Why a filament lamp's resistance rises

By the end of this lesson

By the end you can explain, in terms of temperature and collisions, why the resistance of a filament lamp rises as the current through it increases, and read a resistance from a lamp's I–V characteristic at any point.

A lamp's I–V curve is not a straight line

For a metallic conductor at constant temperature the I–V graph is a straight line through the origin: doubling the p.d. doubles the current, so $R = V/I$ is constant (Ohm's law).

A filament lamp fails that condition. Its characteristic curves over:

p.d. $V$ / V	current $I$ / A	$R = V/I$ / Ω
1.2	0.10	12
3.0	0.19	16
6.0	0.25	24

As the p.d. rises, the current rises more and more slowly. Because $R = V/I$ , the ratio $V/I$ climbs at every step — the resistance is not a fixed property of the lamp.

Two things to keep straight:

The lamp still obeys $R = V/I$ at every point — that equation is the definition of resistance.
What it does not obey is Ohm's law, $I \propto V$ at constant temperature. The filament's temperature is not constant; that is exactly why it is called non-ohmic.

Worked example: Resistance at two operating points

A filament lamp has a p.d. of $2.4\ \text{V}$ when the current is $0.20\ \text{A}$ , and a p.d. of $9.0\ \text{V}$ when the current is $0.30\ \text{A}$ .

Calculate the resistance at each point and comment on the change.

Have a go first?

Quick check

Multiple choiceQuestion 1 · Recall

CalculateQuestion 2 · Apply

Answer the 2 questions above to continue.