Question

If capacitor is disconnected from battery what will be the energy stored in capacitor when separation between them becomes double

Answer 1

When the Capacitor is disconnected from battery, the energy stored  will be  $U^{'}$ = Q²/C

Explanation:

when the battery is disconnected , then the charge on the plates will remain same but the potential difference between the plates will change.

Capacitance = C = ε₀A/d

where d = seperation and A = Area of cross section

when the seperation between the plates is doubled, capacitance becomes

     $C^{'}$     =        ε₀A/2d  = C/2

The potential difference between the plates will be ;

  $V^{'}$ =  Q / $C^{'}$  = 2Q/C

Energy stored will be $U^{'}$ = $\frac{1}{2} X \frac{C}{2}$ X(2Q/C)²

       $U^{'}$ = Q²/C