Question

A $ 1\,\mu F $ capacitor is charged to $50\, V$ potential difference and then discharged through a $10\, mH$ inductor of negligible resistance. The maximum current in the inductor will be

• A. 0.5 A
• B. 1.6 A
• C. 0.16 A
• D. 1.0 A

Answer 1

Answer: (A)

When a charged capacitor is allowed to discharge through a resistance inductor electrical oscillations of constant amplitude are produced in the circuit. These are called $L-C$ oscillations.

The energy stored in charged capacitor is
$U=\frac{1}{2} C V^{2}=\frac{1}{2} L i^{2}$
where, $i$ is current in the circuit and $V$ the potential difference.
$\therefore i=\sqrt{\frac{C}{L}} V$
Given, $C=1 \,\mu F =1 \times 10^{-6} F$,
$ L=10 \,mH =10 \times 10^{-3} H $
$\therefore =50 \,V $
$\therefore i=\sqrt{\frac{1 \times 10^{-6}}{10 \times 10^{-3}}} \times 50=0.5 \,A$