A charged capacitor is connected to an inductor. At time t = 0 the charge on the capacitor is Q = 6μC. At time t = 2 ms the charge on the capacitor is zero for the first time. What is the amplitude of the current at that same instant?
A)2.38 mA
B)4.71 mA
C)0.78 mA
D)1.53 mA
E)1.19 mA

Question

Quizplus · Accepted Answer

The system is an LC circuit undergoing simple harmonic oscillations. The charge on the capacitor and the current in the inductor are related by conservation of energy. At the first instance when the charge is zero, the energy is entirely in the inductor as magnetic energy, which means the current is at its maximum. The maximum current (I_max) can be found using the formula I_max = Q_max * ω, where ω = 2π/T and T = 4 ms (since the charge is zero at t = 2 ms, which is a quarter of the period). Therefore, I_max = 6μC * (2π/4ms) = 4.71 mA.

A Charged Capacitor Is Connected to an Inductor