4.2.3 Electromotive force and potential difference
- Syllabus
- 0625–2026–2027
- Topic
- 4.2.3
- Level
- —
Learning objectives
4.2.3.1Electromotive force (e.m.f.) as the• Define electromotive force (e.m.f.) as the electrical work done by a source in moving a unit charge around a complete circuit4.2.3.2E.m.f. is measured in volts (V)• Know: e.m.f. is measured in volts (V)4.2.3.3Potential difference (p.d.) as the• Define potential difference (p.d.) as the work done by a unit charge passing through a component4.2.3.4P.d. between two points is measured in• Know: the p.d. between two points is measured in volts (V)4.2.3.5Use of voltmeters (analogue and• Describe the use of voltmeters (analogue and digital) with different ranges4.2.3.6E.m.f.: E = W/Q• Recall/use e.m.f.: E = W/Q4.2.3.7P.d.: V = W/Q• Recall/use p.d.: V = W/Q
Define electromotive force
Electromotive force (e.m.f.) is the electrical work done by a source in moving a unit charge around a complete circuit.
| Part | Energy role |
|---|---|
| source such as a cell | transfers energy into the electrical pathway |
| one coulomb moved around the complete circuit | receives an amount of electrical work equal to the e.m.f. in joules per coulomb |
A source with a larger e.m.f. supplies more electrical energy to each coulomb of charge, not necessarily more total charge or current.
Despite its name, e.m.f. is not a force and is not measured in newtons. It describes work done per unit charge by a source around a complete circuit.
Use volts as the unit of e.m.f.
Electromotive force is measured in volts, symbol V.
| Statement | Energy meaning |
|---|---|
| e.m.f. = 1 V | source supplies 1 J to each 1 C |
| e.m.f. = 6 V | source supplies 6 J to each 1 C |
One volt is one joule per coulomb: 1 V = 1 J/C. Include V after a numerical e.m.f. value.
Do not give e.m.f. in amperes, joules, watts or newtons. Joules measure work, while volts measure work per coulomb.
Define potential difference
Potential difference (p.d.) is the electrical work done by a unit charge passing through a component.
| Charge passes through… | Electrical-energy outcome |
|---|---|
| lamp | electrical energy transfers mainly to light and heating |
| resistor or heater | electrical energy transfers mainly to heating |
| motor | electrical energy transfers mainly to mechanical work and heating |
A larger p.d. across a component means that more work is done, or more electrical energy is transferred, for each coulomb passing through it.
Potential difference is measured between two points across a component. It is not current, and it is not the total energy transferred unless the amount of charge is also known.
Use volts as the unit of potential difference
Potential difference between two points is measured in volts, symbol V.
| Statement | Meaning |
|---|---|
| p.d. = 1 V | 1 J is transferred per 1 C passing between the points |
| p.d. = 12 V | 12 J is transferred per 1 C passing between the points |
Both e.m.f. and p.d. are measured in volts because both compare electrical work with charge. Their energy roles differ: a source supplies energy, while a component transfers it from the electrical pathway.
Using the same unit does not make e.m.f. and p.d. identical. State whether the voltage is across a source or between points across a component.
Use analogue and digital voltmeters correctly
A voltmeter measures potential difference between two points. Connect it in parallel across the source or component being measured.
| Step | Safe, accurate action |
|---|---|
| select range | start above the expected voltage; reduce to a suitable lower range for better resolution |
| connect | place one lead at each side of the component; use correct polarity for d.c. |
| analogue | check zero, select the correct scale and read at eye level |
| digital | select V and d.c./a.c. as appropriate; note sign, range and unit |
A negative digital reading or reversed analogue deflection indicates reversed d.c. lead polarity. A high-resistance voltmeter draws very little current so it minimally changes the circuit.
A voltmeter is not placed in series like an ammeter. Connecting it across the wrong pair of points measures a different p.d., even if the reading is numerically plausible.
Calculate e.m.f. from work and charge
For a source, e.m.f. E equals electrical work W supplied per charge Q: E = W / Q.
| Find | Relationship | Units |
|---|---|---|
| e.m.f. | E = W / Q | V |
| work supplied | W = E Q | J |
| charge | Q = W / E | C |
A 9.0 V battery moves 30 C around the circuit: W = E Q = 9.0 × 30 = 270 J. Label the result as energy supplied by the source.
Use the source e.m.f. in this relationship. Do not multiply by time unless a separate current relationship is required and supported by the question.
Calculate p.d. from work and charge
For a component, potential difference V equals electrical work W done per charge Q: V = W / Q.
| Find | Relationship | Units |
|---|---|---|
| p.d. | V = W / Q | V |
| work transferred | W = V Q | J |
| charge | Q = W / V | C |
If a resistor transfers 100 J when 10 C passes, V = W / Q = 100 / 10 = 10 V. If 5.0 C passes through a 2.0 V component, W = 2.0 × 5.0 = 10 J.
V is the symbol for p.d. and also the unit symbol volt in a numerical answer; use context carefully. Work done per charge is not power, which is work done per time.