Distinguish electromotive force from potential difference
Compare source e.m.f. and component p.d. through energy transferred per coulomb.
Section 10 · D.C. circuits
AS Level; Cambridge International Physics 9702, 2025–2027 syllabus, Topic 10. These original circuit diagrams and calculations are study aids; full timed assessment, supervised practical competence and human subject-teacher review remain outstanding.
Before you begin
- Use current, potential difference, resistance, energy and charge with consistent circuit directions.
Work on paper. Try each question before revealing help, and explain why your method works.
Quick readiness check
What does a source e.m.f. measure?
What you will learn
- Define e.m.f. as energy supplied per unit charge around a complete circuit
- Use ε = W/Q
- Distinguish source e.m.f. from component potential difference by energy transfer
A source e.m.f. describes energy supplied per charge
The electromotive force ε of a source is the energy transferred by the source to each unit of charge as it drives charge around a complete circuit. Its unit is the volt: joules per coulomb. Use ε = W/Q for energy supplied W and charge Q.
Despite its name, e.m.f. is not a mechanical force. It is a source energy-per-charge quantity. An ideal source supplies the same energy per coulomb regardless of circuit current; a real source may also transfer some energy internally.
Potential difference describes energy transfer at a component
The p.d. across a component is the energy transferred to or from that component per unit charge passing through it. A resistor transfers electrical energy mainly to thermal energy; a motor transfers some to mechanical output and some to heating.
The source e.m.f. is the energy supplied per charge to the complete circuit, while terminal p.d. and component p.d. describe energy transfer across particular parts. With internal resistance, the source's terminal p.d. can be less than its e.m.f. when current flows.
Pause and explain
What is the unit meaning of a volt?
Worked example
A source supplies 24 J to 3.0 C around a complete circuit. Find its e.m.f. and explain what the answer means.
Show the worked solution
- Use ε = W/Q.
- ε = 24/3.0.
- Interpret volts as joules per coulomb.
Answer ε = 8.0 V: the source supplies 8.0 J per coulomb.
Try a topic test
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Test this topic →From guided practice to a new situation
Write your answer and reasoning first. Use a hint only if you are stuck. The model solution is for self-checking; your written work is not automatically marked.
A battery supplies 18 J of energy to charge that totals 2.0 C. Find its e.m.f.
Give me a hint
Divide energy supplied by charge transferred.
Compare my reasoning
- ε = W/Q.
- ε = 18/2.0.
- State volts and their energy-per-charge meaning.
ε = 9.0 V, or 9.0 J supplied per coulomb.
Look for these in your work
- Source definition used
- Ratio calculated
- Volt interpreted
A 6.0 V component transfers 15 J from electrical stores. Find the charge that passes.
Give me a hint
Rearrange V = W/Q to find Q.
Compare my reasoning
- Q = W/V.
- Q = 15/6.0.
- Give charge in coulombs.
Q = 2.5 C.
Look for these in your work
- Equation rearranged
- Charge calculated
- Coulomb unit stated
A real battery has e.m.f. 12 V and terminal p.d. 10 V while supplying current. Explain why the two voltages can differ in terms of energy per coulomb.
Give me a hint
Compare energy supplied inside the source with energy delivered across its external terminals.
Compare my reasoning
- The e.m.f. represents energy supplied per coulomb by the source.
- The terminal p.d. represents energy delivered per coulomb to the external circuit.
- Some energy per coulomb is transferred inside the source's internal resistance while current flows.
They differ because some source energy per coulomb is transferred internally, leaving a smaller terminal p.d. across the external circuit.
Look for these in your work
- Both energy-per-charge meanings distinguished
- Internal transfer identified
- Loaded condition included
Common mistakes
- Calling e.m.f. a force measured in newtons
- Treating source e.m.f. and terminal p.d. as identical for every loaded real source
- Confusing energy per charge with total energy transferred
What can you explain now?
What does a source e.m.f. measure?
Compare with the explanation
Energy supplied per unit charge around the complete circuit
It is the source's energy transfer per coulomb.
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Make it stick
How can source e.m.f. and terminal potential difference describe different parts of the same energy transfer?
If you needed the solution, close it and solve the problem again from a blank page. A correct answer is stronger when you can explain the reason for each step.