First slide

L - C Oscillations

Question

A condenser of capacity 6μF is fully charged using a 6 volt battery. The battery is removed and a resistanceless 0.2 mH inductor is connected across the condenser. The current which is flowing through the inductor when one-third of the total energy is in the magnetic field of the inductor is :

Moderate

A

0.1 A
B

0.2 A
C

0.4 A
D

0.6 A

Solution

Total energy = Initial energy on capacitor = $\frac{1}{2} {CV}^{2}$
Magnetic field energy = $\frac{1}{2} {LI}^{2}$
$∴ \frac{1}{2} {LI}^{2} = \frac{1}{3} x \frac{1}{2} {CV}^{2} \Rightarrow I = \sqrt{\frac{{CV}^{2}}{3 L}} = \sqrt{\frac{6 x 10^{- 6} x 6 x 6}{3 \times 0.2 \times 10^{- 3}}} = 0.6 A$

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