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An ideal capacitor is charged to a voltage V0 and connected at t = 0 across an ideal inductor L. (The circuit
now consists of a capacitor and inductor alone). If we let ω0 = 1 √LC
the voltage across the capacitor at time t > 0 is given by
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- V0
- V0 cos (ω0 t)
- V0 sin (ω0 t)
- V0 e– ω0t cos (ω0 t)
Correct Option: B
Representation of charged capacitor to voltage V0 in S-domain. When this capacitor is connected to inductor at t > 0, the circuit becomes as,
I L (0+) = 0
and, VL (s) = I(s) · Ls
| V(s) = | ||||
| s2 + | ||||
| LC | ||||
Taking reverse Laplace, we get
v(t) = V0 cos ω0 t,
| ω0 = | ||
| √LC |
Voltage across capacitor will discharge through inductor till voltage across capacitor is zero. When inductors becomes fully charged, it starts charging capacitor till current flow through the circuit is zero.
In this fashion, electrostatic energy gets exchanged into magnetic energy and vice-versa.
