Prove that the total energy stored in a parallel combination of capacitors is equal to the sum of energies stored in the individiual capacitors.

Explanation

Let we have n capacitors of capacitances `C_(1), C_(2), C_(3)`,……`C_(n)` which are connected in parallel combination with each other.
If C is the equivalent capacitance of the combination then
`C=C_(1) + C_(2) + C_(3) +`………`+C_(n)`
Energy stored in parallel combination of capacitors =`1/2 CV^(2)`
where V = potential difference across each capacitor
`U=1/2(C_(1) + C_(2) + C_(3) +.....+C_(n))V^(2)`
`U=1/2C_(1)V^(2) + 1/2C_(2)V^(2) + 1/2 C_(3)V^(2) + ...........+ 1/2C_(n)V^(2)`
`U = U_(1) + U_(2) + U_(3) +........+ U_(n)`
where `U_(1), U_(2), U_(3)`,........... `U_n` be the energies stored in the capacitors `C_(1), C_(2), C_(3),.....,C_(n)` respectively.
`rArr` Total energy stored in parallel combination of capacitors is equal to the sum of energy stored in the individual capacitors.