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 s Va Vb smsinut, where sm 120 V and w 218 radians/second. The inductance L 351 mH. he 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 op 58 degrees and the average power delivered to the circuit by the generator is P 67 W. avg 1) What is Imax, the amplitude of the current oscillations in the circuit? A Submit 2) What is R, the value of the resistance of the circuit? Submit sin(dot)

Explanation / Answer

(1) Pavg = Irms Vrms cos(phi)

Pavg = Im Vm cos(phi) / 2

2 x 67 = Im x 120 x cos58

Im = 2.11 A

2. Pavg = Im^2 R / 2

2 x 67 = 2.11^2 R

R = 30.2 ohm

3. Z = Vm / Im = 120 / 2.11 = 56.87 ohm

Z^2 = R^2 + (XL - XC)^2

56.87^2 = 30.2^2 + (XL - XC)^2

XL - Xc = - 48.2

(218 x 0.351) - Xc = - 48.2

Xc = 124.72 ohm

Xc = 1/ w C

124.72 = 1 / (218 C)

C = 36.8 x 10^-6 F = 36.8 uF

4. XL will inrease and Xc will decrease.
hence w was increased.

5. Pavg = Vm^2 / 2 R

= 120^2 / (2 x 30.2)

= 238.4 W

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