Ah, another fine math problem from the Amateur Extra exam (don’t you just love these?) [E5D18] How many watts are consumed in a circuit having a power factor of 0.71…

# Amateur Extra: Power Factor

Ah, another fine math problem from the Amateur Extra exam (don’t you just love these?) [E5D18]

## How many watts are consumed in a circuit having a power factor of 0.71 if the apparent power is 500 VA?

A. 704 W

B. 355 W

C. 252 W

D. 1.42 mW

Remember that the “power factor” of a circuit is the percentage of power that is actually dissipated by the circuit.  Theoretically, if you apply 500 watts (or volt-amps, VA, its the same thing!) to a circuit, it should use all 500, right?  In reality, its not so.

So, to figure the actual power usage in this circuit, we just multiply the apparent power by the power factor, to get the correct answer, which is B. 355 W.  So what looks like another difficult math problem, is really quite simple. $(500)(0.71) = 355$

So where did the rest go?  It basically disappeared, into the reactance of the circuit, and did no actual work. I know, it can be a bit strange to wrap your head around, but that’s how it works. 