The rms 60 Hz current in an RLC circuit is 1.23 A. The circuit is designed so that the capacitor and the inductor store equal energy in their electric and magnetic fields, respectively. The inductor is a solenoid with 20000 turns, length 24 cm, and diameter 3.45 cm. The capacitor is epoxy-impregnated paper of thickness 0.05 mm with foil on each side, rolled into a cylinder. What length of paper is required? What effective voltages are found across the inductor and the capacitor?

Solution:

The energy stored in the magnetic field is

For the inductor, the back emf is (in magnitude) L(dI/dt). Since I is sinusoidal,

Now V = Q/C for the capacitor. Since I = dQ/dt, we need to integrate to get Q:

Using this in the equation for the energy stored in the electric field,

The equation for a parallel plate capacitor is

Perhaps the numbers could have been selected with more care!