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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. (V) and current (I) for 6--8 settings, then plot V against I. The graph is a straight line with a negative gradient: the y-intercept gives the EMF (E) and the magnitude of the gradient gives the internal resistance (r
The EMF of a cell, written E, 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.
Internal resistance
Every real cell has some resistance of its own, called the internal resistancer. 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 key equation
The relationship between terminal p.d., EMF, and internal resistance is:
V=E−Ir
where:
V = terminal potential difference (what the voltmeter reads across the cell), in V
E = electromotive force of the cell, in V
I = current through the circuit, in A
r = internal resistance of the cell, in Ω
Rearranging: E=V+Ir. The term Ir 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.
2 | Apparatus
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.
3 | Step-by-Step Method
Set up the circuit. Connect the cell, switch, ammeter, and rheostat in a series loop. Connect the voltmeter across the cell terminals (in parallel).
Set the rheostat to maximum resistance. This ensures the initial current is small, protecting the cell and meters.
Close the switch. Read and record the ammeter reading (I) and the voltmeter reading (V) simultaneously.
Open the switch immediately after taking the reading. This prevents the cell from heating up, which would change its internal resistance during the experiment.
Decrease the rheostat resistance slightly to increase the current. Close the switch again, take the next pair of readings, and open the switch.
Repeat for at least 6 data points, spread evenly across the available current range. Aim for 6--8 pairs of V and I.
Record all readings in a table with appropriate column headings and units.
Important practical habits:
Switch off between every reading (cell heating is a major source of error).
Tap connections gently to check they are secure - loose crocodile clips cause contact resistance.
Wait a few seconds after closing the switch for the readings to stabilise before recording.
4 | Raw Data Table Template
Record your data in a table like this:
Reading
I / A
V / V
1
2
3
4
5
6
7
The column headings must include the quantity and unit separated by a forward slash (e.g. I / A).
Record ammeter and voltmeter readings to the precision of the instrument (typically 2 decimal places for both).
Values should cover a good spread - do not cluster all readings at one end of the range.
5 | Plotting the V-I Graph
Axes
y-axis: Terminal p.d. V / V
x-axis: Current I / A
This arrangement matches the equation V=E−Ir, which has the form y=c+mx where the gradient m=−r and the y-intercept c=E.
What the graph looks like
The plotted points should lie close to a straight line with a negative gradient. As current increases, terminal p.d. decreases - exactly what V=E−Ir predicts.
Drawing the best-fit line
Use a transparent ruler.
Draw a single straight line of best fit through the data points.
The line should have roughly equal numbers of points above and below it.
Do not force the line through the origin - the y-intercept carries physical meaning.
Reading off the key values
EMF (E) = y-intercept (the value of V where the line meets the y-axis, i.e. when I=0).
Internal resistance (r) = magnitude of the gradient.
To find the gradient, pick two points on the line (not data points) that are far apart:
gradient=ΔIΔV=I2−I1V2−V1
The gradient will be negative. The internal resistance is the magnitude:
r=∣gradient∣=ΔIΔV
For a detailed walkthrough of gradient calculations and axis-labelling conventions, see the graph skills guide.
6 | Worked Example
Suppose you collect the following data:
I / A
V / 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
Step 1 - Plot the graph
Plot V (y-axis) against I (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.
Step 2 - Draw the best-fit line
The points lie close to a straight line with a negative slope. Draw a best-fit line through them.
Step 3 - Find the y-intercept (EMF)
Extend the best-fit line back to the y-axis. It crosses at approximately V=1.50 V.
Therefore: E≈1.50 V.
Step 4 - Calculate the gradient (internal resistance)
Choose two points on the best-fit line that are well separated. For example:
Point A: (I1,V1)=(0.10,1.44)
Point B: (I2,V2)=(0.70,1.07)
gradient=I2−I1V2−V1=0.70−0.101.07−1.44=0.60−0.37=−0.617 V A−1
The unit of the gradient is V/A, which equals ohms (Ω).
r=∣gradient∣=0.62Ω (2 s.f.)
Summary of results
Quantity
Value
EMF (E)
1.50 V
Internal resistance (r)
0.62 Ω
Verification
Pick any data point to check. At I=0.40 A:
V=E−Ir=1.50−(0.40)(0.62)=1.50−0.248=1.25 V
The measured value was 1.26 V - a close match, confirming the results are consistent.
7 | Sources of Error and Improvements
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
8 | Why the Graph May Not Be Perfectly Straight
Even with careful technique, you may notice slight curvature or scatter. Two main causes:
Cell polarisation
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.
Temperature effects
If the cell heats up (because the switch was left on too long), its internal resistance may change. For most cells, heating causes r to increase, which steepens the graph at higher currents. Switching off between readings minimises this effect.
In both cases, the straight-line model V=E−Ir is still a good approximation over the range of currents used in a typical O-Level practical.
9 | Paper 3 Planning Question Angle
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.
Diagram
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.
Independent and dependent variables
Independent variable: Current I (changed by adjusting the rheostat).
Dependent variable: Terminal p.d. V (measured by the voltmeter).
Controlled variables
Same cell used throughout (do not swap cells mid-experiment).
Same ammeter and voltmeter (so systematic errors are constant).
Temperature of cell kept approximately constant (switch off between readings).
Method summary
State that you will vary the rheostat to obtain at least 6 pairs of V and I, switching off between readings, and plot V (y-axis) against I (x-axis).
Analysis
State that the graph should be a straight line.
EMF = y-intercept.
Internal resistance = magnitude of the gradient.
Safety
Switch off between readings to avoid overheating.
Do not short-circuit the cell (never set the rheostat to zero resistance).
10 | Common Exam Mistakes
These are the errors examiners see most often in Paper 3 and Paper 2 questions on this topic:
Confusing EMF with terminal p.d. - EMF is the total energy per unit charge supplied by the cell. Terminal p.d. is what the voltmeter reads and is always less than EMF when current flows (because of the voltage drop across r).
Plotting axes the wrong way round. - V goes on the y-axis and I on the x-axis. If you swap them, the y-intercept no longer gives EMF and the gradient no longer gives −r.
Forgetting units on the gradient. - The gradient of a V-I graph has units of V/A = Ω. You must state the unit when giving the value of r.
Forcing the line through the origin. - The best-fit line should not pass through (0, 0). The y-intercept is the EMF and is a positive, non-zero value.
Not switching off between readings. - This is both a practical error (cell heats up) and a planning mark (examiners expect you to mention it).
Ignoring the sign of the gradient. - The gradient is negative because V decreases as I increases. Internal resistance is the magnitude of the gradient, so r is always a positive number.
Using data points instead of points on the line for the gradient. - The gradient should be calculated from two well-separated points that lie on the best-fit line, not from raw data points (which may have scatter).
Giving EMF as negative. - EMF is always a positive quantity. A negative y-intercept would indicate an error in your graph or data.
11 | Frequently Asked Questions
What is the purpose of the variable resistor in the internal resistance experiment?
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 V-I graph and find the EMF and internal resistance from the line.
Why do we switch off between readings?
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.
Can I find internal resistance without drawing a graph?
In principle, yes - you could substitute two pairs of V and I values into V=E−Ir 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.
Why is the y-intercept equal to the EMF?
At the y-intercept, I=0. Substituting into V=E−Ir gives V=E−0=E. 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.
What if my graph curves instead of being straight?
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.
How is this experiment different from a simple V-I characteristic?
A V-I characteristic experiment (e.g. for a filament lamp or resistor) plots V across a component against I through it, to investigate how the component's resistance behaves. The internal resistance experiment plots V across the cell against I 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.
