In the U.K.the power companies supply an rms voltage of 240 V to most home outlets.If you were to try and use your standard U.S.rated 1200-W (at 120-V)hair dryer in the U.K.without using a transformer,what would be the average power supplied to the hair dryer?
A)1200 W
B)2400 W
C)4800 W
D)600 W
E)None of the above

Question

Quizplus · Accepted Answer

The power supplied to the hair dryer can be calculated using the formula $P = \frac{V^2}{R}$, where $P$ is power, $V$ is voltage, and $R$ is resistance. The resistance of the hair dryer, designed for 120 V to operate at 1200 W, can be found using $R = \frac{V^2}{P}$ for its intended operation. Substituting 120 V and 1200 W gives $R = \frac{120^2}{1200} = 12 \Omega$. Using the U.K. voltage of 240 V in the power formula gives $P = \frac{240^2}{12} = 4800 W$. Thus, the hair dryer would be supplied with an average power of 4800 W, which is four times its rated power due to the voltage being doubled.

In the UKThe Power Companies Supply an Rms Voltage of 240 V