Confused with how to set up, and execute the steps of this problem. A series RCL

Question

Confused with how to set up, and execute the steps of this problem.

A series RCL circuit driven at angular frequency %u03C9 = 505 rad/s has a capacitive reactance XC = 851 %u03A9, an inductive reactance XL = 551 %u03A9 and a resistance R = 351 %u03A9. The resulting oscillating current has a maximum of Imax = 0.9 A. The resistor, capacitor and inductor are in series with the generator.

1) What is the total impedance, Z?

2) What is the maximum value of the voltage across the capacitor?

3) What is the rms value of the voltage across the resistor?

4) What is the average power consumption of the circuit?

Explanation / Answer

a)

Z=sqrt[R^2+(XL-XC)^2] =sqrt[351^2+(551-851)^2]

Z=461.74 ohms

b)

Vc =IXc =0.9*851 =765.9 V

c)

Irms =Imax/sqrt(2) =0.9/sqrt(2) =0.6364 A

Vr =Irms*R =0.6364*351 =223.38 V

d)

Pav =Irms^2*R =0.6364^2*351 =142.16 W

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