Problem: An RLC series circuit has a 200 Ω resistor and a 25.0 mH inductor. At 8000 Hz, the phase angle is 45.0°. (a) What is the impedance? (b) Find the circuit’s capacitance. (c) If Vrms = 408 V is applied, what is the average power supplied?

FREE Expert Solution

Inductive reactance:

XL=2πfL, where f is the frequency and  L is the inductance.

Capacitive reactance:

XC=12πfC, where C is the capacitance.

Impedance, resistors, capacitors, and inductors are related by:

Z=R2+(XL-XC)2, where R is the resistance. 

(a)

The impedance, Z is obtained by the power factor:

cosϕ=RZZ=Rcosϕ=200cos(45.0°)

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Problem Details

An RLC series circuit has a 200 Ω resistor and a 25.0 mH inductor. At 8000 Hz, the phase angle is 45.0°.

 (a) What is the impedance?

 (b) Find the circuit’s capacitance. 

(c) If Vrms = 408 V is applied, what is the average power supplied?

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