Example 21-1 Traveling Abroad with Your Hair Dryer
Seasoned travelers know that an electric device that works in one country may not work in another. A certain hair dryer
made in the United States, where the rms wall voltage is 120 V, is rated at 1.5 kW. Find the power output of the hair dryer
when connected to a wall outlet in Australia, where the voltage amplitude is 325 V. Treat the resistance of the hair dryer
as the same regardless of the wall voltage. (In reality, the resistance depends somewhat on the temperature of the dryer’s
heating elements, which depends on the operating voltage.)
Set Up
We’ll use Equation 21-6 to find the resistance
of the hair dryer from the given values of
Paverage and Vrms in the United States. We’ll
then use this same equation to find the average
power in Australia. To do this, we’ll need to
know the rms voltage in Australia; we’ll find
this from the given value of the voltage
amplitude V0 by using Equation 21-5.
Solve
Use Equation 21-6 to determine the resistance
of the hair dryer. We assume this has the same
value no matter what the operating voltage.
Find the value of Vrms in Australia; then use this
to determine the average power into the hair
dryer when used in Australia.
Average power into a resistor:
V 2rms
Paverage =
R
Root mean square (rms) voltage:
V0
Vrms = 21V 2 1t22 average =
22
(21-5)
Solve Equation 21-6 for resistance R:
V 2rms
R =
Paverage
Substitute the values in the United States, Vrms = 120 V and
Paverage = 1.5 kW = 1.5 * 103 W:
1120 V2 2
= 9.6 
R =
1.5 * 103 W
(Recall that 1 W = 1 V 2 > .)
In Australia the voltage amplitude is V0 = 325 V, so the rms voltage is
V0
325 V
=
= 230 V
Vrms =
22
22
With this value of Vrms, the average power into the hair dryer is
Paverage,Australia =
Reflect
(21-6)
V 2rms,Australia
R
=
1230 V2 2
9.6 
= 5.5 * 103 W = 5.5 kW
Our result of 5.5 kW is considerably more power than the hair dryer is designed to take in. You may know how hot the
air from a 1500-W hair dryer can be, or perhaps you’ve felt how hot a 100-W bulb can get after it’s been on for a while.
So you can probably imagine how hot 5500 W would make the heating element of the hair dryer. To radiate that much
power, the required temperature of the heating element might well exceed the melting point of the material! We’ll see in
the following section how this hair dryer can be used safely even with the higher voltage provided in Australia.