Question

A sinusoidal voltage V(t) = (200 V) sinωt is applied to a series LCR circuit with L = 10.0 mH, C = 100 nF and R = 20.0 Ω. Find the following quantities: 

(a) The resonant frequency

(b) The amplitude of current at resonance

(c) The quality factor Q of the circuit

(d) The amplitude of the voltage across the inductor at the resonant frequency.

Answer 1

When the LCR circuit is set to resonance, the resonant frequency is \(f = \frac1{2\pi} \sqrt{\frac1{LC}}\).

Quality factor is \(Q = \frac{\omega_0L}{R} = \frac1R\sqrt{\frac LC}\).

(a) Using formula of resonant frequency The resonant frequency, for the circuit is given by

(b) At resonance current is Maximum i.e. I₀

(c) The quality factor Q of the circuit is given by

= 15.8 

(d) At resonance, the amplitude of the voltage across the inductor is