How filament lamps work
Tungsten filament lamps generate visible light by passing an electric current through a wire filament. The wire filament is heated to a high temperature of around 2500 to 3000 degrees Celsius by the current due to electrical resistance.
Tungsten filament lamps have been around since the 1920s. Although they are used in a huge variety of applications we will only be looking at automotive applications in this discussion.
The wire filament has a resistance that varies with temperature. As the temperature rises so does the electrical resistance. This is called a positive temperature coefficient. In operation the filament lamp will start off at ambient temperature. Then, as the current starts to flow the filament will heat up rapidly and the resistance of the filament will also rise. There will be a stable point where the resistance and current settle to the designers values and the lamp will be producing enough heat to glow white hot.
Filament evaporation
Most of the power used by a filament lamp is wasted as heat (95% – 97%) and the light (3% – 5%) is just a by-product. The critical part to understanding the failure of tungsten filament lamps is to realise that a process of filament evaporation takes place. Tungsten at high temperature releases tungsten particles that are deposited on the inside of the glass bulb or combine with the gas filling the bulb. Places where tungsten is evaporated from the filament become smaller in cross section and therefore have reduced physical strength. Weak spots along the filament become places where breakages can occur.
Irregularities in the cross section of the filament can cause hot spots to develop. These hot spots can significantly reduce the lamp service life and make it susceptible to failure from vibration.
This Incandescent light bulb article on Wikipedia discusses filament evaporation in much more detail.
Calculating power dissipation
Ohms Law relates the voltage, resistance, and current in an electrical circuit. Power in an electrical circuit is a product of Voltage and Current.
I measured the cold resistance of a new H4 12Volt 55Watt lamp as 0.6 ohms.
The resistance of a circuit can be calculated as Resistance = Volts squared / Power. To dissipate 55 watts at 12 volts this lamp needs to have an operating resistance of 12 x 12 / 55 = 144 / 55 = 2.62 ohms which is a bit over four times the cold resistance.
The initial power dissipated by a cold filament can be calculated as Power = Volts squared / Resistance which is 12 x 12 / 0.6 = 144 / 0.6 = 240 Watts. You can see that the initial power dissipated in the lamp is around four times that the lamp is designed to operate at normally.
Thermal Shock
Tungsten is a metal with a melting point of 3422 C (3,695 K). In order to manufacture a durable lamp filament tiny amounts of Potassium, Silicon, and Aluminium are added to the Tungsten in a process called doping.