Question

In the given lc circuit if initially capacitor c has charge q on it and 2c has charge 2q on it having inductor

Answer 1

Answer:

Assuming the inductor and capacitor to be ideal (meaning resistance will be zero in the overall circuit). Initially, the capacitor C of the LC circuit carries a charge Qo and current I in the Inductor is zero. Therefore at time T = 0, the charge on the capacitor will be:

q(T=0)=Qo

Current Flowing:

I=0

At time T = t, the capacitor now begins to discharge through the inductor. The current begins to flow in an anti-clockwise direction. Therefore the charge of the capacitor decreases, but the energy of the inductor increases. The energy gets transferred from the capacitor to the inductor.

At this stage, there is the maximum value of the current in the inductor. Then the relationship between the current and the charge will be:

I=−dqdt…………..(1)

The negative sign is added because as the time passes from 0 to t the, charge on the plates of capacitor decreases i.e. charge decreases with respect to time and thus the dq/dt obtained will be negative and this is why we add a negative sign to make a current positive.