The parallel plate capacitors shown in the Figure have capacitance `C_(1) = C and C_(2) = 2C`. The switch `S` is opened. Energy stored in the capacitor system is `U_(1)`. Now the separation between the plates of `C_(1)` is slowly reduced to half its original value. Energy stored in the capacitor system now changes to `U_(2)`.
(a) Which will be larger `- U_(1) or U_(2)` ? Why ?
(b) Calculate work done by the external agent in slowly reducing the distance between the plates of `C_(1)`.
(c) If the plate separation of `C_(1)` is reduced to half and simultaneously the separation between plates of `C_(2)` is doubled, will the energy stored in the capacitor system increase or decrease? Quantify the change in energy.

Answer

(a) `U_(1)gt U_(2)`
(b)`W_(ext)=-(3)/(8) CV^(2)`
(c) No change