1.What is I max , the amplitude of the current oscillations in the circuit? 2.Wh

Question

1.What is Imax, the amplitude of the current oscillations in the circuit?

2.What is R, the value of the resistance of the circuit?

3.What is C, the value of the capacitance of the circuit?

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

A circuit is constructed with an AC generator, a resistor, capacitor and inductor as shown. The generator voltage varies in time as -va-b Emsinat, where En-120 V and = 472 radians/second. The inductance L = 336 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 -55 degrees and the average power delivered to the circuit by the generator is Pavg-147 W E sin(ot)

Explanation / Answer

a) power = (Vrms)*(Irms)

Irms= power/Vrms= 147 W / 120 V = 1,225 Am

Imax= Irms/(2^0,5) =1,225/(2^0,5)= 0,866 Am

b) R= V/Imax= 120 V/ 0,866 Am = 138,56 Ohm

c) w=1/(LC) ^0,5

C= 1/(L*w^2) = 1/(336*0,001*472^2)=13 F

d) In an RLC circuit at resonance, the inductive reactance exactly cancels the capacitive reactance so that the only impedance in the circuit is the resistance R so the current is
V/R

P=V²/R= (120)*(120)/138,56 Ohm = 103.9 W

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