An AC generator supplies an rms voltage of 240 V at 60.0 Hz. It is connected in

Question

An AC generator supplies an rms voltage of 240 V at 60.0 Hz. It is connected in series with a 0.400 H inductor, a 3.70 F capacitor and a 251 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 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?

PLEASE HELP WITH ALL PARTS!!!

Explanation / Answer

Impedance Z = sqrt(R^2+(Xc-XL)^2)

XL = inductive reactanve = wL = 2*pi*f*L = 2*pi*60*0.4 = 150.8 ohms

Xc = capcitive reactance = 1/wc = 1/2*pi*f*C = 1/(2*pi*60*3.7*10^-6) = 716.9 ohms

Z = sqrt(251^2+(716.9-150.8)^2) = 619.25 ohms

++++++++++++++++

Irms = Erms/Z = 240/619.25 = 0.388 A

__________________

Pavg = Erms*Irms = 240*0.388 = 93.12 W

+++++++++++++++++

Imax = Irms*sqrt2 = 0.388*sqrt2 = 0.55 A

_____________

VL = Imax*XL = 0.55*150.8 = 82.94 V

_____________

Vc = Imax*Xc = 0.55*716.9 = 394.3 V

++++++++++++++++++++++++

wo = 1/sqrt(LC)

f = 1/(2*pi*sqrt(0.4*3.7*10^-6)) = 131 Hz

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