Question

A series ac circuit contains a resistor, an inductor of 150 mh, a capacitor of 5.00 m f , and a source with vmax = 240 v operating at 50.0 hz. the maximum current in the circuit is 100 ma. calculate the impedance and the phase angle between the current and the source voltage.

Answer 1

ω=2*pi*f = 2*pi*50 = 314.16

Inductive reactance, ZL = jωL = j*314.16*0.15 = j42.12
Capacitance reactance, ZC = 1/(jωC) =1/(j*314.16*0.005) = -j0.64
Impendance, Z = V/I = 240/0.1 = 2400

Now,
Z=R+j(ZL+ZC) => 2400 = R+ j(45.12-0.64) => 2400 = R + j44.48
Additionally,
2400^2 = R^2+44.48^2 => R = Sqrt (2400^2-44.48^2) = 2399.58 ohms.

Phase angle = arctan (44.48/2399.58) = 1.06°