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I'm looking for a jump start with this one. I'm having trouble getting started.

The tungsten wires of all electric light bulbs are designed to glow at about the same temperature. This requires, as a first approximation, that the power per unit surface area of the filament be the same for all.

a) Show that this leads to the requirement, at constant voltage, that r/l^2 is constant, where r is the radius and l is the length of the filament.

b) If P2/P1 = n is the ratio of the power consumption of two different light bulbs, show that r2/r1 = n^(2/3) and that l2/l1 = n^(1/3).

I've got lots of formulas, but I'm having trouble putting them together to show what a) and b) ask for. I'm sure once I get a), b) will follow easily.

P = I^2*R => I is current; R is resistance

R = pl/A => p is resistivity; A is surface area; l is length

A = [pi]r^2

P = I^2(pl/A) => P = I^2(pl/([pi]r^2))

P = V^2/R where V is potential

V^2 = (I^2)(R^2) => V = IR

So I'm going around in circles and getting nowhere.

Any clues would be greatly appreciated. I have a feeling the answer is staring me straight in the face, but I'm not seeing it.

Thanks much.

The tungsten wires of all electric light bulbs are designed to glow at about the same temperature. This requires, as a first approximation, that the power per unit surface area of the filament be the same for all.

a) Show that this leads to the requirement, at constant voltage, that r/l^2 is constant, where r is the radius and l is the length of the filament.

b) If P2/P1 = n is the ratio of the power consumption of two different light bulbs, show that r2/r1 = n^(2/3) and that l2/l1 = n^(1/3).

I've got lots of formulas, but I'm having trouble putting them together to show what a) and b) ask for. I'm sure once I get a), b) will follow easily.

P = I^2*R => I is current; R is resistance

R = pl/A => p is resistivity; A is surface area; l is length

A = [pi]r^2

P = I^2(pl/A) => P = I^2(pl/([pi]r^2))

P = V^2/R where V is potential

V^2 = (I^2)(R^2) => V = IR

So I'm going around in circles and getting nowhere.

Any clues would be greatly appreciated. I have a feeling the answer is staring me straight in the face, but I'm not seeing it.

Thanks much.

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