Electromotive force and internal resistance — AQA A-Level Physics

This topic explores how real power sources, such as batteries and cells, are not ideal. They possess an internal resistance that causes the terminal potential difference to be less than the electromotive force (emf) when current flows. You will learn the definition of emf as the energy transferred per unit charge from a source, and how to apply the equation emf = I(R + r) to solve circuit problems.

Understanding emf and internal resistance is crucial for analysing practical circuits and is a fundamental concept in A-Level Physics. It links to earlier work on current, potential difference, and resistance, and provides a foundation for more advanced topics like power transfer and efficiency. Mastery of this topic is essential for both exam success and real-world applications in electronics and energy systems.

• →Electromotive force (emf) is the energy transferred from a source per unit charge, measured in volts (V). It is not a force but a potential difference.
• →Internal resistance (r) is the resistance within a source that causes a potential drop when current flows, leading to a terminal p.d. less than the emf.
• →The relationship between emf, current, and resistances is given by emf = I(R + r), where R is the external resistance.
• →Terminal potential difference (V) is the p.d. across the external circuit and is given by V = emf - Ir.
• →A graph of terminal p.d. against current yields a straight line with y-intercept equal to emf and gradient equal to -r.

• Connect the cell, ammeter, variable resistor and switch in series, with the voltmeter connected in parallel across the cell terminals to measure terminal pd.
• Record paired values of current I and terminal pd V over a suitable range, adjusting the variable resistor to vary the current.
• Plot a graph of V (y-axis) against I (x-axis) and draw a line of best fit through the points.
• Determine the emf from the intercept on the V-axis and the internal resistance from the magnitude of the gradient, using r = −gradient.
• Use a high-resistance voltmeter and take readings quickly or switch off between readings to reduce heating and polarisation effects.
• Repeat readings and calculate means, or use a graphical method, to reduce the effect of random errors.

• 💡State clearly that the intercept is the emf and the magnitude of the gradient is the internal resistance, and show the gradient calculation with the coordinates used.
• 💡Explain why a high-resistance voltmeter is used: it draws negligible current so the measured pd is close to the true terminal pd.
• 💡When describing improvements, link each change to the error it reduces, such as switching off to reduce heating or repeating to reduce random error.
• 💡Always write the full equation emf = I(R + r) and rearrange it correctly before substituting numbers. Show all steps clearly to earn method marks.
• 💡When describing graphs, state the physical quantity represented by the gradient and intercept, and include units. For example, 'the gradient is -r, so r = 0.80 Ω'.
• 💡In explanations, use precise terminology: 'energy transferred per unit charge' for emf, and 'potential difference across the external circuit' for terminal p.d. Avoid vague phrases like 'voltage lost'.

• Connecting the voltmeter in series with the cell instead of in parallel across the cell terminals; correct this by placing the voltmeter across the cell so it measures terminal pd.
• Assuming the gradient of the V–I graph equals +r; correct this by recognising the gradient is −r, so r is the magnitude of the gradient.
• Leaving the circuit connected continuously so the cell heats and its internal resistance changes; correct this by switching off between readings and taking readings quickly.
• Students often think emf and terminal p.d. are always the same. Correction: They are only equal when no current flows (open circuit). When current flows, terminal p.d. is less than emf due to internal resistance.
• Students may believe internal resistance is negligible in all cases. Correction: Internal resistance is significant in real cells and must be considered in calculations, especially when high currents are drawn.
• Students sometimes confuse the gradient and intercept on a V-I graph. Correction: For V vs I, the y-intercept is emf and the gradient is -r, not the other way around.

1. 1Start by reviewing the definitions of emf and internal resistance, and derive the equation emf = I(R + r) from energy considerations.
2. 2Practice calculations using the equation for various circuit configurations, including finding current, terminal p.d., and internal resistance.
3. 3Analyse graphs of terminal p.d. against current, identifying emf and internal resistance from intercept and gradient.
4. 4Work through past paper questions on this topic, focusing on explanations and graphical analysis, and mark your answers using the mark scheme.
5. 5Create a summary sheet with key equations, definitions, and common pitfalls, and test yourself using active recall prompts.

• 📋Calculation questions: Often ask for current, terminal p.d., or internal resistance using emf = I(R + r). Advice: Rearrange carefully and show all steps.
• 📋Graph analysis: Given a V-I graph, determine emf and internal resistance. Advice: Remember y-intercept = emf, gradient = -r, and include units.
• 📋Explanation questions: Explain why terminal p.d. is less than emf when current flows. Advice: Use the concept of energy dissipation due to internal resistance.
• 📋Practical-based questions: Describe an experiment to measure emf and internal resistance. Advice: Outline the circuit, measurements, and graphical method.