13.6.3 Filament

The filament of an incandescent bulb is typically made of tungsten. By design, the filament is supposed to be freaking hot (and hence glows) when the rated voltage[1] is connected across it.

The resistivity of tungsten (and other metals too) is highly dependent on temperature. At higher temperature, the metal lattice vibrates more vigorously and saps more energy from the drifting electrons. This corresponds to a higher resistivity, resulting in an increase in the resistance of the filament.

As a result, the I–V graph of a filament is a flattening curve at high V values. By the “wiper lines” leaning more and more towards the V-axis, we can tell that the resistance of the filament increases with V. This is because as the voltage across the filament increases, so does the current, and thus the power dissipation $(P=VI)$ . Higher power dissipation results in a hotter filament, which has a higher resistance. This is why the I–V graph of a filament is straight only at low voltage and power. Once the voltage and power are high enough and the filament starts to heat itself up, the graph starts to flatten.