Question

A capacitor is charged with a battery. When the energy stored in the capacitor is 1 ??, the capacitor is disconnected from the battery in the circuit and connected in series with an inductor with an inductance of 6 ?H. What is the current in the inductor when the load on the capacitor is half the initial maximum value? (The resistance in the circuit can be neglected.)

Answer 1

Here we have given that ,

energy stored in the capacitor Ec = 1 ??,

Inductor with an inductance L = 6 ?H.

Now,

For the current in the inductor when the load on the capacitor is half the initial maximum value can be obtained as,

When the load on the capacitor becomes half which means Q= Qo/2

So that at that time the energy stored by the capacitor will be given as,

Ec' = 1/2 × Q^2/2C = 1/4 × Ec = 0.25 uJ

Now form the energy relation we have

0.5 LI^2 = 0.25 uJ

So that current on the inductor will be

I = 0.2886 Amps

Hence the  current in the inductor when the load on the capacitor is half the initial maximum value will be

I = 0.28867 Amp