Question

If several capacitors are connected in series or parallel, show that the energy stored would be additive in either case.

Answer 1

Given: several capacitors are connected in series or parallel.

To find: show that the energy stored would be additive in either case.

Solution:

• Now we have given that capacitors are connected in series or parallel.

• Consider parallel combination:

• In this, the voltage across each capacitor is same.

• So the energy stored in the combination of the two capacitors will be:

                  E = 1/2CV²

                  E = 1/2(C1 + C2)V²

                  E = 1/2C1V² + 1/2C2V²

                  E = E1 + E2

• Consider series combination:

• In this, the charge on each capacitor is equal.

• So the energy stored in the combination of the two capacitors will be:

                  E = 1/2(Q²/C)

                  E = Q²/2(1/C1 + 1/C2)

                  E = Q²/2C1 + Q²/2C2

                  E = E1 + E2

Answer:

             So we have proved that  the energy stored would be additive in either case.