A hair dryer has a switch that allows it to be used in the US (where the AC voltage is 120 V) and in Europe (where the AC voltage is 230 V). It accomplishes this by having two different resistance settings. When the switch is in the "120 V" position, the hair dryer uses a resistance value that allows it to operate at its rated power of 1380 W when connected to 120 V, and when the switch is in the "230 V" setting, the hair dryer uses a resistance that allows it to still operate at its rated power of 1380 W when connected to 230 V. A tourist takes her 1380 W dual voltage hair dryer to Europe but forgets to set the switch to the "230 V" position. When she plugs it into the 230 V receptacle and turns it on, it begins to smoke. What power does the hair dryer consume as a result of this mistake?

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AyBaba7 AyBaba7 · Answer 1 · 2020-03-16T02:05:33+01:00

Answer:

P = 5072 W

Explanation:

Power consumed by electrical appliances is given as

P = IV

where I = current and V = voltage

But, it can be obtained in form of voltage and resistance alone.

from Ohm's law, V = IR and I = (V/R)

P = IV = (V/R) V = (V²/R)

In the US, where V = 120 V and P = 1380 W, the resistance of the hairdryer would be

P = (V²/R)

R = (V²/P) = (120²/1380)

R = 10.43 Ω

In Europe, where V = 230 V and P = 1380 V

R = (V²/P) = (230²/1380)

R = 38.33 Ω

The hairdryer is taken to Europe with the switch still on 120 V and resistance on 10.43 Ω

The power consumed will be

P = (V²/R) = (230²/10.43)

P = 5072 W

This power consumed is more than twice the hairdryer's power rating! Hence, it smokes when it is turned on with this mistake setting.