An inductance of 2.0 H, a capacitance of 18 μF and a resistance of 10 kΩ are connected to an AC source of 20 V with adjustable frequency. (a) What frequency should be chosen to maximize the current in the circuit? (b) What is the value of this maximum current?

Sol. (a)For current to be maximum in a circuit X base l = X base c (Resonant Condition) ⇒ WL = 1/WC ⇒W^2 = 1/LC = ½ * 18 *10^-6 = 10^6/36 ⇒ W = 10^3/6 ⇒ 2πf = 10^3/6 ⇒ f = 1000/6 * 2π = 26.537 Hz = 27 Hz (b) Maximum Current = E/R (in resonance and) = 20/10 * 10^3 = 2/10^3 A = 2 mA