Question

A capacitor carrying charge and an inductor (both ideal) are connected across each other such that at initial moment , current in the circuit is zero. If the resulting $\text{LC}$ oscillation has a time period of $T.$ Then after what minimum time from the initial moment will the charge on capacitor be maximum.

• A. $T$
• B. $2T$
• C. $\frac{T}{2}$
• D. $\frac{T}{4}$

Answer 1

The correct option is C $\frac{T}{2}$

Since current is zero initally, charge is maximum on the capacitor.

For one complete $\text{LC}$ oscillation :

$t=0$ to $t=\frac{T}{4}\Rightarrow$ complete discharge of capacitor and maximum emf will be induced in the inductor.

$t=\frac{T}{4}$ to $t=\frac{T}{2}\Rightarrow$ charging of capacitor takes place again with emf induced in the inductor, but the polarity will be reversed.

$t=\frac{T}{2}$ to $t=\frac{3T}{4}\Rightarrow$ again discharge of capacitor takes place and maximum emf will be induced in the inductor.

$t=\frac{3T}{4}$ to $t=T\Rightarrow$ Capacitor is charged again to initial state.

$\therefore$ After time $\frac{T}{2}$ the capacitor will be charged to the same initial level, only the polarity will be reversed.

Hence, option ($c$) is correct.