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 =Va - Vb = msint, where m = 120 V and = 388 radians/second. The inductance L = 208 mH. The values for the capacitance C and the resistance R are unkown. What is known is that the current in the circuit leads the voltage across the generator by = 59 degrees and the average power delivered to the circuit by the generator is Pavg = 76 W.

What is Imax, 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?

The value of is now changed, keeping all other circuit parameters constant, until resonance is reached. How was changed?

a) was decreased

b) was increased

What is the average power delivered to the circuit when it is in resonance?

Explanation / Answer

b) R = Em^2/ P = 120^2 / 76 = 189.47 ohms apprx

a) Im = Em/R = 120 / 189.47 = 0.633 A

c) tan 59 = Xc-Xl/R

Xc = XL + tan 59 R = wL + 315.33 = 80.704 +315.33 = 396.034 ohms

1/wC = 396.034 ohms

C = 1/ ( 388 x  396.034) = 6.5 x 10^-6 F

d) w = 1/ sqroot ( LC) = sqroot ( 10^6 x 10^3 / 6.5 x 208 ) = 860 rad /s

w is increased

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