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.

Under what setting does the circuit breaker trip.

Please, no answer without explanation or work shown.

Answer 1

Concepts and reason

The concept required to solve the problem is electric power.

First, find the total power available in the system using the relationship between power, voltage and current. Then find the remaining power after the electric heater draws the required power from the total power. This remaining power is the power setting that will trip the circuit breaker.

Fundamentals

Electrical power is basically the amount of electrical energy transferred in unit time by an electrical circuit. Distribution lines help in the transmission and distribution of the electricity generated at power plants.

Electrical power is measured in Watt. One watt is equal to the energy of one joule per second. The relationship between powers, current and potential difference is:

$P = VI$

Here, $P$ is the power, $V$ is the potential difference, and $I$ is the current in the circuit.

The total power on the system that can be used without tripping the circuit is:

${P_{{\rm{tot}}}} = VI$

Substitute $120\,{\rm{V}}$ for $V$ and $20\,{\rm{A}}$ for $I$ to find ${P_{{\rm{tot}}}}$ .

$\begin{array}{c}\\{P_{{\rm{tot}}}} = \left( {120\,{\rm{V}}} \right)\left( {20\,{\rm{A}}} \right)\\\\ = 2400\,{\rm{W}}\\\end{array}$

The maximum power required for the electric heater to operate is $1500\,{\rm{W}}$ .

The remaining power after the electric heater’s usage is,

$P = {P_{{\rm{tot}}}} - {P_{{\rm{heater}}}}$

Here, ${P_{{\rm{heater}}}}$ is the power used by the heater.

Substitute $2400\,{\rm{W}}$ for ${P_{{\rm{tot}}}}$ and $1500\,{\rm{W}}$ for ${P_{{\rm{heater}}}}$ to find the remaining power.

$\begin{array}{c}\\P = 2400\,{\rm{W}} - 1500\,{\rm{W}}\\\\ = {\rm{900}}\,{\rm{W}}\\\end{array}$

Ans:

The power setting at which the circuit breaker trips is $900\,{\rm{W}}$ .