1. An AC generator supplies an rms voltage of 220 V at 60.0 Hz. It is connected

Question

1. An AC generator supplies an rms voltage of 220 V at 60.0 Hz. It is connected in series with a 0.250 H inductor, a 4.60 ?F capacitor and a 281 ? resistor. What is the impedance of the circuit?

2. What is the rms current through the resistor?

3. What is the average power dissipated in the circuit?

4. What is the peak current through the resistor?

5. What is the peak voltage across the inductor?

6. What is the peak voltage across the capacitor?

7. The generator frequency is now changed so that the circuit is in resonance. What is that new (resonance) frequency?

Explanation / Answer

XL = wL = 2 * pi * 60 * 0.250 = 94.25 Ohm

Xc= 1 / wC = 1 / (2pi * 60 * (4.60 * 10-6) = 576.65 ohm

impedance, Z = sqrt (R2 + (Xc-XL)2) = sqrt (2812 + (576.65 - 94.25)2) = 558 Ohm

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I = V / Z = 220 / 558 = 0.394 A

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P = V * I = 220 * 0.394 = 86.68 Watt

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I(max) = I(rms) * sqrt(2) = 0.394 * sqrt(2) = 0.557 A

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V = Imax * XL = 0.557 * 94.25 = 52.5 V

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V = Imax * 576.65 = 321.2 V

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Xc = XL

2pi * f * 0.250 = 1 / (2pi * f * 4.6 * 10-6)

f = 148 Hz

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