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4.4.3Electrons, Waves and Photons

Determining Internal Resistance

5 min read 5 parts Lesson 36 of 62 Unit quiz

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Section 1 of 5The Experiment

4.4.3 Determining Internal Resistance

Varying the external resistance changes the current, and the terminal p.d. responds in a predictable way.

1
Connect the cell in series with a variable resistor, an ammeter and a switch, with a voltmeter connected across the cell terminals.
2
With the switch open, record the voltmeter reading, which is the e.m.f. because no current flows.
3
Close the switch, set the variable resistor to its largest value and record the current I and terminal p.d. V.
4
Reduce the resistance in steps, recording V and I each time, to obtain at least eight readings across the full range.
5
Open the switch between readings so the cell is not drained, which would otherwise change its e.m.f. and internal resistance.

Section 2 of 5Analysing the Data

Equation
  • Rearranging ε = V + Ir gives V = ε − Ir, which has the form of a straight line, y = c + mx.
Graph
  • Plot terminal p.d. V on the vertical axis against current I on the horizontal axis.
Intercept
  • The vertical intercept is the e.m.f. ε, found where the line meets the axis at zero current.
Gradient
  • The gradient is −r, so the internal resistance is the magnitude of the gradient of the line.

Section 3 of 5Improving Reliability

Improving Reliability
Variables
  • The independent variable is the load resistance and the dependent variables are V and I.
Controls
  • Keep the same cell and use the circuit only briefly, so heating does not alter its properties.
Protection
  • A resistor in series with the cell protects it from large currents when the variable resistor is at its minimum.
Repeats
  • Repeat the readings or use a data logger and draw a best-fit line to reduce random errors.

Section 4 of 5Worked Example

Question

  • A graph of terminal p.d. against current is a straight line passing through 1.50 V on the vertical axis and through the point (0.60 A, 1.20 V).
  • Find the e.m.f. and internal resistance.

  1. The vertical intercept gives ε = 1.50 V.
  2. Gradient = (1.20 − 1.50) / (0.60 − 0) = −0.50 V A⁻¹.
  3. Internal resistance r equals the magnitude of the gradient, 0.50 Ω.
  4. CheckV = ε − Ir = 1.50 − 0.60 × 0.50 = 1.20 V, as measured.
    What the symbols mean: E or ε = e.m.f. (V) · I = current (A) · R = external resistance (Ω) · r = internal resistance (Ω) · V = terminal p.d. (V)

Answer ε = 1.50 V and r = 0.50 Ω.

Section 5 of 5Exam Checklist & Tips

4.4.3 – Key Points for the Exam

  • Variable resistor A component whose resistance can be changed to vary the current.
  • Intercept The value of V where the line crosses the axis at I = 0, equal to e.m.f.
  • Gradient The slope of the V–I line, equal to minus the internal resistance.
  • Best-fit line A line drawn through the data showing the overall trend, with points scattered evenly about it.

Common Mistakes

  • Taking the gradient as +r; the line slopes downwards so the gradient is −r.
  • Leaving the switch closed between readings so the cell warms and drains.
  • Plotting I against V and then reading the wrong quantity from the gradient.
  • Using too few readings or a narrow range of resistance, which reduces accuracy.
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