Question

The amount of work done in increasing the voltage across the plates of the capacitor from $5 \, V$ to $10 \, V$ is $W$ . The work done in increasing it from $10 \, V$ to $15 \, V$ will be

• A. $W$
• B. $0.6 \, W$
• C. $1.25 \, W$
• D. $1.67 \, W$

Answer 1

Answer: (D)

The work done in increasing the potential is given by
$W=d U \propto\left(V_2^2-V_1^2\right) $
$\therefore \frac{W_1}{W_2}=\frac{\left(V_2^2-v_1^2\right)}{\left(V_3^2-v_2^2\right)}$
here $V_1=5 v, V_2=10 V$
and $V_3=15 V$
$\therefore \frac{W}{W_2}+\frac{100-25}{225-100}=\frac{75}{125}$
$\therefore W_2=1.67\, W$