Question

A capacitor is charged by a battery. The battery is removed and another identical uncharged capacitor is connected in parallel. The total electrostatic energy of resulting system

• A. increases by a factor of 2.
• B. increases by a factor of 4.
• C. decreases by a factor of 2.
• D. remains the same.

Answer 1

The correct option is C decreases by a factor of 2.

$U_i=\frac{1}{2}C{V}^2$
After second uncharged capacitor is connected, the charge gets distributed and voltage across both become half.
$U_i=\frac{1}{2}\left[2C\right][\frac{V}{2}{]}^2=\frac{1}{2}{U}_i$
which implies decreases by a factor of 2.