All subjects · Physics · WPH12 (Unit 2)

I-V graphs and why resistance changes

Different components have different current-potential difference (I-V) graphs. Charge carriers explain why resistance changes with temperature and light.

I-V characteristics

Resistance at any point is V / I at that point, not the gradient.

Metals and temperature

Using I = nqvA: in a metal, n (number of conduction electrons per m3) does not change with temperature. Heating makes the lattice ions vibrate more, so conduction electrons collide more often and their drift velocity v falls. For the same p.d., current falls, so resistance rises.

NTC thermistors and temperature

In a semiconductor such as an NTC thermistor, heating gives electrons enough energy to become conduction electrons, so n increases greatly. This effect is much bigger than the extra lattice vibrations, so resistance falls as temperature rises.

LDRs and light

In a light-dependent resistor, absorbed light gives electrons the energy to become conduction electrons. More light means larger n, so resistance falls.

Worked example

A filament lamp passes 0.15 A at 2.0 V and 0.30 A at 6.0 V. Find its resistance at each p.d.

  1. R = 2.0 / 0.15 = 13 Ω
  2. R = 6.0 / 0.30 = 20 Ω

Answer: The resistance rises from 13 Ω to 20 Ω as the filament heats up.

Key idea: R = V/I at each point. Hot metal: more lattice vibrations, lower drift velocity, higher R. NTC thermistor and LDR: more charge carriers (n rises), lower R.

Check yourself

  1. What shape is the I-V graph (I on the y-axis) of a filament lamp?
    • A curve getting less steep as p.d. increases
    • A straight line through the origin
    • Zero current until about 0.6 V, then steep
    • A curve getting steeper as p.d. increases
    Show answer

    A curve getting less steep as p.d. increases. As the filament heats, resistance rises, so each extra volt adds less current.

  2. A filament lamp passes 0.50 A when the p.d. across it is 12 V. Find its resistance at this p.d., in Ω.
    Show answer

    24 Ω. R = V / I = 12 / 0.50 = 24 Ω.

  3. What happens when a diode is reverse biased?
    • Almost no current flows
    • A large current flows
    • It obeys Ohm's law
    • It lights up brightly
    Show answer

    Almost no current flows. A diode has a very high resistance in the reverse direction.

  4. Why does the resistance of a metal increase with temperature?
    • More conduction electrons are released
    • The metal expands, so electrons move faster
    • The charge on each electron increases
    • Lattice ions vibrate more, so electrons collide more and their drift velocity falls
    Show answer

    Lattice ions vibrate more, so electrons collide more and their drift velocity falls. n stays about the same; the drift velocity falls.

  5. Why does the resistance of an NTC thermistor fall as it is heated?
    • The lattice ions stop vibrating
    • More charge carriers are released, so n increases
    • Its length decreases
    • The electrons slow down
    Show answer

    More charge carriers are released, so n increases. The rise in n outweighs the extra lattice vibrations.

  6. Light shining on an LDR gets brighter. What happens to its resistance and why?
    • It rises, because the electrons collide more
    • It stays the same
    • It rises, because n decreases
    • It falls, because more conduction electrons are released
    Show answer

    It falls, because more conduction electrons are released. Absorbed light frees more charge carriers.

  7. On an I-V graph of a non-ohmic component, how do you find its resistance at a point?
    • Find the gradient at that point
    • Divide V by I at that point
    • Find the area under the graph
    • Find the gradient and square it
    Show answer

    Divide V by I at that point. R = V / I is the definition; the gradient of a curve does not give R.

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Last updated 7 November 2026. Spotted a mistake? Tell us.