A square loop of resistance 16 Wis connected with battery of 9 V and internal resistance of 1W. In steady state, find energy stored in capacitor of capacity c = 4 mF as shown (at steady state current divides. symmetrically)

 

Correct Option - 3


Detailed Solution:

Equivalent circuit

$i=\frac{9}{4+1}=1.8\text{?}A$

$\frac{i}{2}=0.9\text{?}A$

(V_P– V_Q) = 0.9 * 6 – 0.9 * 2

V_C = 3.6V

U =  $\frac{1}{2}$ CV² =   $\frac{1}{2}$ * 4 * 3.6 * 3.6mJ

= 25.92mJ

<p><span lang="EN-IN">Equivalent circuit</span></p><div class="photo-widget-full"><div class="figure"><picture><source srcset="" media=" (max-width: 500px)"><img src="https://images.shiksha.com/mediadata/images/1759130522php9zxxOw.jpeg" alt="" width="352" height="259" loading="lazy"></picture></div></div><p><span class="mathml" contenteditable="false"> <math> <mrow> <mi>i</mi> <mo>=</mo> <mfrac> <mrow> <mn>9</mn> </mrow> <mrow> <mn>4</mn> <mo>+</mo> <mn>1</mn> </mrow> </mfrac> <mo>=</mo> <mn>1</mn> <mo>.</mo> <mn>8</mn> <mtext>? </mtext> <mi>A</mi> </mrow> </math> </span></p><p><span class="mathml" contenteditable="false"> <math> <mrow> <mfrac> <mrow> <mi>i</mi> </mrow> <mrow> <mn>2</mn> </mrow> </mfrac> <mo>=</mo> <mn>0</mn> <mo>.</mo> <mn>9</mn> <mtext>? </mtext> <mi>A</mi> </mrow> </math> </span></p><div class="photo-widget-full"><div class="figure"><picture><source srcset="" media=" (max-width: 500px)"><img src="https://images.shiksha.com/mediadata/images/1759130565phpqDIYYk.jpeg" alt="" width="232" height="159" loading="lazy"></picture></div></div><p><span lang="EN-IN"> (V_P– V_Q) = 0.9 * 6 – 0.9 * 2</span></p><p><span lang="EN-IN">V_C = 3.6V</span></p><p><span lang="EN-IN">U =&nbsp;<span class="mathml" contenteditable="false"> <math> <mrow> <mfrac> <mrow> <mn>1</mn> </mrow> <mrow> <mn>2</mn> </mrow> </mfrac> </mrow> </math> </span>&lt;!- [if gte mso 9]>&lt;xml&gt; <o:OLEObject Type="Embed" ProgID="Equation.DSMT4" ShapeID="_x0000_i1025" DrawAspect="Content" ObjectID="_1820655894"> </o:OLEObject>&lt;/xml&gt;&lt;! [endif]-&gt;CV² = &lt;!- [if gte mso 9]>&lt;xml&gt; <o:OLEObject Type="Embed" ProgID="Equation.DSMT4" ShapeID="_x0000_i1026" DrawAspect="Content" ObjectID="_1820655895"> </o:OLEObject>&lt;/xml&gt;&lt;! [endif]-&gt;&nbsp;<span class="mathml" contenteditable="false"> <math> <mrow> <mfrac> <mrow> <mn>1</mn> </mrow> <mrow> <mn>2</mn> </mrow> </mfrac> </mrow> </math> </span>* 4 * 3.6 * 3.6</span><span lang="EN-IN">m</span><span lang="EN-IN">J</span></p><p><span lang="EN-IN">= 25.92</span><span lang="EN-IN">m</span><span lang="EN-IN">J</span></p>

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