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TL;DR
Connect a voltmeter across a cell and an ammeter in series with a variable resistor. Vary the resistance, record terminal p.d. () and current () for 6--8 settings, then plot against . The graph is a straight line with a negative gradient: the y-intercept gives the EMF () and the magnitude of the gradient gives the internal resistance (
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Use the O-Level Physics Experiments hub to find companion drills for every Paper 3 skill. For circuit-wiring fundamentals, see the ammeter and voltmeter connection guide.
The EMF of a cell, written , is the total energy transferred per unit charge by the cell when it drives current around a complete circuit. It is measured in volts (V). EMF is not a force - the name is historical.
When no current flows (open circuit), the terminal p.d. equals the EMF because there is no energy lost inside the cell.
Every real cell has some resistance of its own, called the internal resistance . It arises from the chemical paste, electrolyte, and electrode contacts inside the cell. When current flows, charge must pass through this internal resistance, so some energy is dissipated inside the cell as heat.
The relationship between terminal p.d., EMF, and internal resistance is:
where:
Rearranging: . The term is sometimes called the "lost volts" - the p.d. dropped across the internal resistance.
As current increases, the terminal p.d. falls. This is the physical basis of the experiment.
You will need:
| Item | Purpose |
| Cell or battery (e.g. 1.5 V) | Source of EMF to be measured |
| Ammeter (0--1 A, 0.01 A resolution) | Measures current in the circuit |
| Voltmeter (0--2 V, 0.01 V resolution) | Measures terminal p.d. across the cell |
| Variable resistor (rheostat) | Varies the external resistance to change current |
| Switch | Allows circuit to be opened between readings |
| Connecting wires (at least 6) | Completes the circuit |
The ammeter is connected in series with the rheostat and cell. The voltmeter is connected in parallel across the cell terminals. If you need a refresher on these connections, see the ammeter and voltmeter guide.
Important practical habits:
Record your data in a table like this:
| Reading | / A | / V |
| 1 | ||
| 2 | ||
| 3 | ||
| 4 | ||
| 5 | ||
| 6 | ||
| 7 |
This arrangement matches the equation , which has the form where the gradient and the y-intercept .
The plotted points should lie close to a straight line with a negative gradient. As current increases, terminal p.d. decreases - exactly what predicts.
To find the gradient, pick two points on the line (not data points) that are far apart:
The gradient will be negative. The internal resistance is the magnitude:
For a detailed walkthrough of gradient calculations and axis-labelling conventions, see the graph skills guide.
Suppose you collect the following data:
| / A | / V |
| 0.10 | 1.44 |
| 0.20 | 1.38 |
| 0.30 | 1.32 |
| 0.40 | 1.26 |
| 0.50 | 1.19 |
| 0.60 | 1.14 |
| 0.70 | 1.07 |
Plot (y-axis) against (x-axis). Choose sensible scales: for example, y-axis from 1.00 V to 1.50 V and x-axis from 0.00 A to 0.80 A. Plot each point with a small cross.
The points lie close to a straight line with a negative slope. Draw a best-fit line through them.
Extend the best-fit line back to the y-axis. It crosses at approximately V.
Therefore: V.
Choose two points on the best-fit line that are well separated. For example:
The unit of the gradient is V/A, which equals ohms ().
| Quantity | Value |
| EMF () | 1.50 V |
| Internal resistance () | 0.62 |
Pick any data point to check. At A:
The measured value was 1.26 V - a close match, confirming the results are consistent.
The cell/meter errors below are specific to this experiment. For the cross-experiment error bank that contrasts, for example, parallax on a metre rule against zero error on an ammeter, see our O-Level Physics sources of error guide.
| Source of error | Effect | Improvement |
| Cell heats up during extended use | Internal resistance changes, graph deviates from a straight line | Switch off between readings; allow the cell to cool |
| Contact resistance at terminals | Adds extra, variable resistance; readings become inconsistent | Clean terminals with emery paper; use firm clip connections |
| Cell runs down over time | EMF decreases during the experiment | Take readings quickly; repeat the experiment with a fresh cell |
| Ammeter has non-zero resistance | Measured current is slightly lower than true value | Use a digital ammeter with very low internal resistance |
| Voltmeter draws some current | Voltmeter reading is slightly lower than true terminal p.d. | Use a high-impedance digital voltmeter |
| Parallax error when reading analogue meters | Incorrect values recorded | Read the meter at eye level; use the mirror strip if provided |
Even with careful technique, you may notice slight curvature or scatter. Two main causes:
As current flows, chemical by-products can accumulate on the electrodes, temporarily increasing the internal resistance. This effect is more noticeable at higher currents and with older cells. It causes the graph to curve slightly downward at the high-current end.
If the cell heats up (because the switch was left on too long), its internal resistance may change. For most cells, heating causes to increase, which steepens the graph at higher currents. Switching off between readings minimises this effect.
In both cases, the straight-line model is still a good approximation over the range of currents used in a typical O-Level practical.
If you are asked to plan this experiment in Paper 3, structure your answer using these headings. For the full marking breakdown, see the Paper 3 marking guide.
Draw a clear, labelled circuit diagram showing the cell, ammeter (in series), voltmeter (across cell terminals), rheostat, switch, and connecting wires. Use standard circuit symbols.
State that you will vary the rheostat to obtain at least 6 pairs of and , switching off between readings, and plot (y-axis) against (x-axis).
These are the errors examiners see most often in Paper 3 and Paper 2 questions on this topic:
The variable resistor (rheostat) lets you change the external resistance, which changes the current flowing through the circuit. By recording the terminal p.d. at different currents, you build up the data needed to plot the - graph and find the EMF and internal resistance from the line.
When current flows through the cell, some energy is dissipated as heat inside the cell. If the cell heats up, its internal resistance changes, which means the graph will not be a straight line. Switching off between readings keeps the cell at approximately the same temperature throughout the experiment.
In principle, yes - you could substitute two pairs of and values into and solve the simultaneous equations. However, this method relies on only two data points and gives no way to check for anomalies. The graph method uses all your data, averages out random errors, and is what examiners expect.
At the y-intercept, . Substituting into gives . So the terminal p.d. when no current flows equals the EMF. In practice, you cannot measure this directly (you need some current to get a reading), but the best-fit line extrapolates back to this zero-current value.
A slight curve usually indicates that the cell's internal resistance changed during the experiment - most likely because the cell heated up or because of chemical polarisation at the electrodes. Mention this as a source of error and suggest switching off between readings as an improvement. For the gradient calculation, draw the best straight line through the majority of the data and note any anomalous points.
For a related circuit experiment that also uses an ammeter and voltmeter, see our resistance of a wire experiment guide.
A V-I characteristic experiment (e.g. for a filament lamp or resistor) plots across a component against through it, to investigate how the component's resistance behaves. The internal resistance experiment plots across the cell against in the circuit, to investigate the cell itself. The setup looks similar - both use a rheostat, ammeter, and voltmeter - but the voltmeter position and the quantity being investigated are different.
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