Resistance changes with temperature and lightEdexcel A-Level Physics: Revision notes

Every explanation in this topic uses the same model. For a conductor with n charge carriers per unit volume, each of charge q, moving at mean drift velocity v through cross-section A:

I = nqvA

For a given p.d., the current (and so the resistance) depends on how many carriers there are (n) and on how freely they drift (v). Resistance changes with temperature or light only if n or v change. The two effects that can change are:

• lattice vibrations: the metal or semiconductor ions vibrate with larger amplitude when hot, so collisions with moving charge carriers are more frequent and v falls
• number of carriers n: heating or light can free more electrons from atoms

In a metal the number of conduction electrons per unit volume is already very large (about 10²⁸–10²⁹ m⁻³) and heating hardly changes it. As the temperature rises the ions vibrate with larger amplitude, so conduction electrons collide with them more frequently. The mean drift velocity decreases for a given p.d., so the current falls and the resistance increases.

The change is fairly small and steady. For example, a platinum coil of 100 Ω at 0 °C has a larger resistance at higher temperature, which is why it is used in resistance thermometers.

For the same p.d., a smaller current means a smaller v = I/nqA.

A negative temperature coefficient (NTC) thermistor is made from a semiconductor, which has far fewer charge carriers than a metal. On heating, more electrons gain enough energy to break free from their atoms, so n increases greatly. The lattice vibrations also increase and reduce v, but the increase in n is far greater than the decrease in v.

Overall the current for a given p.d. rises, so the resistance decreases, by a large factor over a modest temperature range.

Worked example: a thermistor has 8.0 kΩ at 15 °C and 1.2 kΩ at 60 °C. Across 5.0 V, P = V²/R gives 3.1 mW at 15 °C and 21 mW at 60 °C. The power rises as the resistance falls.

A light-dependent resistor (LDR) is also made from a semiconductor. Photons of light are absorbed and give electrons enough energy to escape from their atoms. The number of conduction electrons per unit volume n increases, so the current for a given p.d. rises and the resistance falls as the light intensity rises.

Worked example: an LDR of 1.5 kΩ in bright light and 90 kΩ in the dark, across 3.0 V, carries 2.0 mA in bright light and 33 μA in the dark.

Unlike the thermistor, the change is caused by light rather than heating, and the explanation depends only on the change in n.

• Metal, temperature rises: n roughly constant, v falls, so resistance rises (slightly).
• NTC thermistor, temperature rises: n increases a lot, v falls a little, so resistance falls (a lot).
• LDR, light increases: n increases, so resistance falls.

The key difference is the starting number of carriers. A metal already has huge n, so extra heating cannot add to it significantly, while a semiconductor has few carriers, so adding even a small number gives a large fractional increase.

Worked example: an LDR has current 0.30 mA in a dim room and 15 mA in sunlight at 6.0 V. R changes from 20 kΩ to 400 Ω, a factor of 50, so n must rise by about 50 times if v is nearly unchanged.