Question

An oscillating LC circuit is set up with an inductor with L = 60 mH and a capacitor with C = 4.0 µF with a maximum voltage of 3.0 V. Initially, at t = 0, the capacitor is fully charged.

(a) What is the maximum value of the current through the circuit?

(b) How long after t = 0 will it take before the current in the circuit is at a maximum for the first time?

(c) What is the maximum rate of change of the current in the circuit?

(d) What is the total energy stored in the circuit?

Answer 1

We assume the circuit is lossless.

The energy in a capacitor is 1/2 * C * V^2 = 3.3 x 10^-6 J
If you use volts, that will give you a charge in coulombs. But you must express the capacitance in Farads (i.e., 1.3 x 10^-6 F). You can solve the equation to find the maximum voltage across the capacitor. Knowing that, Q (charge) = C*V, using coulombs, farads, and volts.

For the inductor, the stored energy is 1/2 * L * I^2 = 3.3 x 10^-6 J . You can solve that and find I, which will be in amperes, if you used Henries for the inductance (i.e., 0.45 x 10^-3 H)

For the final question, just calculate the voltage across the capacitor when the charge is half of maximum. For example, if the max voltage is 50 volts, then with half the charge, the voltage will be 25 volts, since Q = CV. You can find the energy in the cap, and the rest of the energy will be in the inductor. Again, use E = 1/2 * L * I^2 to solve for current, I.