Question

A circuit consists of a resistance R, and an inductance L in parallel connected, which is in series with a second resistance R2. This system is applied a voltage of angular frequency w. Find the total impedance.​

Answer 1

The impedance of the inductor is ω L:

This is in parallel wth R giving a resistance of the parallel combination:

1 / Rp = 1 / ω L + 1 / R

Rp = (ω L * R) / (ω L + R) for the impedance of the parallel combination

Total resistance (impedance) Rt = Rp + R2 = Z

One can use the term impedance to show that the resulting current is not in phase with the resulting voltage

phase angle φ - cos φ = ω L / Rt

V = I Z shows the relation of voltage and urrent