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Physics · Electricity

Current, resistance and potential difference

Use \(V = IR\) to link potential difference, current and resistance, and describe how to investigate the factors affecting resistance (Required Practical 3).

  • 6 key terms
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Warm-up

Answer each one, then check.

  1. 1

    Write the unit of resistance.

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    Ohm (\(\Omega\))

  2. 2

    What is the unit of potential difference?

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    Volt (V)

  3. 3

    Where is a voltmeter connected?

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    In parallel across the component

  4. 4

    What does a longer wire do to resistance?

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    Increases it

  5. 5

    What is a current?

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    A flow of charge

Learning Objectives

  1. 1Explain that current depends on resistance and potential difference.
  2. 2Recall and apply \(V = IR\).
  3. 3Describe how to investigate the resistance of a wire and of combinations of resistors (Required Practical 3).
  4. 4Interpret graphs of resistance against length.

V = IR

potential difference \(=\) current \(\times\) resistance \(V = IR\)

The greater the resistance of a component, the smaller the current for a given potential difference across it. Questions use the term potential difference; voltage also gains credit.

Method: Resistance and Length of a Wire

Required Practical 3, part 1.

  1. 1 Set up

    Connect the circuit with the ammeter in series and the voltmeter across the wire.
  2. 2 Set the length

    Clip the crocodile clips at 0.20 m, and record the pd and current.
  3. 3 Switch off between readings

    This keeps the wire at a constant temperature.
  4. 4 Repeat

    Take readings at 0.40 m, 0.60 m, 0.80 m and 1.00 m.
  5. 5 Calculate

    For each length \(R = V \div I\).
  6. 6 Plot

    Draw a graph of resistance against length: a straight line through the origin.

Method: Resistors in Series and Parallel

Required Practical 3, part 2.

  1. 1 Series

    Connect known resistors in series, measure V and I, calculate R = V ÷ I.
  2. 2 Parallel

    Repeat with the same resistors in parallel.
  3. 3 Compare

    The series combination has a larger resistance than either resistor; the parallel combination has a smaller one.

Calculating Current

A 12 V battery is connected across a 4.0 Ω resistor. Calculate the current.

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  1. 1 Rearrange \(I = V \div R\)
  2. 2 Substitute \(I = 12 \div 4.0\)
  3. 3 Answer \(I = 3.0\) A

Answer3.0 A

Calculating Potential Difference

A current of 0.50 A flows through a 20 Ω resistor. Calculate the potential difference across it.

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  1. 1 Write the equation \(V = IR\)
  2. 2 Substitute \(V = 0.50 \times 20\)
  3. 3 Answer \(V = 10\) V

Answer10 V

Calculating Resistance

A voltmeter reads 6.0 V and an ammeter reads 20 mA. Calculate the resistance.

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  1. 1 Convert the current \(20\) mA \(= 0.020\) A
  2. 2 Rearrange \(R = V \div I\)
  3. 3 Substitute \(R = 6.0 \div 0.020\)
  4. 4 Answer \(R = 300\ \Omega\)

Answer\(300\ \Omega\)

Getting Good Results

Why we switch off between readings.

  • Heating

    A current makes the wire hotter, and a hotter metal wire has a higher resistance.

  • Constant temperature

    Use a low current and switch off between readings.

  • Zero errors

    Check the meters read zero before starting.

  • Repeat

    Repeat and average to reduce random errors.

Predict the Graph

A student measures the resistance of 20 cm, 40 cm, 60 cm, 80 cm and 100 cm of a wire. What does the graph of resistance against length look like? A 30 cm length has a resistance of 1.8 Ω; what is the resistance of 90 cm?

1. Sketch the axes.

2. Use the ratio of lengths.

A good answer shows: A straight line through the origin: resistance is directly proportional to length. 90 cm is three times as long, so R = 5.4 Ω.

Can I...?

  1. 1Recall V = IR.
  2. 2Rearrange for I or R.
  3. 3Convert mA to A.
  4. 4Describe the resistance of wire method.
  5. 5Explain why the wire is switched off between readings.
  6. 6Draw a graph of R against length.
  7. 7Say what happens to resistance in series and parallel.
  8. 8Use the correct units.

Summary & Exam Focus

  • \(V = IR\).
  • Ammeter in series, voltmeter in parallel.
  • Longer wire means greater resistance.
  • Switch off between readings to keep the temperature constant.

Exam focus

A potential difference of 9.0 V is applied across a resistor and the current is 0.30 A. Calculate the resistance. (2 marks) (2 marks)

State the equation, substitute and give the unit Ω.

Key terms

The vocabulary this lesson expects you to use. Each one is linked from the first place it appears above.

Resistance
How much a component opposes the flow of current.
Ohm
The unit of resistance (Ω).
Potential difference
The energy transferred per coulomb; measured in volts.
Voltmeter
Measures pd; connected in parallel.
Constant temperature
Kept the same so the resistance does not change for other reasons.
Directly proportional
Doubling one quantity doubles the other.

Practice questions

Have a go at each one before you open its answer.

  1. Question 1 Calculate 2 marks

    The potential difference across a resistor is 9.0 V and the current through it is 0.30 A. Calculate the resistance of the resistor. Use the equation: potential difference = current × resistance

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    Model answer

    \(R = V \div I = 9.0 \div 0.30 = 30\ \Omega\)

    Mark scheme

    • Correct substitution — 1 mark
    • 30 Ω — 1 mark
  2. Question 2 Calculate 2 marks

    A current of 0.15 A flows through a 40 Ω resistor. Calculate the potential difference across the resistor.

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    Model answer

    \(V = IR = 0.15 \times 40 = 6.0\) V

    Mark scheme

    • Correct substitution — 1 mark
    • 6.0 V — 1 mark
  3. Question 3 Use the graph 4 marks

    A student investigates how the resistance of a wire depends on its length. The graph shows the results. (a) Describe the relationship shown by the graph. (b) Use the graph to find the resistance of 70 cm of the wire. (c) Suggest why the student switched off the current between readings.

    A straight line graph through the origin showing resistance against length of a wire.
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    Model answer

    (a) The resistance is directly proportional to the length (a straight line through the origin). (b) 4.2 Ω. (c) To stop the wire heating up, because a hotter wire has a higher resistance.

    Mark scheme

    • Straight line through the origin, or directly proportional — 1 mark
    • 4.2 Ω (accept 4.1 to 4.3) — 1 mark
    • To keep the temperature constant or stop the wire heating — 1 mark
    • Because temperature affects resistance — 1 mark
  4. Question 4 Describe 6 marks

    Describe an investigation to show how the resistance of a wire depends on its length. Your answer should include a circuit diagram description, the measurements you would take, and how you would keep the test fair and safe.

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    Model answer

    See levels-of-response scheme.

    Mark scheme

    • Level 3 (5 to 6 marks): a complete method with a correct circuit (ammeter in series, voltmeter across the wire), several lengths, calculation of R = V ÷ I for each, a graph, and control of temperature or safety — 5 to 6 marks
    • Level 2 (3 to 4 marks): a method with most of the equipment and measurements, but with gaps in the detail or control — 3 to 4 marks
    • Level 1 (1 to 2 marks): simple statements about measuring current and pd for wires — 1 to 2 marks
  5. Question 5 Explain 3 marks

    Two identical resistors are connected first in series and then in parallel. Explain, without calculation, how the total resistance of each arrangement compares with the resistance of one resistor.

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    Model answer

    In series the total resistance is greater than one resistor because the current has to pass through both. In parallel the total resistance is less than one resistor because there are two paths for the current.

    Mark scheme

    • Series greater — 1 mark
    • Parallel less — 1 mark
    • A reason for either — 1 mark
  6. Question 6 Calculate 3 marks

    A voltmeter reads 6.0 V and an ammeter reads 20 mA. Calculate the resistance of the component.

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    Model answer

    \(I = 0.020\) A; \(R = 6.0 \div 0.020 = 300\ \Omega\)

    Mark scheme

    • Converts 20 mA to 0.020 A — 1 mark
    • Correct substitution — 1 mark
    • 300 Ω — 1 mark

Quick check

  1. The unit of resistance is the...

    1. Avolt
    2. Bampere
    3. Cohm
    4. Dwatt
    Show answerHide answer

    C: ohm

    Resistance is measured in ohms (Ω).

  2. If the pd across a fixed resistor doubles, the current...

    1. Ahalves
    2. Bstays the same
    3. Cquadruples
    4. Ddoubles
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    D: doubles

    \(I = V \div R\).

  3. A 6 V supply across a 12 Ω resistor gives a current of...

    1. A0.5 A
    2. B2 A
    3. C72 A
    4. D6 A
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    A: 0.5 A

    \(6 \div 12 = 0.5\) A.

  4. A longer wire has...

    1. Aa smaller resistance
    2. Ba greater resistance
    3. Cno resistance
    4. Dthe same resistance
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    B: a greater resistance

    Resistance increases with length.

  5. Why switch off the current between readings?

    1. ATo save the battery only
    2. BTo reset the ammeter
    3. CThe wire would heat up and its resistance would change
    4. DTo stop the voltmeter reading
    Show answerHide answer

    C: The wire would heat up and its resistance would change

    Temperature affects resistance.

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