Question

An ideal capacitor is charged to a voltage VO and connected at t=0 across an ideal inductor L. If  ω = \(\frac{1}{\sqrt{LC}}\), the voltage across the capacitor at time t>0 is ____________

(a) VO

(b) VO cos(ωt)

(c) VO sin(ωt)

(d) VO e^-ωtcos(ωt)

I got this question in an international level competition.

This is a very interesting question from Dot Convention in Magnetically Coupled Circuits topic in division Resonance & Magnetically Coupled Circuit of Network Theory

Answer 1

Right answer is (b) VO cos(ωt)

For explanation: Voltage across capacitor will discharge through inductor up to voltage across the capacitor becomes zero. Now, inductor will start charging capacitor.

Voltage across capacitor will be decreasing from VO and periodic and is not decaying since both L and C is ideal.

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