Pop quiz, hotshot: The brightness of a light bulb depends on the bulb's
Sure, for *identical* bulbs, voltage and/or current will kind of relate to brightness. For a fixed resistance, the equations I2R and V2/R show that with the same resistance, power, and therefore brightness, will increase as current or voltage increases. However, you'll eventually get into trouble assuming that a bulb carrying more current is necessarily brighter than one carrying less current.
It's pretty straightforward to show experimentally that voltage does not necessarily correlate with a bulb's brightness. Just get a bunch of miniature flashlight bulbs and holders from Radio Shack or Harbor Freight or somewhere. Be sure to get bulbs with different voltage and current ratings, so that their resistances are different. Connect them in parallel to a battery -- they will take the same voltage, but will NOT be just as bright as one another.
Michael Gray, a veteran of my 2010 AP Summer Institute and a frequent contributor to this column, came up with a much cleverer and more subtle demonstration. He showed with a single light bulb that the bulb's brightness depends on the power, not the voltage or current. How? He measured the bulb's brightness directly with a Vernier light sensor. Of course! Brilliant.
He connected a bulb to a battery. He showed that, by the equation V2/R, doubling the bulb's voltage should not just double the bulb's brightness, but quadruple the brightness. He darkened the room, and placed a light sensor a fixed distance from the bulb. He zeroed the sensor for the ambient light, and turned the bulb on. When he doubled the bulb's voltage, the sensor reading quadrupled. Physics works.
I will certainly use this demonstration next year. Thanks, Michael!