Resistors: The resistance of a filament lamp increases as the temperature of the filament increases.

The idea

A filament lamp contains a thin metal wire that glows when current passes through it. As the current increases, more energy is transferred to the filament each second, so its temperature rises. In a metal, higher temperature makes the ions vibrate more strongly, which increases the number of collisions with the moving electrons and so increases resistance. This means the current–potential difference graph curves: the gradient decreases as potential difference increases, showing that resistance is not constant. At low potential differences the filament is cool and resistance is lower; at higher potential differences it is hot and resistance is higher.

What earns the marks

• State that a larger current through a filament transfers more energy per second, increasing the filament's temperature.
• Explain that increased temperature makes the metal ions vibrate more, increasing collisions with electrons and so increasing resistance.
• Describe the current–potential difference graph for a filament lamp as a curve whose gradient decreases as potential difference increases.
• Use R = V ÷ I at two points on the characteristic to show that resistance is larger at the higher potential difference.
• Recognise that the lamp is non-ohmic because its resistance changes, so it does not obey Ohm's law.

Common mistakes and how to put them right

• Claiming that resistance increases because current is 'used up'.

  Put it right by explaining that current is the same throughout the series circuit and heating causes the resistance change.

• Saying the graph is a straight line that simply bends.

  Put it right by describing a curve of decreasing gradient.

• Thinking resistance falls as the filament gets hotter.

  Put it right by linking higher temperature to more ion vibration and greater resistance.

Exam tips

• When comparing resistances from a graph, calculate V ÷ I at each point and state the numerical values with units.
• Use the phrase 'energy transferred to the filament increases its temperature' to link current to heating.
• Sketch the characteristic with axes labelled potential difference and current, showing the curve flattening at higher values.