Super confused please help!

Question

A series RCL circuit driven at angular frequency w = 597 rad/s has a capacitive reactance XC = 864 W, an inductive reactance XL = 599 W and a resistance R = 357 W. The resulting oscillating current has a maximum of Imax = 0.9 A. The resistor, capacitor and inductor are in series with the generator.

(a) What is the total impedance, Z?
Z = W

(b) What is the maximum value of the voltage across the capacitor?
V = V

(c) What is the rms value of the voltage across the resistor?
V = V

(d) What is the average power consumption of the circuit?
P = W

Answer 1

This looks to be a standard textbook type problem.   The total impedance is given by

Z = sqrt( R² +(XL-XC)²) =  444.6 Ω

 

The max emf is given by E_max = I_max Z =  400.1 V.

 

The maximum voltage across the capacity is  V_c = I_max XC =  777.6 V

The maximum voltage across the resistor   V_R =  I_max R =  321 V,  so the RMS value is .707 (321) = 226.9 V

The average power is   (1/2) E_max I_max (R/Z) = 144.57 watt.

    The factor of 1/2 in this last line is due to the needed conversion to RMS.  The factor of R/Z is the cosine of the

phase lag angle.