Define electromotive force (e.m.f.) as the electrical work done by a source in moving a unit charge around a complete circuit
4.2.3 Electromotive Force (e.m.f.) and Potential Difference
Learning Objective
Define electromotive force (e.m.f.) as the electrical work done by a source in moving a unit charge round a complete circuit (AO1).
Key Definitions (AO1)
- Electromotive force (e.m.f.) – E: the electrical work done by a source in moving a unit charge round the whole circuit. Unit: volt (V).
- Potential difference (p.d.) – V (or Vab): the work done per unit charge between two points of a circuit. Unit: volt (V).
- Terminal p.d. (terminal voltage): the p.d. measured across the external terminals of a source when a current is flowing.
- Internal resistance – r: the resistance inherent to the source itself.
Supplementary Equations (AO2)
These are the equations that the Cambridge syllabus expects you to quote exactly.
| Quantity | Equation | Notes |
|---|---|---|
| Electromotive force, E | \(E = \dfrac{W}{Q}\) | Work W done by the source on charge Q |
| Potential difference, V | \(V = \dfrac{W}{Q}\) | Work done between two points |
| Ohm’s law (external resistor) | \(V = I R\) | R = external resistance |
Extended Content (optional for deeper study)
Although not required for the core IGCSE exam, the relation involving internal resistance is frequently used in problem‑solving.
- Terminal p.d. with internal resistance: \(V = E - I r\)
- Interpretation: the term \(I r\) represents the energy lost as heat inside the source.
Symbols and Units
| Symbol | Quantity | Unit |
|---|---|---|
| E | Electromotive force | Volt (V) |
| V (or Vab) | Potential difference (terminal p.d.) | Volt (V) |
| W | Electrical work | Joule (J) |
| Q | Charge | Coulomb (C) |
| I | Current | Ampere (A) |
| R | External resistance | Ohm (Ω) |
| r | Internal resistance of the source | Ohm (Ω) |
Conceptual Explanation (AO2)
- Inside a source (battery, generator, solar cell, etc.) chemical, mechanical or solar processes push charges from a lower‑potential region to a higher‑potential region.
- Each coulomb of charge gains energy; the amount of work done on one coulomb of charge is the e.m.f. of the source.
- If the circuit is open (no current), no internal drop occurs, so the measured p.d. across the terminals equals the e.m.f.: \(V = E\).
- When the circuit is closed, a current I flows. The source’s internal resistance r causes a voltage drop of \(I r\). The terminal p.d. therefore falls to
\(V = E - I r\) (extended content). - The external load of resistance R obeys Ohm’s law: the p.d. across it is \(V = I R\).
- The term \(I r\) represents the energy dissipated as heat inside the source.
Diagram (recommended)
Worked Example
Problem: A 12 V battery has an internal resistance of \(0.5\ \Omega\). It supplies a current of \(2\ \text{A}\) to an external resistor.
- e.m.f. \(E = 12\ \text{V}\) (given).
- Internal voltage drop \(I r = 2\ \text{A} \times 0.5\ \Omega = 1\ \text{V}\).
- Terminal voltage (extended content) \(V = E - I r = 12\ \text{V} - 1\ \text{V} = 11\ \text{V}\).
- External resistance Using Ohm’s law, \(R = V/I = 11\ \text{V} / 2\ \text{A} = 5.5\ \Omega\).
Key Points for the Exam (AO1 & AO2)
- e.m.f. is a property of the source; it does not change with the current drawn (ideal source).
- Terminal p.d. can be less than the e.m.f. because of the internal resistance: \(V = E - I r\) (optional knowledge).
- When no current flows, \(V = E\) (open‑circuit condition).
- Quote the supplementary equations exactly as written.
- Keep sign conventions clear: e.m.f. is taken as positive when it drives current in the direction of traversal.
Common Misconceptions
- e.m.f. ≠ terminal voltage when current flows. They are equal only in the open‑circuit condition.
- e.m.f. changes with load. For a real source the e.m.f. remains constant; only the terminal voltage varies.
- Ignoring internal resistance. At high currents the drop \(I r\) can be significant and must be included in calculations (advanced).
Summary
Electromotive force quantifies the ability of a source to do electrical work on a unit charge as it travels round a complete circuit. It is defined by the supplementary equation E = W / Q and expressed in volts. The potential difference measured across the terminals while current flows is reduced by the internal resistance of the source according to V = E – I r (extended content). Mastering the distinction between e.m.f. and terminal p.d., and using the exact supplementary equations, is essential for solving IGCSE Physics problems involving real‑world sources.