Required practicals › EMF and internal resistance of a cell

REQUIRED PRACTICAL 6

EMF and internal resistance of a cell

Measuring how the terminal potential difference of a cell falls as the current drawn from it rises, and extracting the emf and internal resistance.

Theory: EMF and internal resistance

What you are trying to do

Measure how a cell's terminal pd falls as the current drawn from it rises, and extract the emf and internal resistance from the graph.

Apparatus

  • The cell under test, in a holder
  • Variable resistor to set the current
  • Ammeter in series, voltmeter across the cell's terminals
  • A switch, kept open except while reading

Variables

  • Independent: the current, set by the variable resistor
  • Dependent: the terminal pd
  • Control: the cell itself: temperature and state of charge, protected by keeping the switch open between readings

Method

A real cell modelled as a perfect emf in series with an internal resistance, hidden inside the caseinside the batteryε = 1.5 Vr = 0.50 ΩR = 2.5 ΩI = 0.50 Aterminal pd V = 1.25 V
FIG. 1The model being tested: a perfect emf in series with a small internal resistance, both hidden inside the cell's case.
  1. Set the variable resistor for a small current, close the switch, read both meters quickly, open the switch again.
  2. Step the resistance down to raise the current, covering as wide a current range as the cell sensibly allows, and repeat the sweep to check for drift.

Analysis

  1. The loop equation V = ε − Ir is already straight-line shaped: plot V against I.
Terminal pd against current: the intercept is the emf and the gradient is minus the internal resistanceIVεintercept: the emfgradient = −revery extra amp costs another Ir of terminal pd
FIG. 2The intercept on the V axis is the emf, because only at I = 0 are there no lost volts; the gradient is minus the internal resistance.
  1. Read ε from the intercept and r from the gradient, quoting r positive and noting the gradient is negative.

A worked set of readings

One sweep, switch closed only to read:

I / AV / V
0.201.40
0.401.30
0.601.20
0.801.10
1.001.00

The line has gradient -0.50 V A⁻¹ and V-axis intercept 1.50 V, so ε = 1.50 V and r = 0.50 Ω. Every row agrees: for instance 1.20 + 0.60 × 0.50 = 1.50 V.

Where the uncertainty comes from

  • The cell running down: Sustained current warms the cell and depletes it, drifting both ε and r mid-experiment; the open-switch habit is the control that matters most.
  • Meter resolution: The terminal pd changes by fractions of a volt across the whole sweep; a digital voltmeter's 0.01 V resolution is what makes the gradient readable.
  • Extrapolation: The intercept lies beyond the smallest measurable current, so the emf rests on extrapolating the line; a wide current range anchors it.
  • Ammeter position: The ammeter's own small resistance sits in the loop but outside the voltmeter's bracket, so it does not corrupt V or I; being able to say why is worth a mark.

What earns the marks

  • The switch stays open between readings, and the reason is thermal and chemical drift of the cell.
  • Intercept is ε; gradient is minus r. Both identifications are asked constantly.
  • The terminal pd equals the emf only at zero current; a high-resistance voltmeter alone across the cell reads (very nearly) ε for that reason.
  • Quote r as a positive resistance with the gradient stated negative.

Safety

Low voltages throughout; the only real hazard is a near-short at the lowest resistance settings, which heats the cell and the rheostat. Keep currents modest and the switch open when not reading.

Method and analysis here follow the standard approach; your school may vary the apparatus. Always follow your teacher’s risk assessment in the lab.