An RLC circuit has voltage supplied to it at a frequency of 13.0 kHz with a phase difference between the current and the voltage of magnitude 0.20 rad. If the circuit has a capacitance of 5.0 µF and an inductance of 0.050 H, find the resistance of the circuit.

Answer 1

F = 13 kHz.
L = 0.050 H.
C = 5.0 uF.
A=0.2rad * (360Deg/6.28rad)=11.46 Deg.
phase diff.

Xl = 6.28*13000Hz*0.05 = 4082 Ohms.
Xc = 1 / (6.28*13000Hz*5*10^-6) = 2.45 Ohms.

tan(11.46) = (Xl-Xc)/R = 4080 / R.
R = 4080 / tan(11.46) = 20,124 Ohm.