Question

1. In L-C oscillation, maximum charge on the capacitor can be q. If at any instant electric energy and magnetic energy associated with circuit is equal, then charge on capacitor at that instant is:

a. Q/SQRT 2 B. Q/2 C. SQRT 3 Q/ 2 D. 3Q/2

Answer 1

The charge on the capacitor at instant is Q√2

There is no current in the circuit when the condenser has its maximum charge and the energy contained in the inductor will be zero.

Total energy = U = Electrical energy = 1/2Q²/C

Let the changed charge on capacitor be = Q.

Then, the electrical energy will be = 1/2Q²/C and

Magnetic energy = 1/2Q²'/C

Total energy = electrical energy +magnetic energy

As this is conserved, therefore,

U= 1/2Q'²/C + 1/2Q'²/C or

= 1/2Q²C = Q'²/C or

= Q'² = Q²/2 or

Q' = Q√2