Question

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 1850 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 1850 W when connected to 230 V.
A tourist takes her 1850 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.
A) What power does the hair dryer consume as a result of this mistake?

Answer 1

Answer:

$P\approx 3545.83W$

Explanation:

The electric power in watts produced by an electric current can be calculated as:

$P=VI$

Where:

$V=Voltage\\I=Electric\hspace{3}current$

Now, let:

$V_1=120V\\V_2=230V$

When the switch is in the 120 V position, the electric current is:

$P_1=V_1*I_1\\\\1850=120*I_1\\\\I_1=\frac{1850}{120}=15.41666667\approx15.42A$

When the switch is in the 220 V position, the electric current is:

$P_2=V_2*I_2\\\\1850=230*I_2\\\\I_2=\frac{1850}{230}=8.043478261\approx8.04A$

Now, if the tourist plugs the dryer into a 230 V receptable without changing it to the 230 position, the power would be the product between the voltage of the receptacle and the current using by the dryer in its 120 V position:

$P=V_2*I_1=230*15.43=3545.833333\approx3545.83W$

As you can see, the power consume as a result of this mistake is by far greater than 1850W, that's the reason why it begins to smoke.