EMF and internal resistance

Practical method

Aim

Determine the emf and internal resistance of a cell from a graph of terminal p.d. against current.

Variables

Independent variable: load resistance (and so current)
Dependent variable: terminal p.d.
Control variables: the same cell; short readings to avoid the cell running down.

Apparatus

• Cell
• Variable resistor (or resistance box)
• Ammeter
• High-resistance voltmeter
• Switch
• Protective resistor

Method

1. Connect the cell in series with the ammeter, variable resistor, protective resistor and switch; connect the voltmeter across the cell.
2. Close the switch briefly and record V and I. Open it between readings.
3. Repeat for at least six settings of the variable resistor.
4. Plot V against I. From V = ε − Ir, the intercept is ε and the gradient is −r.

Sample results

Single cell.

Analysis

V falls linearly with I. Intercept = 1.55 V = ε; gradient = −0.80 V A⁻¹, so r = 0.80 Ω.

Uncertainty

Voltmeter ±0.01 V and ammeter ±0.01 A give scatter of a few per cent. Using steepest and shallowest lines gives r = 0.80 ± 0.05 Ω.

Errors and improvements

Risk assessment

Common mistakes

• Reading r as the gradient without the minus sign.
• Connecting the voltmeter across the load only.
• Leaving the switch closed.

Worked analysis

From the graph: ε = 1.55 V. At I = 0.40 A, V = 1.23 V, so lost volts = 0.32 V and r = \(\dfrac{0.32}{0.40}\) = 0.80 Ω.

Common misconception

Emf is not a force; it is the energy supplied per coulomb, equal to the terminal p.d. only when no current flows.