A series RLC circuit is shown in the figure. The circuit is powered by an AC sou

Question

A series RLC circuit is shown in the figure. The circuit is powered by an AC source. The peak emf of the AC source is 50 volt. The resistance is R = 340 ; the capacitance is C = 50 F; the inductance is L = 42 mH.

What is the resonant frequency of this RLC circuit (in the unit of Hertz (Hz))? _____Hz

At resonant frequency, how much is the reactance of the inductor? _____

What is the peak current in the circuit at resonance? _____A

At resonant frequency, how much is the reactance of the capacitor? _____

Explanation / Answer

a)  Resonant frequency of this RLC circuit = 1 / 2 pi * sqrt [L C]

= 1 / [2 pi * sqrt [42 * 10-3 * 50 * 10-6] ] = 109.82 Hz

b) XL = 2 pi f L = 2 pi * 109.82 * 42 * 10-3= 28.98 ohms

c) peak current in the circuit at resonance = Vmax / R = 50 / 340 = 0.147 A

d) XC = 1 / 2 pi f C = 1 / 2 pi * 109.82 * 50 * 10-6 = 28.98 ohms

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