Question

An ideal capacitor is charged to a voltage V and connected at t=0 across an ideal inductor L. If we take ω = (frac{1}{sqrt{LC}}), the voltage across the capacitor at time t>0 will be?

(a) V

(b) V cos(ωt)

(c) V sin(ωt)

(d) Ve^-ωt cos(ωt)

Answer 1

Correct answer is (b) V cos(ωt)

The best explanation: Voltage across the capacitor will discharge through inductor unless the voltage across the capacitor becomes zero. Now, the inductor will start charging the capacitor. Voltage across the capacitor will be decreasing from V and will be periodic. But it will not be decaying with time, since both L and C are ideal.

              ∴ Voltage across the capacitor at time t>0 is given by V cos (ωt).