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 voltage across the inductor is a maximum is:
A) T
B) T/4
C) T/2
D) T/1
E) 2T

Question

Quizplus · Accepted Answer

In a series LC circuit, the voltage across the capacitor and inductor oscillate with a period T given by:

T = 2π√(LC)

At t=0, the capacitor is charged and the current is 0, so the voltage across the capacitor is maximum and the voltage across the inductor is 0. As time progresses, the charged capacitor will discharge through the inductor, causing a current to flow. The current will then charge the capacitor in the opposite polarity. As the voltage across the capacitor decreases, the voltage across inductor increases. At some point, the voltage across the inductor will reach a maximum value, and the capacitor will be fully charged in the opposite polarity.

The maximum voltage across the inductor occurs midway through the oscillation when the charge on the capacitor is equal and opposite to the initial charge. This occurs at t = T/2. So the next time the voltage across the inductor is a maximum is at t = T/2 after t = 0. Therefore, the answer is C) T/2.

A Charged Capacitor and an Inductor Are Connected in Series