Question

A 1500-W electric heater is plugged into the outlet of a 120-V circuit that has a 20-A circuit breaker. You plug an electric hair dryer into the same outlet. The hair dryer has power settings of 600 W, 900 W, 1200 W, and 1500 W. You start with the hair dryer on the 600-W setting and increase the power setting until the circuit breaker trips. What power setting caused the breaker to trip?

Short answer

The power setting that caused the breaker to trip is 900 W

Step-by-step solution

Definition of power

Amount of energy transferred per unit time.

Given Data:

Heater with power P =1500 W

Outlet voltage V =120 V

Current I =20 A

The dryer has power settings of 600 W,900 W,1200 W, and 1500 W.

Step 2:

The relation between power and current is,

P=VI

Substituting the values in the above expression, we get,

$$\begin{gathered} \mathrm{I}=\frac{\mathrm{P}}{\mathrm{V}} \\ \mathrm{I}=\frac{1500\mathrm{W}}{120\mathrm{V}} \\ \mathrm{I}=12.5\mathrm{A} \end{gathered}$$

The total current allowed is 20 A

Current through dryer must be less than,

20 A-12.5 A = 7.5 A

The power dissipated is,

P = VI = (120V) (7.5A) = 900 W

Thus, the power setting that caused the breaker to tip is 900 W.