If the potential difference across a capacitor is increased from 5 ~V to 15 ~V , then the ratio of final energy to initial energy stored in the capacitor is

Correct answer: (D) 9 : 1. Initial energy W_1=1/2 CV_1^2 Final energy W_2=1/2 CV_2^2 ∴ W_2/(~W_1)= (V_2/(~V_1) )^2= (15/5 )^2=(3)^2=9

Q126 / 150 · MHT CET 2021 (24 Sep Shift 1) · Physics

If the potential difference across a capacitor is increased from $5 \mathrm{~V}$ to $15 \mathrm{~V}$, then the ratio of final energy to initial energy stored in the capacitor is

A
1 : 3
B
27 : 1
C
3 : 1
Correct answer
D
9 : 1

Solution

Initial energy $\mathrm{W}_1=\frac{1}{2} \mathrm{CV}_1^2$ Final energy $\mathrm{W}_2=\frac{1}{2} \mathrm{CV}_2^2$ $$ \therefore \frac{\mathrm{W}_2}{\mathrm{~W}_1}=\left(\frac{\mathrm{V}_2}{\mathrm{~V}_1}\right)^2=\left(\frac{15}{5}\right)^2=(3)^2=9 $$

Hence, the correct answer is option: 'D'.

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