Question

You plan to take your hair dryer to Europe, where the electrical outlets put out 240 V instead of the 120 V seen in the United States. The dryer puts out 1600 W at 120 V. (a) What could you do to operate your dryer via the 240-V line in Europe? (b) What current will your dryer draw from a European outlet? (c) What resistance will your dryer appear to have when operated at 240 V across the inductor, the capacitor, and the resistor?

Short answer

a)To operate the dryer, use a step down transformer with $\frac{{\mathrm{N}}_2}{{\mathrm{N}}_1}=0.5$.The dryer will draw a current I=6.67A.c)The dryer will appear to have a resistance $\mathrm{R}=36\mathrm{\Omega }$.

Step-by-step solution

Step-1: Formulas used  

A transformer is a device that transfers electric energy from one alternating-current circuit to one or more other circuits, either increasing (stepping up) or reducing (stepping down) the voltage.

$\frac{{\mathbf{N}}_{\mathbf{2}}}{{\mathbf{N}}_{\mathbf{1}}}\mathbf{=}\frac{{\mathbf{V}}_{\mathbf{2}}}{{\mathbf{V}}_{\mathbf{1}}}$

The expression for average power is

${\mathbf{P}}_{\mathbf{avg}}\mathbf{=}{\mathbf{V}}_{\mathbf{1}}{\mathbf{I}}_{\mathbf{1}}$

The Ohm’s law relation to get the amplitude voltage V in the circuit.

V=IR

Step-2: Calculations for ratio of turns.

$$\begin{gathered} V_1=240V \\ {V}_2=120V \end{gathered}$$

$$\begin{gathered} \frac{{\mathrm{N}}_2}{{\mathrm{N}}_1}=\frac{120}{240\mathrm{V}} \\ =0.5 \end{gathered}$$

Therefore, to operate the dryer, use a step down transformer with $\frac{{\mathrm{N}}_2}{{\mathrm{N}}_1}=0.5$.

Step-3: Calculations for power.

At resonance,

$$\begin{gathered} {\mathrm{P}}_{\mathrm{avg}}={\mathrm{V}}_1{\mathrm{I}}_1 \\ {\mathrm{P}}_{\mathrm{av}}=1600\mathrm{W} \\ {\mathrm{I}}_1=\frac{1600\mathrm{W}}{240\mathrm{V}} \\ =6.67\mathrm{A} \end{gathered}$$

Therefore, the dryer will draw a current I=6.67 A .

Step-4: Calculations for effective resistance of dryer.

$$\begin{gathered} \mathrm{R}=\frac{{\mathrm{V}}_1}{{\mathrm{I}}_1} \\ =\frac{240\mathrm{V}}{6.67\mathrm{A}} \\ =36\mathrm{\Omega } \end{gathered}$$

Therefore, to operate the dryer, use a step down transformer with $\frac{{\mathrm{N}}_2}{{\mathrm{N}}_1}=0.5$.The dryer will draw a current I=6.67 A .c) The dryer will appear to have a resistance $\mathrm{R}=36\mathrm{\Omega }$.