Question

A capacitor is charged with a battery and energy stored is $U$. After disconnecting the battery, another identical uncharged capacitor is connected in parallel with it. The energy stored in each capacitor is now

• A. $\frac{U}{2}$
• B. $\frac{U}{4}$
• C. $4U$
• D. $2U$

Answer 1

The correct option is B $\frac{U}{4}$

Let the capacitance of the capacitor be $C$ and initial charge be $q$ on connecting to the battery.

Energy stored in the capacitor will be

$U=\frac{q^2}{2C}$

When the battery is disconnected and an identical capacitor connected in parallel, charge on each capacitor is $q/2$ (Since the potential difference across them will be the same).

Now, energy stored in each capacitor will be

$U^{\prime }=\frac{(q/2{)}^2}{2C}=\frac{1}{4}\frac{q^2}{2C}=\frac{U}{4}$

Hence, option $\left(b\right)$ is correct.