Question

If potential difference across a capacitor is changed from $15V$ to $30V$, work done is $W$. The work done when potential difference is charged from $30V$ to $60V$, will be:

• A. $W$
• B. $2W$
• C. $3W$
• D. $4W$

Answer 1

The correct option is D $4W$

From relation of work done

$W=\frac{1}{2}C{V}^2,$ so $W\propto V^2$

As $V_2=60-30=30V,V_1=30-15=15V$

Hence $\frac{W_2}{W_1}={\left(\frac{V_2}{V_1}\right)}^2$

Or $W_2={\left(\frac{30}{15}\right)}^{2}W$ $W_1=W$

$W_2=4W$