If the charge on a capacitor is increased by 2C, the energy stored in it increases by 44%. The original charge on the capacitor is (in C)

Correct Option - 3


Detailed Solution:

$U_i=\frac{Q^2}{2C}$

Uf = 1.44 Ui

Qf = Q + 2

$1.44U_i=\frac{{\left(Q+2\right)}^2}{2C}$

$\Rightarrow 1.44\frac{Q^2}{2C}=\frac{{\left(Q+2\right)}^2}{2C}$

$\Rightarrow 1.2Q=Q+2$

0.2 Q = 2

Q = 10 C

<p><math><mrow><msub><mrow><mi>U</mi></mrow><mrow><mi>i</mi></mrow></msub><mo>=</mo><mfrac><mrow><msup><mrow><mi>Q</mi></mrow><mrow><mn>2</mn></mrow></msup></mrow><mrow><mn>2</mn><mi>C</mi></mrow></mfrac></mrow></math></p><p>Uf = 1.44 Ui</p><p>Qf = Q + 2</p><p><math><mrow><mn>1</mn><mo>.</mo><mn>4</mn><mn>4</mn><msub><mrow><mi>U</mi></mrow><mrow><mi>i</mi></mrow></msub><mo>=</mo><mfrac><mrow><msup><mrow><mrow><mo> (</mo><mrow><mi>Q</mi><mo>+</mo><mn>2</mn></mrow><mo>)</mo></mrow></mrow><mrow><mn>2</mn></mrow></msup></mrow><mrow><mn>2</mn><mi>C</mi></mrow></mfrac></mrow></math></p><p><math><mrow><mo>⇒</mo><mn>1</mn><mo>.</mo><mn>4</mn><mn>4</mn><mfrac><mrow><msup><mrow><mi>Q</mi></mrow><mrow><mn>2</mn></mrow></msup></mrow><mrow><mn>2</mn><mi>C</mi></mrow></mfrac><mo>=</mo><mfrac><mrow><msup><mrow><mrow><mo> (</mo><mrow><mi>Q</mi><mo>+</mo><mn>2</mn></mrow><mo>)</mo></mrow></mrow><mrow><mn>2</mn></mrow></msup></mrow><mrow><mn>2</mn><mi>C</mi></mrow></mfrac></mrow></math></p><p><math><mrow><mo>⇒</mo><mn>1</mn><mo>.</mo><mn>2</mn><mi>Q</mi><mo>=</mo><mi>Q</mi><mo>+</mo><mn>2</mn></mrow></math></p><p>0.2 Q = 2</p><p>Q = 10 C</p><div class="photo-widget-full"><div class="figure"><picture><source srcset="" media=" (max-width: 500px)"><img src="https://images.shiksha.com/mediadata/images/1753179450phpBoAH9y.jpeg" alt="" width="135" height="101" loading="lazy"></picture></div></div>

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