An AC generator supplies an RMS voltage of 120 V at 60 Hz given by equation: V=V

Question

An AC generator supplies an RMS voltage of 120 V at 60 Hz given by equation:

V=V0*sin(?t+?V) and I=I0*sin(?t+?I)

This generator is connected in series to a 75 ohm resistor, 325 mH inductor, and a 50 uF capacitor.

At the instant when the generator voltage is decreasing through 45 V, what is the instantaneous voltage across the inductor?

Explanation / Answer

a) Z = (R^2 + (XL-XC)^2)^0.5 = 143.2 ohm ? = arctan(XL_XC/R) = 58.417 degrees V/V_max = sin? >>>>> 45/120 = sin? >>>> ? = 22.02431 degrees sin(?+?) = sin(58.417+22.02431) = 0.986116 V = (V/Z)*0.986116 * XL = (120/143.2)*0.986116 * (2*3.1416*60*325e-3) = 101 V

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