In an RLC series AC circuit where R 370 Ohm L 021 H and C

In an RLC series AC circuit where R - 370 Ohm, L = 0.21 H, and C = 1.5 MuF, the power supply is epsilon = 170 sin(1500 rad/s t) V. Find a) the impedance Z; the phase angle for the current, and explain which of them is leading in phase, the voltage or the current; the rms current in the circuit.

Solution

angular frequency, w = 1500 rad/s

Inductive reactance, XL = w L = 1500 x 0.21 =315 ohm

capacitive reactance, Xc = 1 / wC = 1/ (1500 x 1.5 x 10^-6) = 444.44 ohm

R = 370 ohm

a) impedance = sqrt[ R^2 + (XL - Xc)^2 ]

       = sqrt[ 370^2 + (315 - 444.44)^2] =392 ohm

b) phase angle = tan^-1 [ (XL- XC) / R ]   = - 19.28 Deg

current leading

c) Irms = Vrms / Z

Vrms = Vmax /sqrt(2) = 170 / sqrt(2) =120.21 Volt

Irms = 120.21 / 392 = 0.307 A