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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?

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?

Grade:10

1 Answers

Deepak Patra
askIITians Faculty 471 Points
9 years ago
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

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