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## Homework Statement

A heater is plugged into the same 120-V AC outlet as an 800-W hair dryer. If the total rms current drawn is 16.7A, then calculate the power rating of the heater.

## Homework Equations

P

_{av}=[itex]\frac{1}{2}[/itex]I

^{2}

_{peak}R

## The Attempt at a Solution

I

_{rms}=I

_{peak}/[itex]\sqrt{2}[/itex]

So, I

_{peak}=16.7A x [itex]\sqrt{2}[/itex]

Solving for R in the P

_{av}equation: 2P

_{av}/I

^{2}

_{peak}=R

(2 x 800W)/(16.7A x [itex]\sqrt{2}[/itex])

^{2}= 2.87 ohms.

I'm assuming that in an outlet, the heater and the dryer are in parallel, so V=V

_{1}=V

_{2}and I

_{total}=I

_{1}+I

_{2}

Using ohms law V/R=I, 120V/2.86 ohms= 41.81 A. Since this is too high, I know I'm looking at this problem completely wrong. I wanted to use that to find I

_{2}, solve for R, and find the power of the heater.

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