## Mastering Physics Solutions: Resistance of a Heater

Resistance of a Heater

Part A = 12.5 A
Part B = 9.6 ohms
Part C = 16.1 minutes

Solutions Below:

A 1500-W heater is designed to be plugged into a 120-V outlet.

Part A

What current will flow through the heating coil when the heater is plugged in?
Express your answer for the current numerically, to three significant figures.

The formula for power is W = I2 * R. The problem doesn’t give us either of these, but we know that V = IR, so we can substitute:

W = I2 * R
W = I * V
1500 = I * 120

I = 12.5 A

Part B

What is R, the resistance of the heater?
Express your answer numerically, to three significant figures.

The formula for power is W = I2 * R. The current from part A is 12.5 A, so just subsitute:

W = I2 * R
1500 = (12.5)2 * R
1500 = 156.25 * R

R = 9.60 ohms

Part C

How long does it take to raise the temperature of the air in a good-sized living room (3.00m x 5.00m x 8.00m) by 10.0°C? Note that the specific heat of air is 1006 J/(kg * °C) and the density of air is 1.20 kg/m3.
Express your answer numerically in minutes, to three significant figures.

The room is 3.00 x 5.00 x 8.00 = 120m3. So there is 144 kg of air in the room (1.20 kg/m3 * 120m3). This means it takes 144 * (10.0 * 1006) = 1448640 J of energy to raise the temperature by 10 degrees. At 1500 W (1 J/s) it will take 1448640 / 1500 = 965.76 seconds, or 16.1 minutes (965.76 / 60).

t = 16.1 minutes

Tagged with: