Question

In Europe the standard voltage in homes is 220 V instead of the 120 V used in the United States. Therefore a "100-W" European bulb would be intended for use with a 220-V potential difference (see Problem 25.40). (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?

Answer 1

Answer:

a) The US power rating for the european bulb must be 27.27 W

b) The current in the United Stated for the european bulb is 0.227A

Explanation:

First of all the bulb is not going to light in 120V like it does in 220V, the bright is going to be much lower (near 1/4). Now, lets take a look on a circuit perspective:

The bulb in a circuit is modeled like a simple resistor, so we have a resistor conected to a voltage source, see figure 1. There we have a current $I_{1}$ given by:

$I_{1}=\frac{V_{1} }{R}$

Where $V_{1}$ is the 220v Input voltage, R is the resistance from the bulb. In the problem we have the power consumption in watts given by:

$W_{1}= V_{1]*I_{1}$

Clearing $I_{1}$

$I_{1} =\frac{I_{1}}{W_{1} } =\frac{100}{220} =0.4545 A$

Now, from ohm's law

$\frac{V_{1}  }{I_{1} } =R=\frac{220  }{0.4545 }=484 ohm$

So 484 ohm is the resistance from the bulb.

Now in the circuit lets replace the voltage source from 220v to 120v and lets calculate the current, and the power consuptiom

$I_{2}= \frac{V_{2}}{R}=\frac{110}{484}  =0.227 A$

And the power consuptiom:

$W_{2}= V_{2]*I_{2}=110*0.227=27.27Watts$