IGCSE Physics 0625 – Electromotive Force and Potential Difference
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 around a complete circuit.
Key Definitions
Electromotive Force (e.m.f.): The energy supplied by a source (battery, generator, solar cell, etc.) to move a unit charge once round the circuit. It is measured in volts (V).
Potential Difference (p.d.): The work done per unit charge between two points of a circuit. Also measured in volts.
Terminal \cdot oltage: The p.d. across the external terminals of a source when current is flowing.
Internal Resistance (\$r\$): The resistance inherent to the source itself.
Mathematical Relationship
The e.m.f. of a source is defined by the work \$W\$ done on a charge \$Q\$:
\$\text{e.m.f.} = \frac{W}{Q}\$
When a current \$I\$ flows, part of the e.m.f. is lost overcoming the internal resistance, giving the terminal voltage \$V\$:
\$V = \text{e.m.f.} - I r\$
Symbols and Units
Symbol
Quantity
Unit
e.m.f.
Electromotive force
Volt (V)
V
Terminal potential difference
Volt (V)
W
Electrical work
Joule (J)
Q
Charge
Coulomb (C)
I
Current
Ampere (A)
r
Internal resistance
Ohm (Ω)
Conceptual Explanation
Inside a source, chemical, mechanical or solar processes move charges from lower to higher potential.
This movement does work on each charge; the amount of work per coulomb is the e.m.f.
When the circuit is open (no current), the measured p.d. across the terminals equals the e.m.f.
When the circuit is closed, current \$I\$ flows. The source’s internal resistance \$r\$ causes a voltage drop \$I r\$, so the terminal p.d. is reduced.
Example Calculation
Consider a 12 V battery with an internal resistance of \$0.5\ \Omega\$ delivering a current of \$2\ \text{A}\$ to a load.
e.m.f. = \$12\ \text{V}\$ (given).
Voltage drop inside the battery: \$I r = 2\ \text{A} \times 0.5\ \Omega = 1\ \text{V}\$.
e.m.f. is a property of the source; it does not depend on the current drawn.
Terminal p.d. can be less than e.m.f. because of internal resistance.
When no current flows, \$V = \text{e.m.f.}\$.
Always keep track of sign conventions: the e.m.f. is considered positive when it drives current in the direction of the defined circuit traversal.
Suggested diagram: A simple circuit showing a battery (with e.m.f. \$\mathcal{E}\$ and internal resistance \$r\$), a switch, and an external resistor \$R\$. Label the e.m.f., internal voltage drop \$I r\$, and terminal voltage \$V\$ across the resistor.
Common Misconceptions
Confusing e.m.f. with the voltage measured across a live circuit; remember e.m.f. is the open‑circuit voltage.
Assuming the e.m.f. changes with load; it remains constant for an ideal source.
Neglecting internal resistance in calculations for high‑current devices.
Summary
Electromotive force quantifies the ability of a source to do electrical work on a unit charge as it travels around a complete circuit. It is expressed as \$ \text{e.m.f.} = W/Q \$ and measured in volts. The terminal potential difference observed when a current flows is reduced by the internal resistance of the source according to \$ V = \text{e.m.f.} - I r \$. Understanding this distinction is essential for analysing real‑world circuits and for success in the IGCSE Physics exam.