A 120-V hair dryer has two settings: 950 W and 1450 W.
- At which setting do you guess the resistance to be higher? After making a guess, determine the resistance at
- the lower setting, and
- the higher setting.
- as P increases, R decreases
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This is Giancoli Answers with Mr. Dychko. Knowing that power equals voltage squared, divided by R, we can solve this for R, by multiplying both sides by R over P. And we'll see that R, which is what you get on the left side because the P's would cancel, equals V squared over P. Because the R's will cancel on the right side leaving us with P in the bottom. So as power goes up, resistance goes down, because we're dividing by the power. So when you divide by a big number, you end up with a small quotient. So as power increases, resistance decreases. So the resistance in each case, then, is gonna be: 120 volts squared, divided by 950 watts, and that'll be 15 ohms, when the hairdryer is on the 950 watts setting; and the resistance at the 1450 watts s etting will be 120 volts squared divided by 1450, which will give 9.9 ohms. And so sure enough, we have a smaller resistance when there's a larger power.
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