A charged capacitor and an inductor are connected in series. At time t = 0 the current is zero, but the capacitor is charged. If T is the period of the resulting oscillations, the next time, after t = 0 that the energy stored in the electric field of the capacitor is a maximum is:
A) T
B) T/4
C) T/2
D) T/1
E) 2T

Question

Quizplus · Accepted Answer

When a charged capacitor and an inductor are connected in series, the energy stored in the electric field of the capacitor and the energy stored in the magnetic field of the inductor oscillate back and forth. The period of these oscillations is given by T = 2π√(LC), where L is the inductance and C is the capacitance.

At time t = 0, the capacitor is charged and the current is zero. The energy stored in the electric field of the capacitor is given by U = 1/2CV^2, where V is the voltage across the capacitor. Since the current is zero, there is no voltage across the inductor and hence no energy stored in its magnetic field.

The next time that the energy stored in the electric field of the capacitor is a maximum is when the capacitor is fully charged and the current is at a maximum. This occurs at time T/2, since the current oscillates between zero and its maximum value twice during each period T. Therefore, the answer is C) T/2.

A Charged Capacitor and an Inductor Are Connected in Series