In an ideal parallel LC circuit, the capacitor is charged by connecting it to a dc source which is then disconnected. The current in the circuit :-

Question

In an ideal parallel LC circuit, the capacitor is charged by connecting it to a dc source which is then disconnected. The current in the circuit :- (A) becomes zero instantaneously. (B) grows monotonically. (C) decays monotonically. (D) oscillates instantaneously.

Tardigrade Admin · Accepted Answer

<img class="img-fluid question-image" alt="image" src="https://cdn.tardigrade.in/img/question/physics/167c403263afa2cdbfdc5505344cbe65-.png" /> ( q / C )+ L ( di / dt )=0 ⇒ ( d 2 q / dt 2)+( q / LC )=0 which is equation of oscillatory motion. ⇒ q = q 0 sin ω t ⇒ ( dq / dt )= i = q 0 ω cos ω t where ω=(1/√ LC ) ⇒ current starts oscillation.

Q. In an ideal parallel $L C$ circuit, the capacitor is charged by connecting it to a $d c$ source which is then disconnected. The current in the circuit :-

becomes zero instantaneously.

grows monotonically.

decays monotonically.

oscillates instantaneously.

$\frac{q}{C} + L \frac{d i}{d t} = 0$
$\Rightarrow \frac{d ^{2} q}{d t ^{2}} + \frac{q}{L C} = 0$
which is equation of oscillatory motion.
$\Rightarrow q = q_{0} sin ω t$
$\Rightarrow \frac{d q}{d t} = i = q_{0} ω cos ω t$
where $ω = \frac{1}{L C}$
$\Rightarrow$ current starts oscillation.

Q. In an ideal parallel LC circuit, the capacitor is charged by connecting it to a dc source which is then disconnected. The current in the circuit :-