Question

A series RLC circuit has a capacitor with a capacitance of 32.0 ?F , an inductor with an inductance of 0.400 H and a resistor with a resistance of 137 ?. The circuit has a rms current of 5.40 A when the frequency is 55.0 Hz. What is ?_rms, the phase angle and the average power loss?

The ?_rms:

The Phase Angle:

The Average Power Loss:

Answer 1

Impedance is given by:

Z = sqrt (R^2 + (XL - Xc)^2)

when f = 55 Hz

XL = w*L = 2*pi*f*L = 2*pi*55**0.4 = 31.21 ohm

Xc = 1/(wC) = 1/(2*pi*f*C) = 1/(2*pi*55*32*10^-6) = 90.43 ohm

Z = sqrt (137^2 + (31.21 - 90.43)^2) = 149.25 ohm

Z = 149.25 ohm

We know that

Vrms = irms*Z

Vrms = 5.40*149.25 = 805.95 V

Part B

phase angle is given by:

phi = arctan ((XL - Xc)/R)

phi = arctan ((31.21 - 90.43)/137)

phi = -23.39 deg

Part C

Avg power loss is given by:

P = Vrms*Irms*cos phi

P = 805.95*5.40*cos (-23.38 deg)

P = 3994.79 W