Giancoli 7th Edition textbook cover
Giancoli's Physics: Principles with Applications, 7th Edition
18
Electric Currents
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18-2 and 18-3: Electric Current, Resistance, Ohm's Law
18-4: Resistivity
18-5 and 18-6: Electric Power
18-7: Alternating Current
18-8: Microscopic View of Electric Current
18-10: Nerve Conduction

Question by Giancoli, Douglas C., Physics: Principles with Applications, 7th Ed., ©2014, Reprinted by permission of Pearson Education Inc., New York.
Problem 33
Q

A 120-V hair dryer has two settings: 950 W and 1450 W.

  1. At which setting do you guess the resistance to be higher? After making a guess, determine the resistance at
  2. the lower setting, and
  3. the higher setting.
A
  1. as P increases, R decreases
  2. 15Ω15 \Omega
  3. 9.9Ω9.9 \Omega
Giancoli 7th Edition, Chapter 18, Problem 33 solution video poster
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VIDEO TRANSCRIPT

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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