Question

In the given circuit the capacitor (C) may be charged through resistance R by a battery V by closing switch `(S_1)`. Also when `(S_1)` is opend and `(S_2)` is closed the capacitor is connected in series with inductor (L).

When the capacitor gets charged compleely, (=`(S_1)` is opened and `(S_2)` is closed, Then,
A. at t=0 energy strored in the circuit is purely in the form of magnetic energy
B. at any time tgt0, current in the circuit is in the same direction
C. at tgt0, thre is no exchange of energy between the inductor and capacitor
D. at any time tgt0, instantaneous current in the circuit may be `Vsqrt((C)/(V))`

Answer 1

Correct Answer - D
(d) The instantaneous charge on plate at any time t during discharging is
`Q=Q_(0) cos (omega)t`
`:. Instantaneous current,
`I=(dQ)/(st)=(Q_0)omega sin omega t`

`:. The magnitude of maximum current
`I_(max)=Q_(0) omega`
Here, `Q_(0)=CV and omega-1/(sqrt(LC))`
`:. I_(max)=CV xx 1/(sqrt(LC)) = Vsqrt((C)/(L))`.