A plug-in electric space heater has a power rating of 500 W (i.e., it consumes 5

Question

A plug-in electric space heater has a power rating of 500 W (i.e., it consumes 500 W when plugged into the 120 V household system). For some reason, you are too cold and decide to add a second identical space heater. The problem is, you only have one plug outlet. So, knowing a little electronics, you decide to hook them together in series. Concerning this scenario, which of the following statements is true?

a. Each heater produces 500 W of heating power. Therefore, the two of them will produce 1,000 W of heating power, and you will get warmer.

b. Each heater now only consumes 250 W, for a total power output of 500 W. You didn't accomplish anything, you're just as cold as before.

c. Each heater now produces only 125 W for a total of 250 W. Therefore, you get even colder.

d. None of the above is true because we didn't factor in the 120 V.

Explanation / Answer

b. Each heater now only consumes 250 W, for a total power output of 500 W. You didn't accomplish anything, you're just as cold as before.

Explanation:

when only one bulb is connected, P = V^2/R

==> R = 120^2/500 = 28.8 ohms

when two bulbs are connected,

V1 = 120/2 = 60 volts

V2 = 120/2 = 60 volts

Pnet = P1 + P2 = V1^2/R1 + V2^2/R1 = 60^2/28.8 + 60^2/28.8   = 500 watts

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