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4.7 Required Practical: Resistance of a Wire

GCSE Physics · AQA · Chapter 4: Electric Circuits

A free GCSE Physics lesson for AQA (8463) from OBA School: required practical: investigating how the resistance of a wire depends on its length. Watch the video, read the explanation and worked examples, then try the revision questions. You can work through the full lesson, with every video, practice quizzes and printable worksheets with mark schemes, in our free online course.

What you will learn

  • Set up a circuit with an ammeter and voltmeter to measure the resistance of a length of wire
  • Identify the independent, dependent and control variables, and the hazards and how to reduce them
  • Calculate resistance from V and I, plot R against length and find the gradient
  • Explain sources of error, including contact resistance and heating, and suggest improvements

Key words

  • Independent variable: The variable you change: here, the length of wire between the clips.
  • Dependent variable: The variable you measure: here, the resistance (from the p.d. and current).
  • Control variable: A variable kept the same so the test is fair: wire material, diameter, temperature.
  • Systematic error: An error that shifts every reading by the same amount, e.g. a zero error or contact resistance.
  • Random error: Unpredictable scatter in readings; reduced by repeating and taking a mean.
  • Resolution: The smallest change a measuring instrument can show, e.g. 1 mm on a metre rule.

Aim and apparatus

Aim: to find out how the resistance of a wire depends on its length.

Apparatus: battery or low-voltage power supply, switch, ammeter, voltmeter, variable resistor, a length of thin resistance wire (e.g. constantan) taped along a metre rule, two crocodile clips, connecting leads.

Method

1. Tape the wire along the metre rule so it is straight and tight. Fix one crocodile clip at the 0 cm mark.

2. Set up the circuit. Attach the sliding clip at 10 cm.

3. Close the switch. Use the variable resistor to set a small current (e.g. 0.20 A). Record the ammeter and voltmeter readings, then open the switch straight away.

4. Move the sliding clip 10 cm further along and repeat step 3, keeping the current the same.

5. Continue up to 80–100 cm. Repeat the whole set of readings two more times and find mean values.

6. Calculate the resistance for each length using R = V ÷ I.

  • independent; In this practical length of wire between the clips (cm or m)
  • dependent; In this practical resistance of the wire (calculated from V and I)
  • control; In this practical material of the wire; diameter (thickness) of the wire; temperature of the wire (small current, switch off between readings); same current

Hazards and safety

  • wire carrying current; Risk wire gets hot – burns to fingers; Control use a small current; switch off between readings; do not touch the wire while the switch is closed
  • short length of wire; Risk very small resistance → large current; Control start at 10 cm, not 0 cm; keep the variable resistor in the circuit

Results and analysis

  • 0.20; p.d. V (V) 0.266; Current I (A) 0.20; Resistance R = V ÷ I (Ω) 1.33
  • 0.40; p.d. V (V) 0.504; Current I (A) 0.20; Resistance R = V ÷ I (Ω) 2.52
  • 0.60; p.d. V (V) 0.746; Current I (A) 0.20; Resistance R = V ÷ I (Ω) 3.73
  • 0.80; p.d. V (V) 0.984; Current I (A) 0.20; Resistance R = V ÷ I (Ω) 4.92
  • The points lie on a straight line: resistance increases steadily with length. Doubling the length doubles the resistance (apart from the small intercept), so R is directly proportional to L.
  • Why? A longer wire means each electron has more ions to collide with on its way through.
  • The gradient is the resistance per metre of this wire: (4.90 − 0.10) ÷ 0.80 = 6.0 Ω/m.

Worked example: using the gradient

Predict the resistance of 2.5 m of the same wire.
R = 6.0 Ω/m × 2.5 m

Answer: about 15 Ω

Evaluation: errors and improvements

  • Contact resistance: the clips do not touch the wire perfectly, adding a little resistance to every reading. This is a systematic error – the line does not quite pass through the origin. It does not change the gradient.
  • Heating: if the current is too big or left on, the wire warms up and its resistance rises, so later readings are too high. Keep the current small and switch off between readings.
  • Measuring length: it is hard to see exactly where the clip touches the wire; read at eye level to avoid parallax. A metre rule has a resolution of 1 mm.
  • Random errors are reduced by repeating readings and calculating a mean; ignore anomalous results when finding the mean.

Exam tip: Improvements: use clips with a thin, sharp edge; use a wider range of lengths; take more readings; use digital meters with a higher resolution (e.g. 0.01 V).

Common mistakes

  • Connecting the voltmeter across the whole circuit or the battery instead of across the wire between the clips.
  • Leaving the current on so the wire heats up and its resistance changes.
  • Saying “resistance is proportional to length” when the line has a clear intercept – mention the contact resistance.
  • Plotting V against L without keeping the current the same – calculate R = V ÷ I for each length.

Revision questions

Try these, then check your answers below each one.

Question 1. In the investigation of how the resistance of a wire depends on its length, what is the independent variable? (Choose from: the length of the wire, the resistance of the wire, the current, the diameter of the wire.)

Answer: the length of the wire

Working: You change the length between the clips and measure the resistance (dependent).

Question 2. Why should the switch be opened between readings? (Choose from: To stop the wire heating up, which would change its resistance, To reset the ammeter to zero, To make the current larger, To change the length of the wire.)

Answer: To stop the wire heating up, which would change its resistance

Working: A current heats the wire; a hotter wire has a higher resistance, so temperature must be kept constant.

Question 3. With 50 cm of wire between the clips, the voltmeter reads 1.25 V and the ammeter reads 0.25 A. Calculate the resistance of this length of wire.

Answer: 5 Ω

Working: R = 1.25 ÷ 0.25 = 5.0 Ω.

Related lessons

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This lesson is section 4.7 (AGCPH0407) of our free GCSE Physics course for AQA. In the full course you get every video for this section, a self-marking practice quiz, a printable worksheet with a mark scheme, chapter tests, and your progress saved. Go to the full GCSE Physics course.

 

 

 

 

 

 

 

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