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A capacitor of capacity $C$ has charge $Q$ and stored energy is $W$. If the charge is increased to $2 Q$, the stored energy will be
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The correct answer is:
$4 W$
We know that the energy stored in a capacitor is given by:
$\mathrm{W}=\frac{\mathrm{Q}^2}{2 \mathrm{C}}$
Now, if the charge $Q$ increases to 2Q, then the change in energy will be given by:
$\begin{aligned} & \mathrm{W}^{\prime}=\frac{(2 \mathrm{Q})^2}{2 \mathrm{C}} \\ & \Rightarrow \frac{4 \mathrm{Q}^2}{2 \mathrm{C}}=4 \mathrm{~W}\end{aligned}$
$\mathrm{W}=\frac{\mathrm{Q}^2}{2 \mathrm{C}}$
Now, if the charge $Q$ increases to 2Q, then the change in energy will be given by:
$\begin{aligned} & \mathrm{W}^{\prime}=\frac{(2 \mathrm{Q})^2}{2 \mathrm{C}} \\ & \Rightarrow \frac{4 \mathrm{Q}^2}{2 \mathrm{C}}=4 \mathrm{~W}\end{aligned}$
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