Curious question on resistance, current and light-bulb output?

Question

An incandescent bulb's power rating increases with light output, P=V*I. Voltage is constant, so higher wattage bulbs use more energy because of higher current flow per time unit. I've always assumed that all lightbulb filaments use the same tungsten alloy composition, ie have the same resistivity and the only difference between them was in the thickness and length of the filaments.

To allow a higher current flow (at higher wattage), resistance must be lowered, ie use a thicker filament so the higher current causes higher heat output through the filament. I believe that thicker filaments allow higher current because the larger cross-section of a conducter allows higher rate of electron flow per unit time.

Yet I seem to recall that it was the higher rated bulbs that had the THINNER filaments with more coils, etc increasing the length as well. How can this be? Is my memory at fault here (100W bulbs here in the UK no longer on sale so unable to check!)?

Answer 1

Your assumptions in the first two paragraphs are seemingly correct. Same flavor of tungsten is used, it is geometry which must change such that resistance must change.



Resistance must decrease, such that more power can be dissipated. R = V^2/P is your equation to which to pay attention.



However, if you notice in higher power rated bulb filaments, the filaments are cross-connected, enabling more paths for current to flow, decreasing equivalent resistance.



You see, the design of these filaments is subjected to an additional consideration. Thermal considerations, primarily involving selection of surface area, based on the physical model of gray body radiation. They need to design the correct surface area, such that the temperature of the tungsten fits in a certain range during operation. It must be hot enough to glow with a seemingly white spectrum, BUT, it must glow cold enough, such that the tungsten doesn't melt.

Answer 2

You can only use tungsten filaments at a standard temperature which is a certain fraction of the melting point of tungsten.So the only way to get more light output is to increase the surface area of the filament.For instance you could use any number of separate bulbs in parallel or you could effectively engineer several ordinary filaments in parallel in the same glass envelope;lstly you might design a ribbon shaped filament so that you increase the ratio of emitting surface area to cross section.

Answer 3

One problem with increasing the thickness or shortening the wire is that the energy density increases. So for a 100W light bulb, the filament will get hotter than a 30W bulb with the same length. Most likely, the 100W bulbs use a different alloy of tungsten or adjust the properties to achieve the proper light output, power density, and temperature rise.