The total energy in an LC circuit is 5.0 *10^-⁶ J. If L = 25 mH the maximum current is: A) 10 mA B) 14 mA C) 20 mA D) 28 mA E) 40 mA

Question

Quizplus · Accepted Answer

The total energy in an LC circuit can be written as:
E = (1/2) * L * I^2 + (1/2) * C * V^2
where L is the inductance, C is the capacitance, I is the current, and V is the voltage.

Given: E = 5.0 * 10^-16 J, L = 25 mH = 25 * 10^-3 H

At maximum current, all the energy is in the inductor as the capacitor is fully discharged. Therefore, the energy stored in the inductor is equal to the total energy in the circuit:
(1/2) * L * I^2 = E
(1/2) * 25 * 10^-3 * I^2 = 5.0 * 10^-16
I^2 = (2 * 5.0 * 10^-16) / (25 * 10^-3)
I = 20 * 10^-3 A = 20 mA

Therefore, the maximum current is 20 mA, which corresponds to choice C.

The Total Energy in an LC Circuit Is 5