What determines the brightness of bulbs?

[erinec]

Homework Statement

This is not a specific problem, but I am wondering, what exactly determines the brightness of identical bulbs? The current going through it? The voltage? Something else? Thanks.

Homework Equations

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The Attempt at a Solution

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[jambaugh]

The brightness will be directly a function of temperature of the filament and how much surface area the filament has. But the cause of the temperature is ohmic heating which is proportional to the current times the voltage drop across the filament (amps times volts = watts). This voltage in turn is proportional to the resistance times the current and so you get Power = R I^2 = V^2/R.

Assuming your voltage source is a constant then making a brighter bulb involves reducing the resistance. You make a thicker filament. But you don't want the temperature to change so you make it thicker and longer so there's more surface area to radiate the energy. (Too hot and the filament will melt and the bulb burns out, too cool and you are making a heat lamp instead of a light).

In general the resistance will be proportional to the length over the cross sectional area of the filament or length/radius^2.

Thus the power utilized will be proportional to voltage^2 * radius^2/length.
Let's say P = C r^2/L

The surface area will likewise be proportional to length * radius and that will be proportional to the power radiated. Let's say P = DrL.
Multiply the two and you'll see that P^2 = CDr^3, or P is proportional to r^3/2 given the conditions of constant voltage and fixed temperature.