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_m sin omega t, where epsilon_m = 120 V and omega = 465 radians/second. The inductance L = 233 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 voltage cross the generator by phi = 34 degrees and the average power delivered to the circuit by the generator is P_avg = 110 W. What is I_max, the amplitude of the current oscillations in the circuit? A What is R, the value of the resistance of the circuit? Ohm What is C, the value of the capacitance of the circuit? mu F The value of omega is now changed, keeping all other circuit parameters constant, until resonance is reached. How was omega changed? omega was decreased omega was increased What is the average power delivered to the circuit when it is in resonance? W

Explanation / Answer

Real power
P_RMS = P_avg = 110 W

Apparent power
pf = P / S = cos
S = P / cos = 110W / cos 34° = 132.68 VA

Applied RMS voltage
= 0.707 _MAX = 0.707 * 120V = 84.84V

RMS current
I = S / = 132.68 VA / 84.84V = 1.564 A

P = I² R
R = ( P / I² ) = ( 110W / (1.564A)² ) = 6.70

I_MAX = I / 0.707 = 1.564 / 0.707 = 2.212 A

i = 2.212A sin (465 t - 34°)

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