Question

A series RLC circuit has a resistance of 22 Ω , a capacitance of 0.82 μF , and an inductance of 240 mH . The circuit is connected to a variable-frequency source with a fixed rms voltage output of 12 V.

Part A

If the frequency that is supplied is set at the circuit's resonance frequency, what is the rms voltage across each of the circuit elements?

Express your answers using two significant figures separated by commas.

Answer 1

Frequency, f = 1/ 2 pi sqrt(LC)

F = 1/(2 pi x sqrt(0.24 x 0.82 x 10^-6)) = 358.76 Hz

Xl = 2 pi x 358.76 x 0.24 = 541 ohm

Xc = 1/(2 pi x 358.76 x 0.82 x 10^-6) = 541 ohm

Impedance, Z = 22 ohm

Current I = 12/22 = 0.545 A

Vr = 0.545 x 22 = 11.99 V

Vc = 0.545 x 541 = 295.09 V

Vl = 0.545 x 541 = 295.09 V

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