Current, resistance and potential difference: the length of a wire at constant temperature

The idea

For a metallic wire kept at constant temperature, resistance is directly proportional to length. Doubling the length doubles the resistance because the charge carriers must travel through twice as many lattice ions, so they make more collisions that oppose their flow. This relationship is described by R ∝ L, and it holds only while temperature and the material and thickness of the wire stay the same. A useful method is to connect a wire in series with an ammeter and a cell, place a voltmeter in parallel across a measured length, and calculate R = V ÷ I for several lengths. Plotting resistance against length should give a straight line through the origin.

What earns the marks

• State that resistance is directly proportional to the length of a metallic wire when temperature is constant, so R ∝ L.
• Explain the proportionality in terms of charge carriers colliding with more lattice ions as the wire gets longer, which increases opposition to current.
• Describe a valid method: measure current with an ammeter in series and potential difference with a voltmeter across a measured length, then calculate R = V ÷ I.
• Interpret a graph of resistance against length as a straight line through the origin, and use it to predict resistance at a new length.
• Recognise that the relationship only applies if the material, cross-sectional area and temperature of the wire are kept constant.

Common mistakes and how to put them right

• Thinking resistance is inversely proportional to length.

  Put it right: For a wire at constant temperature, resistance increases as length increases, so R ∝ L.

• Connecting the voltmeter in series with the wire.

  Put it right: A voltmeter is connected in parallel across the length being tested so it measures the potential difference across that section.

• Ignoring temperature changes caused by a large current.

  Put it right: Use a small current or switch off between readings so the wire stays at approximately constant temperature.

Exam tips

• When describing the method, name each component and state where it is connected: ammeter in series, voltmeter in parallel across the measured length.
• Use the phrase 'directly proportional' only when you can justify a straight-line graph through the origin.
• If asked to improve the investigation, suggest measuring length with a ruler and keeping the wire taut, and repeating readings to reduce random error.