Question

An ideal L-C circuit (zero resistance) includes an inductor with inductance L and a capacitor with capacitance C, maximum charge on the capacitor Q, and a oscillation period T. If we change out the inductor for one with an inductance 4L, and we reduce the maximum charge on the capacitor to Q/2, what is the new period of the L-C circuit?

Answer 1

We know the oscillation period of an LC circuit is given by

Now, in the second case, the inductance is increased to 4L.

Also, the maximum charge across the capacitor has been reduced to Q/2, but this does not affect the capacitance of the capacitor as capacitance depends on Area of plates and the distance between them and not on the charge. ()

Thus, the new period will be

Thus, the new period will be (1/2)times the old period.