Question

Capacitance C1 = 2C2 = 2C3 and potential
difference across C1, C2and C3 are V1,V2 and
V3respectively then :
(1) V1 = V2 = V3
(2) V1 = 2V2 = 2V3
(3) 2V1 = V2 = V3
(4) 2V1 = 2V2= V3​

Answer 1

Answer:

Energy stored in a capacitor = 1/2QV = 1/2CV^2 = 1/2(Q^2/C)

Now, in a series connection, the Q across each capacitor is same.

And 1/Ceq = 1/C1 + 1/C2 + 1/C3

Hence, energy in series connection = Q^2/2 * ( 1/C1 + 1/C2 + 1/C3)

Also, since,for any capacitor V= Q/C, so in this circuit Q/C1 + Q/C2 + Q/C3 = V

Hence, energy in series connection becomes = Q/2 * V

Hence, energy in series connection becomes = Q/2 * V

Now in parallel connection, V across each capacitor is same.

And Ceq = C1+ C2+C3

Hence energy stored in parallel connection = 1/2*V^2 ( C1+ C2+C3)

Also, since,for any capacitor V= Q/C, so in this circuit C1V + C2V + C3V = Q

Hence, energy in series connection becomes = 1/2QV

Hence, energy in series and parallel connection is same.