A circuit contains a 20 ohm resistor and an inductor with an inductance of 0.093 H if the circuit has a frequency of 60Hz what is the total impedance of the circuit?

The expression for the current (I) is simply the voltage (V) divided by the total impedance (Z).

In your example its (40+j25) V divided by (R + / - j) Ohms.

We aren't given the dc resistance of the inductor so assuming it is zero.

Resistance of resistor is 20 Ohms.

Reactance of inductor is 2 * Pi * Freq * Inductor value in Henries. gives

2*3.14*79.5*0.6 = 299.7 Ohms.

So total impedance Z is (20+j299.6) Ohms....say (20+j300) Ohms

Now Complex series current I = V/Z = (40+j25) V / (20+j300) Ohms

Rather than taking surds we simplify to polar form here.

V = (40+j25) = 47.17 Volts at phase angle 32 degrees

Z = (20+j300) = 300.7 Ohms at phase angle 86.2 degrees

So current is 47.17 V /300.7 Ohms and phase angle is (32 degrees

• 86.2 degrees)

I = 0.157 Amps at angle -54.2 degrees

Changing this to rectangular form gives (0.092 -j0.127) Amps