Question

N identical capacitors are joined in parallel and the combination is charged to a potential v. Now if they are separated and then joined in series then energy of combination will

Answer 1

Let capacitance of each capacitor is C.
N capacitors are joined in parallel combination,
so, Ceq = C + C + C + C ..... N times = NC

total charge = equivalent capacitance × potential
= NC × v

now, when all capacitors are joined in series combination.
so, 1/Ceq = 1/C + 1/C + 1/C + ... N times
Ceq' = C/N

Let new potential across the combination is V'
so, charge = (C/N)V'

according to conservation of energy,
$U_{parallel}=U_{series}$

or, 1/2 Ceq v² = 1/2 Ceq' V'²

or, (NC)v² = (C/N)V'²

or, v²/N² = V'²

or, V' = v/N

hence, when the capacitors are joined in series potential v/N but energy of the combination will be same.