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P4 RP Required Practical: Resistance

GCSE Combined Science · AQA · Chapter P4: Electric Circuits

A free GCSE Combined Science: Trilogy lesson for AQA (8464) from OBA School: required practical: how the length of a wire affects its resistance, and resistors in series and in parallel. 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 circuits with an ammeter and a voltmeter to measure the resistance of a wire and of combinations of resistors
  • 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 use the gradient
  • Test the rules for resistors in series and in parallel using measured values
  • Explain sources of error, including contact resistance, heating and tolerance, and suggest improvements

Key words

  • Independent variable: The variable you change: the length of wire, or the arrangement of resistors.
  • 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.
  • Tolerance: How far a resistor’s real value may be from the value printed on it, e.g. ±5%.

Part 1: length of a wire – aim, apparatus and method

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

1. Tape a thin resistance wire (e.g. constantan) along a 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. 0.25 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 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)
  • 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

Part 1: results and analysis

  • 0.20; p.d. V (V) 0.290; Current I (A) 0.25; Resistance R = V ÷ I (Ω) 1.16
  • 0.40; p.d. V (V) 0.530; Current I (A) 0.25; Resistance R = V ÷ I (Ω) 2.12
  • 0.60; p.d. V (V) 0.790; Current I (A) 0.25; Resistance R = V ÷ I (Ω) 3.16
  • 0.80; p.d. V (V) 1.040; Current I (A) 0.25; Resistance R = V ÷ I (Ω) 4.16
  • The points lie on a straight line: resistance increases steadily with length. Apart from the small intercept, doubling the length doubles the resistance, so R is directly proportional to L.
  • Why? In a longer wire each electron has more ions to collide with on its way through.
  • The gradient is the resistance per metre of this wire: (4.15 − 0.15) ÷ 0.80 = 5.0 Ω/m.

Worked example: using the gradient

Predict the resistance of 1.8 m of the same wire.
R = 5.0 Ω/m × 1.8 m

Answer: about 9.0 Ω

Part 2: resistors in series and in parallel

Aim: to measure the total resistance of two resistors in series and in parallel and compare it with the individual resistances.

1. Measure V and I for R1 on its own, then for R2 on its own. Open the switch after each reading.

2. Connect R1 and R2 in series with the voltmeter across both. Record V and I.

3. Connect R1 and R2 in parallel with the voltmeter across the pair. Record V and I.

4. Repeat and find means. Calculate each resistance with R = V ÷ I.

  • R1 alone (15 Ω label); p.d. V (V) 3.00; current I (A) 0.197; R = V ÷ I (Ω) 15.2
  • R2 alone (33 Ω label); p.d. V (V) 3.00; current I (A) 0.092; R = V ÷ I (Ω) 32.6
  • R1 and R2 in series; p.d. V (V) 3.00; current I (A) 0.063; R = V ÷ I (Ω) 47.6
  • R1 and R2 in parallel; p.d. V (V) 3.00; current I (A) 0.289; R = V ÷ I (Ω) 10.4
  • Series: expected R1 + R2 = 15.2 + 32.6 = 47.8 Ω. Measured 47.6 Ω – the rule is supported.
  • Parallel: measured 10.4 Ω, which is less than the smaller resistor (15.2 Ω) – the rule is supported.

Worked example: percentage difference

The labels say 15 Ω and 33 Ω, so the expected series resistance is 48 Ω. The measured value is 47.6 Ω.
percentage difference = (48 − 47.6) ÷ 48 × 100

Answer: 0.8% – well within a ±5% resistor tolerance

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 or resistors warm up and their resistance rises. 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.
  • Resistor tolerance: real values can differ from printed values, so use your measured single-resistor values to work out expected totals.
  • 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 or 0.001 A).

Common mistakes

  • Connecting the voltmeter across the battery instead of across the wire (or the whole combination) being tested.
  • 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.
  • Expecting the parallel total to lie between the two resistances – it is less than the smallest.
  • 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. The diagram shows the circuit for investigating how the resistance of a wire depends on its length. Two meters are marked X and Y. Which meter is the voltmeter? (Choose from: X, Y, Neither.)

Answer: Y

Working: Meter Y is connected across the wire between the two clips (in parallel), so it is the voltmeter. Meter X is in series in the loop, so it is the ammeter.

Question 2. Why should the switch be opened between readings in this practical? (Choose from: To stop the wire heating up, which would change its resistance, To reset the voltmeter 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 40 cm of wire between the clips, the voltmeter reads 1.30 V and the ammeter reads 0.25 A. Calculate the resistance of this length of wire.

Answer: 5.2 Ω

Working: R = 1.30 ÷ 0.25 = 5.2 Ω.

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This lesson is section P4 RP (AGCSC3306) of our free GCSE Combined Science 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 Combined Science course.

 

 

 

 

 

 

 

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