Power loss when fan is connected; finding current

[vizakenjack]

Homework Statement

An electric fan which is plugged into a 115 V(rms), 60 Hz socket in your house can be considered as made up of a 1500 Ω resistor in series with a 1.4 H inductance. How much power is dissipated by this electric fan on the average? (in W)

Homework Equations

P = IV = I^2 R
I = V/Z(impedance) or I = V/R

The Attempt at a Solution

Find Z, then I, then P.

My question is, however, why couldn't I use I = V/R?? The other formula to find current? Why wasn't it valid here? Because V/R is for capacitors... or? Can someone explain.

 

[axmls]

Because V/R is for capacitors

What do you mean by this?

The reason you have to use Z instead of R is that you're now dealing with complex quantities, because of the inductance. Why is this important? Because the inductor will affect the phase of the input signal, so complex numbers allow us to represent that.

Not only that, but why would you be able to use V=IR? You have the voltage drop across a resistor in series with the inductor, but there is no "constant" resistance in that case. You have to rely on your steady-state AC techniques.