An inductor of inductance 2.0 mH is connected across a charged capacitor of capacitance 5.0 μ F and the resulting L-C circuit is set oscillating at its natural frequency. Let Q denote the instantaneous charge on the capacitor and I the current in the circuit. It is found that the maximum value of Q is 200 μ C . When Q = 100 μ C, what is the value of dI / dt ?

Step-by-step solution

This is a problem of L - C oscillations. Charge stored in the capacitor oscillates simple harmonically as Q = Q 0 sin ( ω t ± ϕ ) Here, Q 0 = maximum value of Q = 200 μ C = 2 × 10 − 4 C ω = 1 LC = 1 2 × 10 - 3 5.0 × 1 0 - 6 = 10 4 s -1 At t = 0 , Q = Q 0 then Q ( t ) = Q 0 cos ω t ... (i) I t = dQ dt = - Q 0 ω sin ω t and ... (ii) dI t dt = - Q 0 ω 2 cos ω t ... (iii) Q = 100 μ C or Q 0 2 cos ω t = 1 2 or ω t = π 3 dI dt = 2.0 × 1 0 - 4 C 1 0 4 s -1 2 1 2 dI dt = 1 0000 A / s