In a damped LC circuit, the amplitude of the oscillating charge decreases exponentially. If the charge amplitude drops to 1 e of its initial value in 5 ms and the inductance of the circuit is 20 mH , the resistance of the circuit is:

Step-by-step solution

The amplitude of charge in a damped LC circuit varies with time as: Q = Q₀ e^ - Rt 2L The charge amplitude drops to 1 e of its initial value when the exponent is -1 . Rt 2L = 1 Rearranging for resistance R : R = 2L t Given L = 20 mH = 20 10⁻³ H and t = 5 ms = 5 10⁻³ s : R = 2 20 10⁻³ 5 10⁻³ = 40 5 = 8 Answer: 8