Question

31. In an LC oscillator circuit L = 10 mH, C = 40uF.
If initially at t = 0 the capacitor is fully charged with
4uC then find the current in the circuit when the
capacitor and inductor share equal energies.
(1) 0.2 mA
42, 4.4 mA
(3) 0.3 mA
(4) 2 ma

Answer 1

Answer:

So the correct option is (2)

Explanation:

Initial energy stored in capacitor U

This energy is all stored in the capacitor = $\frac{1}{2} \frac{q_{0}^2}{C} = 0.5 \times \frac{(4 \mu C)^{2} }{40 \mu F} = 0.2 \mu J$

The energy that the capacitor and inductor will share equally  = 0.1$\mu J$

therefore

$\frac{1}{2} Li^{2}$ = $0.1 \mu J$       ⇒  i = $\sqrt{\frac{2 \times 0.1 \mu J}{L} } = \sqrt{\frac{2 \times 0.1 \mu J}{10 mH} } = 4.4 mA$

So the correct option is (2)