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 charge on the capacitor is a maximum is:
A)T/4
B)T/2
C)T
D)3T/2
E)2T

Question

Quizplus · Accepted Answer

When the capacitor is charged initially, it has maximum charge and zero potential difference across it. As the switch is closed, the capacitor starts discharging through the inductor, causing the development of voltage across the inductor. This voltage opposes the flow of current through the circuit, and as a result, the current starts decreasing.

When the current reaches zero, all the stored energy is in the magnetic field of the inductor. As the capacitor is now completely discharged, the potential difference across it is maximum, and it starts charging in the opposite direction.

The process repeats itself, and a periodic oscillation is set up between the capacitor and the inductor. The time period of this oscillation is given by:

T = 2π√(LC)

where L is the inductance and C is the capacitance of the circuit.

At t = T/4, the current in the circuit is maximum, and the potential difference across the capacitor is zero. Therefore, the charge on the capacitor is not a maximum at this time.

At t = T/2, the current is zero, and the potential difference across the capacitor is maximum. Therefore, the charge on the capacitor is also maximum at this time.

Therefore, the next time after t = 0 that the charge on the capacitor is a maximum is T/2.

A Charged Capacitor and an Inductor Are Connected in Series