In europe the standard voltage in homes is 220 v instead of the 120 v used in the united states. therefore "100-w" european bulb would be intended for use with a 220-v potential difference. (a) if you bring a "100-w" european bulb home to the untied states, what should be its us power rating? (b) how much current will the 100-w european bulb draw in normal use in the united states?

One very handy dandy formula for electrical power used by a device is

Power = (voltage)² / (resistance)

I can see two ways to solve the problem using this formula.

Way #1:

We know the bulb uses 100 watts when goosed with 220V.  What is the bulb's resistance ?

Power = (voltage)² / (resistance)

100 w = (220v)² / R

Divide each side by (220v)² :

1/R = (100w) / (220v)²

Take the reciprocal of each side:

R = (220v)²/(100w)

R = 484 ohms

OK. Now plug the bulb into 120 volts:

Power = (voltage)² / (resistance)

Power = (120v)² / (484 ohms)

Power = 29.75 watts

and

Current = (voltage) / (resistance)

Current = (120v) / (484 ohms)

Current = 0.248 Ampere

Way #2:

Power = (voltage)² / (resistance)

Just look at that formula for a second.  It says that the power used is proportional to the (voltage) SQUARED.  This may be all the information we really need.

Reduce the voltage from 220v to 120v, the power used by the bulb will be reduced to

(120/220)²  = (0.5454)²  =  0.2975 of the original power  

And there you go.  0.2975 of the original 100w is 29.75 watts.

And finally, using Way #2:

Power = (voltage) x (current)

29.75w = (120v) x (current)

Current = (29.75 / 120) (w/v)

Current = 0.248 Ampere

Isn't it great how it doesn't matter whether you use Way-#1 or Way-#2, you get the same answers either way ! ? !  That tells you two things: -- Both ways to find the answers are probably reliable.  -- The answers are probably correct.

You're a good bot.  Go tell your masters that you successfully tricked a Ace into spending a half hour of his time on your purposeless question.