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.