A circuit is constructed with an AC generator, a resistor, capacitor and inducto

Question

A circuit is constructed with an AC generator, a resistor, capacitor and inductor as shown. The generator voltage varies in time as epsilon = V_a . V_b = epsilon_msinomegat, where epsilon_m = 120 V and omega = 259 radians/second. The inductance L = 265 mH. The values for the capacitance C and the resistance R are unknown. What is known is that the current in the circuit leads the voltages across the generator by = 14 degrees and the average power delivered to the circuit by the generator is P_avg = 52 W. What is I_max, the amplitude of the current oscillations in the circuit ? What is R, the value of the resistance of the circuit? What is C, the value of the capacitance of the circuit?

Explanation / Answer

Power P = V I

current i = P/V

i = 52/(120)

Imax = 0.44 Amps

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power factor cos theta = R/Z

so

R = Z cos theta

R = V cos theta /i

R = 120 * cos52/0.44

R = 168 ohms

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use phase angle

tan theta = (XL-Xc)/R

XL-Xc = 168 * tan 52

Xc = XL - 215.30

Xc = (w L) - 215.3

Xc = 259* 0.265 - 215.3

Xc = 1/WC = 146.66

C = 1/(259 * 146.66)

C = 26.36 uF

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