Question

A circuit consists of a resistor in series with an inductor and an ac generator that supplies a voltage of 150 V. The inductive reactance is 53 ohms, and the current in the circuit is 1.45 A. Find the average power delivered to the circuit.

Answer 1

The magnitude of the current is:

I = V/Z = 1.45 A

From this, the magnitude of the impedance "Z" is:

Z = V/I = 150/1.45 = 103.45 ohms

| Z | = sqrt( XL^2 + R^2)

where "XL" is the "reactance" of the inductor.

Z^2 = XL^2 + R^2

R^2 = Z^2 - XL^2

R = sqrt( Z^2 - XL^2 ) = sqrt( 103.45^2 - (53)^2 ) = 88.84 ohms

There is no average power developed in the inductor, only the resistor develops average power.

P = I^2 * R = (1.45)^2*88.84 = 186.7861W