An AC generator supplies an rms voltage of 110 V at 50.0 Hz. It is connected in

Question

An AC generator supplies an rms voltage of 110 V at 50.0 Hz. It is connected in series with a 0.200 H inductor, a 4.70 F capacitor and a 236 resistor.

What is the impedance of the circuit?

What is the rms current through the resistor?

What is the average power dissipated in the circuit?

What is the average power dissipated in the circuit?

What is the peak current through the resistor?

What is the peak voltage across the inductor?

What is the peak voltage across the capacitor?

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

Explanation / Answer

First you have calculate each impedance:

XL = wL = 2*pi*50* 0.200 = 62.83 Ohm

Xc= 1/wC = 1/(2pi*50*(4.7*10^-6) =677.25 ohm

1. Total impedance, Z = sqrt (R^2 + (Xc-XL)^2)= 658.18Ohm

2. I =V/Z = 110/658.18 =0.167 Ampere

3. P =V*I = 110* 0.167 = 18.37 Watt

4. I(max) = I(rms) * sqrt(2) = 0.236 Ampere

5. V= I(max) * XL =14.82 Volt

6. V= I(max) * 758 = 159.83 Volt

7) for the resonance,

XL =Xc
the resonance is 1/ 2* pi* sqrt (L*C) = 164.15 Hertz

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