Question

A 531.7-W space heater is designed for operation in Germany, where household electrical outlets supply 230 V (rms) service. What is the power output of the heater when plugged into a 120-V (rms) electrical outlet in a house in the United States? Ignore the effects of temperature on the heater's resistance.

Answer 1

Answer:

P=144.74W

Explanation:

We can model the power output of a resistance by using the following formula:

$P=\frac{V^{2}}{R}$

Wehre P is the power output, V is the rms voltage and R is the resistance. The resistance of the space heater will remain the same, so we can calculate it from the power output in Germany and its rms voltage. So when solving for R, we get:

$R=\frac{V^{2}}{P}$

and we can now use the provided data:

$R=\frac{(230V)^{2}}{531.7W}$

which yields:

R= 99.49 Ω

Once we know what the heater's resistance is, we can now go ahead and calculate the power outpor of the heater in the U.S.

$P=\frac{V^{2}}{R}$

so

$P=\frac{(120V)^{2}}{99.49\Omega}$

P=144.74W