Question

In Europe the standard voltage in homes is 220 V instead of the 120 used in the United States. Therefore a “100-W” European bulb would be intended for use with a 220-V potential difference (see Problem 25.36). (a) If you bring a “100-W” European bulb home to the United States, what should be its U.S. power rating? (b) How much current will the 100-W European bulb draw in normal use in the United States?

Short answer

1. The U.S power rating for a 100-W European bulb is 29.8 W.
2. The current drawn by a 100-W European bulb is 0.248 A.

Step-by-step solution

(a) Determination of the U.S power rating for 100-W European bulb.

The expression of power is,

$P=\frac{V^2}{R}$

The ratio of power dissipation for the U.S to the European is,

$$\begin{gathered} \frac{{\mathrm{P}}_{\mathrm{US}}}{{\mathrm{P}}_{\mathrm{E}}}=\frac{{\mathrm{V}}_{\mathrm{US}}^2/\mathrm{R}}{{\mathrm{V}}_{\mathrm{E}}^2/\mathrm{R}} \\ ={\left[\frac{{\mathrm{V}}_{\mathrm{US}}}{{\mathrm{V}}_{\mathrm{E}}}\right]}^2 \\ ={\left[\frac{120\mathrm{V}}{220\mathrm{V}}\right]}^2 \\ {\mathrm{P}}_{\mathrm{US}}=(100\mathrm{W}){\left[\frac{120\mathrm{V}}{220\mathrm{V}}\right]}^2 \\ =29.8\mathrm{W} \end{gathered}$$

Thus, the U.S power rating for the 100-W European bulb is 29.8 W.

(b) Determination of the current drawn by 100-W European bulb.

Expression of power in terms of voltage and current is,

P = Vl

Solve for current I,

$$\begin{gathered} \mathrm{l}=\frac{\mathrm{P}}{\mathrm{V}} \\ =\frac{\left(29.8\mathrm{W}\right)}{\left(120\mathrm{V}\right)} \\ =0.248\mathrm{A}. \end{gathered}$$

Thus, the current drawn by 100-W European bulb is