;0&#34; class=&#34;eqnarray&#34; style=&#34;table-layout:auto&#34;&gt; &lt;tr id=&#34;a0000000005&#34;&gt; &lt;td style=&#34;width:40%; border:none&#34;&gt;&amp;#160;&lt;/td&gt; &lt;td style=&#34;vertical-align:middle; text-align:right; border:none&#34;&gt; [mathjaxinline]\displaystyle \tan \phi = \dfrac {\omega L - 1/(\omega C)}{R}[/mathjaxinline] &lt;/td&gt; &lt;td style=&#34;width:40%; border:none&#34;&gt;&amp;#160;&lt;/td&gt; &lt;td style=&#34;width:20%; border:none&#34; class=&#34;eqnnum&#34;&gt; &lt;span&gt;(&lt;span&gt;2&lt;/span&gt;)&lt;/span&gt; &lt;/td&gt; &lt;/tr&gt; &lt;/table&gt; &lt;p&gt; The time average power delivered by the battery is given by: &lt;/p&gt; &lt;table id=&#34;a0000000006&#34; cellpadding=&#34;7&#34; width=&#34;100%&#34; cellspacing=&#34;0&#34; class=&#34;eqnarray&#34; style=&#34;table-layout:auto&#34;&gt; &lt;tr id=&#34;a0000000007&#34;&gt; &lt;td style=&#34;width:40%; border:none&#34;&gt;&amp;#160;&lt;/td&gt; &lt;td style=&#34;vertical-align:middle; text-align:right; border:none&#34;&gt; [mathjaxinline]\displaystyle &amp;lt;P&amp;gt; = \dfrac {1}{2}I_0 V_0\cos (\phi )[/mathjaxinline] &lt;/td&gt; &lt;td style=&#34;width:40%; border:none&#34;&gt;&amp;#160;&lt;/td&gt; &lt;td style=&#34;width:20%; border:none&#34; class=&#34;eqnnum&#34;&gt; &lt;span&gt;(&lt;span&gt;3&lt;/span&gt;)&lt;/span&gt; &lt;/td&gt; &lt;/tr&gt; &lt;/table&gt; &lt;p&gt;&lt;b class=&#34;bfseries&#34;&gt;(Part a)&lt;/b&gt; Using the trigonometric identity [mathjaxinline]1+ \tan ^2(\phi )=\dfrac {1}{\cos ^2(\phi )}[/mathjaxinline], and eq. (2), obtain an expression of [mathjaxinline]\cos (\phi )[/mathjaxinline] in terms of [mathjaxinline]R[/mathjaxinline], [mathjaxinline]L[/mathjaxinline], [mathjaxinline]C[/mathjaxinline], and omega for [mathjaxinline]\omega[/mathjaxinline]. &lt;/p&gt; &lt;p&gt; &lt;p style=&#34;display:inline&#34;&gt;[mathjaxinline]\cos (\phi )=[/mathjaxinline] &lt;/p&gt; &lt;div class=&#34;inline&#34; tabindex=&#34;-1&#34; aria-label=&#34;Question 1&#34; role=&#34;group&#34;&gt;&lt;div id=&#34;inputtype_checkpoint_w13_31_2_1&#34; class=&#34;text-input-dynamath capa_inputtype inline textline&#34;&gt; &lt;div class=&#34;unanswered inline&#34;&gt; &lt;input type=&#34;text&#34; name=&#34;input_checkpoint_w13_31_2_1&#34; id=&#34;input_checkpoint_w13_31_2_1&#34; aria-describedby=&#34;status_checkpoint_w13_31_2_1&#34; value=&#34;&#34; class=&#34;math&#34; size=&#34;60&#34;/&gt; &lt;span class=&#34;trailing_text&#34; id=&#34;trailing_text_checkpoint_w13_31_2_1&#34;/&gt; &lt;span class=&#34;status unanswered&#34; id=&#34;status_checkpoint_w13_31_2_1&#34; data-tooltip=&#34;Not yet answered.&#34;&gt; &lt;span class=&#34;sr&#34;&gt;unanswered&lt;/span&gt;&lt;span class=&#34;status-icon&#34; aria-hidden=&#34;true&#34;/&gt; &lt;/span&gt; &lt;p id=&#34;answer_checkpoint_w13_31_2_1&#34; class=&#34;answer&#34;/&gt; &lt;div id=&#34;display_checkpoint_w13_31_2_1&#34; class=&#34;equation&#34;&gt;`{::}`&lt;/div&gt; &lt;textarea style=&#34;display:none&#34; id=&#34;input_checkpoint_w13_31_2_1_dynamath&#34; name=&#34;input_checkpoint_w13_31_2_1_dynamath&#34;/&gt; &lt;/div&gt; &lt;/div&gt;&lt;/div&gt; &lt;/p&gt; &lt;p&gt; &lt;div class=&#34;solution-span&#34;&gt; &lt;span id=&#34;solution_checkpoint_w13_31_solution_1&#34;/&gt; &lt;/div&gt;&lt;/p&gt; &lt;p&gt;&lt;b class=&#34;bfseries&#34;&gt;(Part b)&lt;/b&gt; Use the expression of [mathjaxinline]\cos (\phi )[/mathjaxinline] obtained in part (a) and [mathjaxinline]I_0[/mathjaxinline] from eq. (1) in eq. (3) to write [mathjaxinline]&amp;lt;P&amp;gt;[/mathjaxinline] in terms of V_0 for [mathjaxinline]V_0[/mathjaxinline], [mathjaxinline]R[/mathjaxinline], [mathjaxinline]L[/mathjaxinline], [mathjaxinline]C[/mathjaxinline], and omega for [mathjaxinline]\omega[/mathjaxinline]. &lt;/p&gt; &lt;p&gt; &lt;p style=&#34;display:inline&#34;&gt;[mathjaxinline]&amp;lt;P_{battery}&amp;gt;=[/mathjaxinline] &lt;/p&gt; &lt;div class=&#34;inline&#34; tabindex=&#34;-1&#34; aria-label=&#34;Question 2&#34; role=&#34;group&#34;&gt;&lt;div id=&#34;inputtype_checkpoint_w13_31_3_1&#34; class=&#34;text-input-dynamath capa_inputtype inline textline&#34;&gt; &lt;div class=&#34;unanswered inline&#34;&gt; &lt;input type=&#34;text&#34; name=&#34;input_checkpoint_w13_31_3_1&#34; id=&#34;input_checkpoint_w13_31_3_1&#34; aria-describedby=&#34;status_checkpoint_w13_31_3_1&#34; value=&#34;&#34; class=&#34;math&#34; size=&#34;60&#34;/&gt; &lt;span class=&#34;trailing_text&#34; id=&#34;trailing_text_checkpoint_w13_31_3_1&#34;/&gt; &lt;span class=&#34;status unanswered&#34; id=&#34;status_checkpoint_w13_31_3_1&#34; data-tooltip=&#34;Not yet answered.&#34;&gt; &lt;span class=&#34;sr&#34;&gt;unanswered&lt;/span&gt;&lt;span class=&#34;status-icon&#34; aria-hidden=&#34;true&#34;/&gt; &lt;/span&gt; &lt;p id=&#34;answer_checkpoint_w13_31_3_1&#34; class=&#34;answer&#34;/&gt; &lt;div id=&#34;display_checkpoint_w13_31_3_1&#34; class=&#34;equation&#34;&gt;`{::}`&lt;/div&gt; &lt;textarea style=&#34;display:none&#34; id=&#34;input_checkpoint_w13_31_3_1_dynamath&#34; name=&#34;input_checkpoint_w13_31_3_1_dynamath&#34;/&gt; &lt;/div&gt; &lt;/div&gt;&lt;/div&gt; &lt;/p&gt; &lt;p&gt; &lt;div class=&#34;solution-span&#34;&gt; &lt;span id=&#34;solution_checkpoint_w13_31_solution_2&#34;/&gt; &lt;/div&gt;&lt;/p&gt; &lt;p&gt;&lt;b class=&#34;bfseries&#34;&gt;(Part c)&lt;/b&gt; Which of the following figures best represents a plot of the time average power [mathjaxinline]&amp;lt;P&amp;gt;[/mathjaxinline] vs. [mathjaxinline]\omega[/mathjaxinline], &lt;/p&gt; &lt;center&gt; &lt;img src=&#34;/assets/courseware/v1/ecef105dd7bfec2f917845336b9c78c2/asset-v1:MITx+8.02.3x+1T2019+type@asset+block/images_checkpoint_w13_31.svg&#34; width=&#34;660&#34;/&gt; &lt;/center&gt; &lt;p&gt; &lt;div class=&#34;wrapper-problem-response&#34; tabindex=&#34;-1&#34; aria-label=&#34;Question 3&#34; role=&#34;group&#34;&gt;&lt;div class=&#34;choicegroup capa_inputtype&#34; id=&#34;inputtype_checkpoint_w13_31_4_1&#34;&gt; &lt;fieldset aria-describedby=&#34;status_checkpoint_w13_31_4_1&#34;&gt; &lt;div class=&#34;field&#34;&gt; &lt;input type=&#34;checkbox&#34; name=&#34;input_checkpoint_w13_31_4_1[]&#34; id=&#34;input_checkpoint_w13_31_4_1_choice_0&#34; class=&#34;field-input input-checkbox&#34; value=&#34;choice_0&#34;/&gt;&lt;label id=&#34;checkpoint_w13_31_4_1-choice_0-label&#34; for=&#34;input_checkpoint_w13_31_4_1_choice_0&#34; class=&#34;response-label field-label label-inline&#34; aria-describedby=&#34;status_checkpoint_w13_31_4_1&#34;&gt; &lt;text&gt;Figure 1&lt;/text&gt; &lt;/label&gt; &lt;/div&gt; &lt;div class=&#34;field&#34;&gt; &lt;input type=&#34;checkbox&#34; name=&#34;input_checkpoint_w13_31_4_1[]&#34; id=&#34;input_checkpoint_w13_31_4_1_choice_1&#34; class=&#34;field-input input-checkbox&#34; value=&#34;choice_1&#34;/&gt;&lt;label id=&#34;checkpoint_w13_31_4_1-choice_1-label&#34; for=&#34;input_checkpoint_w13_31_4_1_choice_1&#34; class=&#34;response-label field-label label-inline&#34; aria-describedby=&#34;status_checkpoint_w13_31_4_1&#34;&gt; &lt;text&gt;Figure 2&lt;/text&gt; &lt;/label&gt; &lt;/div&gt; &lt;div class=&#34;field&#34;&gt; &lt;input type=&#34;checkbox&#34; name=&#34;input_checkpoint_w13_31_4_1[]&#34; id=&#34;input_checkpoint_w13_31_4_1_choice_2&#34; class=&#34;field-input input-checkbox&#34; value=&#34;choice_2&#34;/&gt;&lt;label id=&#34;checkpoint_w13_31_4_1-choice_2-label&#34; for=&#34;input_checkpoint_w13_31_4_1_choice_2&#34; class=&#34;response-label field-label label-inline&#34; aria-describedby=&#34;status_checkpoint_w13_31_4_1&#34;&gt; &lt;text&gt;Figure 3&lt;/text&gt; &lt;/label&gt; &lt;/div&gt; &lt;span id=&#34;answer_checkpoint_w13_31_4_1&#34;/&gt; &lt;/fieldset&gt; &lt;div class=&#34;indicator-container&#34;&gt; &lt;span class=&#34;status unanswered&#34; id=&#34;status_checkpoint_w13_31_4_1&#34; data-tooltip=&#34;Not yet answered.&#34;&gt; &lt;span class=&#34;sr&#34;&gt;unanswered&lt;/span&gt;&lt;span class=&#34;status-icon&#34; aria-hidden=&#34;true&#34;/&gt; &lt;/span&gt; &lt;/div&gt; &lt;/div&gt;&lt;/div&gt; &lt;/p&gt; &lt;p&gt; &lt;div class=&#34;solution-span&#34;&gt; &lt;span id=&#34;solution_checkpoint_w13_31_solution_3&#34;/&gt; &lt;/div&gt;&lt;/p&gt; &lt;p&gt; &lt;b class=&#34;bfseries&#34;&gt;Principle of a tuner&lt;/b&gt; &lt;/p&gt; &lt;p&gt; At resonance, when [mathjaxinline]\omega = \omega _0=1/\sqrt {LC}[/mathjaxinline], the time average power transfered by the AC power source to the circuit is at its maximum. In the left figure below, a plot of [mathjaxinline]&amp;lt;P&amp;gt;[/mathjaxinline] vs. [mathjaxinline]\omega[/mathjaxinline] is shown for two different values of [mathjaxinline]R[/mathjaxinline]. As indicated on the figure, larger and smaller values of the resistance, correspond to smaller and larger values of the maximum average power input, respectively, as expected from the [mathjaxinline]1/R[/mathjaxinline] in the power formula. Not as obvious is the fact that the width of the peak is larger for larger [mathjaxinline]R[/mathjaxinline]. This happens because, if [mathjaxinline]R[/mathjaxinline] is big, the term [mathjaxinline](\omega L - 1/\omega C)[/mathjaxinline] has to change by a larger factor (hence needing a bigger change in [mathjaxinline]\omega[/mathjaxinline]) to make the same proportional change in the denominator. &lt;/p&gt; &lt;center&gt; &lt;img src=&#34;/assets/courseware/v1/57768bcad685b9ddb74f4cfa8470bc27/asset-v1:MITx+8.02.3x+1T2019+type@asset+block/images_checkpoint_w13_31b.svg&#34; width=&#34;495&#34;/&gt; &lt;/center&gt; &lt;p&gt; As shown in the right figure above, the width of the peak [mathjaxinline]\Delta \omega[/mathjaxinline] is measured by the difference of frequencies obtained when [mathjaxinline]&amp;lt;P&amp;gt; = \dfrac {&amp;lt;P(\omega _0)&amp;gt;}{2}[/mathjaxinline]. Doing some math you can show that [mathjaxinline]\Delta \omega = \dfrac {R}{L}[/mathjaxinline]. &lt;/p&gt; &lt;p&gt; The principle of a radio tuner is based on the resonance of an AC circuit with the frequency we desire to detect. The antenna of the radio will receive thousands of sine waves. The job of a tuner is to select one sine wave from the thousands of radio signals that the antenna receives. This is achieved by setting [mathjaxinline]\omega _0=1/\sqrt {LC}[/mathjaxinline] equal to the desired frequency. &lt;/p&gt; &lt;/div&gt; &lt;div class=&#34;action&#34;&gt; &lt;input type=&#34;hidden&#34; name=&#34;problem_id&#34; value=&#34;Maximum Power in a Driven RLC Circuit&#34; /&gt; &lt;div class=&#34;submit-attempt-container&#34;&gt; &lt;button type=&#34;button&#34; class=&#34;submit btn-brand&#34; data-submitting=&#34;Submitting&#34; data-value=&#34;Submit&#34; data-should-enable-submit-button=&#34;True&#34; aria-describedby=&#34;submission_feedback_checkpoint_w13_31&#34; &gt; &lt;span class=&#34;submit-label&#34;&gt;Submit&lt;/span&gt; &lt;/button&gt; &lt;div class=&#34;submission-feedback&#34; id=&#34;submission_feedback_checkpoint_w13_31&#34;&gt; &lt;span class=&#34;sr&#34;&gt;Some problems have options such as save, reset, hints, or show answer. These options follow the Submit button.&lt;/span&gt; &lt;/div&gt; &lt;/div&gt; &lt;div class=&#34;problem-action-buttons-wrapper&#34;&gt; &lt;/div&gt; &lt;/div&gt; &lt;div class=&#34;notification warning notification-gentle-alert is-hidden&#34; tabindex=&#34;-1&#34;&gt; &lt;span class=&#34;icon fa fa-exclamation-circle&#34; aria-hidden=&#34;true&#34;&gt;&lt;/span&gt; &lt;span class=&#34;notification-message&#34; aria-describedby=&#34;checkpoint_w13_31-problem-title&#34;&gt; &lt;/span&gt; &lt;div class=&#34;notification-btn-wrapper&#34;&gt; &lt;button type=&#34;button&#34; class=&#34;btn btn-default btn-small notification-btn review-btn sr&#34;&gt;Review&lt;/button&gt; &lt;/div&gt; &lt;/div&gt; &lt;div class=&#34;notification warning notification-save is-hidden&#34; tabindex=&#34;-1&#34;&gt; &lt;span class=&#34;icon fa fa-save&#34; aria-hidden=&#34;true&#34;&gt;&lt;/span&gt; &lt;span class=&#34;notification-message&#34; aria-describedby=&#34;checkpoint_w13_31-problem-title&#34;&gt;None &lt;/span&gt; &lt;div class=&#34;notification-btn-wrapper&#34;&gt; &lt;button type=&#34;button&#34; class=&#34;btn btn-default btn-small notification-btn review-btn sr&#34;&gt;Review&lt;/button&gt; &lt;/div&gt; &lt;/div&gt; &lt;div class=&#34;notification general notification-show-answer is-hidden&#34; tabindex=&#34;-1&#34;&gt; &lt;span class=&#34;icon fa fa-info-circle&#34; aria-hidden=&#34;true&#34;&gt;&lt;/span&gt; &lt;span class=&#34;notification-message&#34; aria-describedby=&#34;checkpoint_w13_31-problem-title&#34;&gt;Answers are displayed within the problem &lt;/span&gt; &lt;div class=&#34;notification-btn-wrapper&#34;&gt; &lt;button type=&#34;button&#34; class=&#34;btn btn-default btn-small notification-btn review-btn sr&#34;&gt;Review&lt;/button&gt; &lt;/div&gt; &lt;/div&gt; &lt;/div&gt; " data-graded="False"> <p class="loading-spinner"> <i class="fa fa-spinner fa-pulse fa-2x fa-fw"></i> <span class="sr">Loading&hellip;</span> </p> </div> </div> </div> <div class="vert vert-1" data-id="block-v1:MITx+8.02.3x+1T2019+type@problem+block@802_Quizzes_F"> <div class="xblock xblock-public_view xblock-public_view-problem xmodule_display xmodule_ProblemBlock" data-request-token="04a14dec05d811f0a17b0affe2bbc7c1" data-usage-id="block-v1:MITx+8.02.3x+1T2019+type@problem+block@802_Quizzes_F" data-init="XBlockToXModuleShim" data-block-type="problem" data-runtime-class="LmsRuntime" data-course-id="course-v1:MITx+8.02.3x+1T2019" data-has-score="True" data-graded="False" data-runtime-version="1"> <script type="json/xblock-args" class="xblock-json-init-args"> {"xmodule-type": "Problem"} </script> <div id="problem_802_Quizzes_F" class="problems-wrapper" role="group" aria-labelledby="802_Quizzes_F-problem-title" data-problem-id="block-v1:MITx+8.02.3x+1T2019+type@problem+block@802_Quizzes_F" data-url="/courses/course-v1:MITx+8.02.3x+1T2019/xblock/block-v1:MITx+8.02.3x+1T2019+type@problem+block@802_Quizzes_F/handler/xmodule_handler" data-problem-score="0.0" data-problem-total-possible="1.0" data-attempts-used="0" data-content=" &lt;h3 class=&#34;hd hd-3 problem-header&#34; id=&#34;802_Quizzes_F-problem-title&#34; aria-describedby=&#34;block-v1:MITx+8.02.3x+1T2019+type@problem+block@802_Quizzes_F-problem-progress&#34; tabindex=&#34;-1&#34;&gt; Tuning Resonance &lt;/h3&gt; &lt;div class=&#34;problem-progress&#34; id=&#34;block-v1:MITx+8.02.3x+1T2019+type@problem+block@802_Quizzes_F-problem-progress&#34;&gt;&lt;/div&gt; &lt;div class=&#34;problem&#34;&gt; &lt;div&gt; &lt;p&gt;A variable capacitor within an LC circuit is used to tune a radio to a desired frequency. You are initially tuned to Boston&#39;s local NPR station, which transmits at a frequency of 89.7 MHz. If you switch your radio to a music station playing at 107.9 MHz by tuning your capacitor from a value of \(C_{A}\) to \(C_{B}\), how is the new capacitance related to the initial capacitance? Express your answer as the ratio \(C_{B}/C_{A}\). (Note: the answer field will parse mathematical operations OR you can use the calculator provided at the bottom of the screen.)&lt;/p&gt; &lt;div class=&#34;inline&#34; tabindex=&#34;-1&#34; aria-label=&#34;Question 1&#34; role=&#34;group&#34;&gt;&lt;div id=&#34;inputtype_802_Quizzes_F_2_1&#34; class=&#34; capa_inputtype inline textline&#34;&gt; &lt;div class=&#34;unanswered inline&#34;&gt; &lt;input type=&#34;text&#34; name=&#34;input_802_Quizzes_F_2_1&#34; id=&#34;input_802_Quizzes_F_2_1&#34; aria-describedby=&#34;status_802_Quizzes_F_2_1&#34; value=&#34;&#34;/&gt; &lt;span class=&#34;trailing_text&#34; id=&#34;trailing_text_802_Quizzes_F_2_1&#34;/&gt; &lt;span class=&#34;status unanswered&#34; id=&#34;status_802_Quizzes_F_2_1&#34; data-tooltip=&#34;Not yet answered.&#34;&gt; &lt;span class=&#34;sr&#34;&gt;unanswered&lt;/span&gt;&lt;span class=&#34;status-icon&#34; aria-hidden=&#34;true&#34;/&gt; &lt;/span&gt; &lt;p id=&#34;answer_802_Quizzes_F_2_1&#34; class=&#34;answer&#34;/&gt; &lt;/div&gt; &lt;/div&gt;&lt;/div&gt; &lt;div class=&#34;solution-span&#34;&gt; &lt;span id=&#34;solution_802_Quizzes_F_solution_1&#34;/&gt; &lt;/div&gt;&lt;/div&gt; &lt;div class=&#34;action&#34;&gt; &lt;input type=&#34;hidden&#34; name=&#34;problem_id&#34; value=&#34;Tuning Resonance&#34; /&gt; &lt;div class=&#34;submit-attempt-container&#34;&gt; &lt;button type=&#34;button&#34; class=&#34;submit btn-brand&#34; data-submitting=&#34;Submitting&#34; data-value=&#34;Submit&#34; data-should-enable-submit-button=&#34;True&#34; aria-describedby=&#34;submission_feedback_802_Quizzes_F&#34; &gt; &lt;span class=&#34;submit-label&#34;&gt;Submit&lt;/span&gt; &lt;/button&gt; &lt;div class=&#34;submission-feedback&#34; id=&#34;submission_feedback_802_Quizzes_F&#34;&gt; &lt;span class=&#34;sr&#34;&gt;Some problems have options such as save, reset, hints, or show answer. These options follow the Submit button.&lt;/span&gt; &lt;/div&gt; &lt;/div&gt; &lt;div class=&#34;problem-action-buttons-wrapper&#34;&gt; &lt;/div&gt; &lt;/div&gt; &lt;div class=&#34;notification warning notification-gentle-alert is-hidden&#34; tabindex=&#34;-1&#34;&gt; &lt;span class=&#34;icon fa fa-exclamation-circle&#34; aria-hidden=&#34;true&#34;&gt;&lt;/span&gt; &lt;span class=&#34;notification-message&#34; aria-describedby=&#34;802_Quizzes_F-problem-title&#34;&gt; &lt;/span&gt; &lt;div class=&#34;notification-btn-wrapper&#34;&gt; &lt;button type=&#34;button&#34; class=&#34;btn btn-default btn-small notification-btn review-btn sr&#34;&gt;Review&lt;/button&gt; &lt;/div&gt; &lt;/div&gt; &lt;div class=&#34;notification warning notification-save is-hidden&#34; tabindex=&#34;-1&#34;&gt; &lt;span class=&#34;icon fa fa-save&#34; aria-hidden=&#34;true&#34;&gt;&lt;/span&gt; &lt;span class=&#34;notification-message&#34; aria-describedby=&#34;802_Quizzes_F-problem-title&#34;&gt;None &lt;/span&gt; &lt;div class=&#34;notification-btn-wrapper&#34;&gt; &lt;button type=&#34;button&#34; class=&#34;btn btn-default btn-small notification-btn review-btn sr&#34;&gt;Review&lt;/button&gt; &lt;/div&gt; &lt;/div&gt; &lt;div class=&#34;notification general notification-show-answer is-hidden&#34; tabindex=&#34;-1&#34;&gt; &lt;span class=&#34;icon fa fa-info-circle&#34; aria-hidden=&#34;true&#34;&gt;&lt;/span&gt; &lt;span class=&#34;notification-message&#34; aria-describedby=&#34;802_Quizzes_F-problem-title&#34;&gt;Answers are displayed within the problem &lt;/span&gt; &lt;div class=&#34;notification-btn-wrapper&#34;&gt; &lt;button type=&#34;button&#34; class=&#34;btn btn-default btn-small notification-btn review-btn sr&#34;&gt;Review&lt;/button&gt; &lt;/div&gt; &lt;/div&gt; &lt;/div&gt; " data-graded="False"> <p class="loading-spinner"> <i class="fa fa-spinner fa-pulse fa-2x fa-fw"></i> <span class="sr">Loading&hellip;</span> </p> </div> </div> </div> </div> </div>