A capacitor of capacitance 1 μF is charged to a potential of 1V. It is connected in parallel to an inductor

Q: A capacitor of capacitance 1 μF is charged to a potential of 1V. It is connected in parallel to an inductor of inductance 10-3 H . The maximum current that will flow in the circuit has the value

(a) $  \sqrt{1000} $ mA

(b) 1 mA

(c) 1 A

(d) 1000 mA

Ans: (a)

Sol: Charge on capacitor,

q0 = C V

= 1 × 10-6 × 1

q0 = 10-6 C

As , $ \displaystyle q = q_0 sin\omega t$

On differentiating w,r.t time

$ \displaystyle I = \frac{dq}{dt}$

$ \displaystyle I = q_0 \omega cos\omega t$

Maximum current , Io = q0 ω

$ \displaystyle = \frac{q_0}{\sqrt{LC}} $

$ \displaystyle = \frac{10^{-6}}{\sqrt{10^{-3} \times 10^{-6} }} $