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Electromotive Force & Potential Difference

Key idea: Understand electromotive force (e.m.f.) and potential difference, use V = W/Q and W = QV, and know when to apply each in O Level questions.

  • SEC G3 Physics 2027
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Learning objectives

  • State current as rate of charge flow measured in amperes
  • Distinguish conventional current from electron flow
  • Apply charge equals current multiplied by time
  • Define source e.m.f. as work done per unit charge around a circuit
  • Calculate total e.m.f. for sources in series
  • Define component potential difference as work done per unit charge
  • State resistance as potential difference divided by current
  • Apply resistance equals potential difference divided by current
  • Apply wire-resistance proportionalities for length and cross-sectional area
  • Describe the effect of temperature on metallic resistance
  • Sketch and interpret required current–voltage characteristics

1. Definition

A. Electromotive force (e.m.f.)

The electromotive force, ε (V), of a source is the work done per unit charge by the source in driving charge around a complete circuit (energy supplied per coulomb).

B. Potential difference (p.d.)

The potential difference, V (V), across a component is the work done per unit charge in driving charge through the component (energy transferred per coulomb).

What you need for this course

You should be able to define e.m.f. and p.d. as energy transferred per unit charge, in volts, and distinguish the two ideas.

2. Key Ideas

  • Unit: 1 V = 1 J C⁻¹.
  • Relationship: V = W/Q, so W = QV.
  • For a source, we often write: ε = W/Q (same unit: V).
QuantityWhere you use itMeaning (energy per coulomb)
e.m.f. εsource (cell/battery/power supply)energy supplied to charges
p.d. Vcomponent (lamp/resistor/motor)energy transferred by charges

3. Detailed Explanations

A. What does “work done per unit charge” mean?

If 1 C of charge gains (or transfers) 1 J of energy, the voltage is:

V = W/Q = 1/1 = 1 V

So a higher voltage means more energy per coulomb.

B. “Energy story” around a circuit

  • The source supplies electrical energy to charges (this is the e.m.f.).
  • Components (lamp, motor, resistor) transfer electrical energy into other forms (this is the p.d. across the component).

At O Level, you can write:

  • e.m.f. = “energy per coulomb given by the source”
  • p.d. = “energy per coulomb used/transferred by the component”
Charge-flow directions in a simple circuitA closed circuit containing a cell and lamp. Conventional current arrows run clockwise from the positive terminal; electron-flow arrows run anticlockwise. The source electromotive force and component potential difference are labelled as quantities measured in volts.+−lampconventional currentelectron drift in metalsource: e.m.f.measured in voltscomponent: p.d.measured in voltsCharge circulates; it is not used up.In a single series loop, current has the same value at every point.
The source supplies energy per coulomb; components transfer energy per coulomb. Charge continues around the closed circuit and is not consumed.

C. Measuring voltage (voltmeter)

To measure p.d., connect a voltmeter in parallel across the component.

Voltmeter connection in parallel

Circuit with ammeter in series and voltmeter connected in parallel across a resistor to measure potential difference.

A cell and ammeter form a series loop with a resistor, while a voltmeter is connected across the resistorA cell and ammeter form a series loop with a resistor, while a voltmeter is connected across the resistor
Connect the voltmeter in parallel across the component whose p.d. is measured.
View figure data
Voltmeter measurement topology
PartConnection
AmmeterIn series in the main loop
VoltmeterIn parallel across the resistor
ResistorIn the conducting loop with the cell and ammeter
Safety

A voltmeter goes in parallel. If you connect it in series, you won’t measure the correct p.d.

Analogy (optional)

Voltage is like a “height difference” for charges: larger voltage means more energy per coulomb.

4. Common Mistakes

  • Saying “e.m.f. is a force” (it is not a force; it is energy per charge).
  • Mixing up where they apply: e.m.f. is for the source, p.d. is for a component.
  • Writing the unit wrongly: use 1 V = 1 J C⁻¹.
  • Forgetting that a voltmeter must be in parallel.

5. Exam Tips

  1. If the question says “energy supplied per coulomb by the source”, use e.m.f..
  2. If it says “energy transferred per coulomb in a component”, use p.d..
  3. For calculations, use V = W/Q or W = QV (with J, C, V).
  4. For measurements, state: “voltmeter in parallel”.

6. Worked Examples

Modelled example 1

Voltage from energy and charge

Core

Problem

A source supplies 6.0 J of energy when 2.0 C passes through it. Find the e.m.f. and interpret the result.
Study the worked solution

  1. Calculate energy supplied per coulomb

    Method

    Divide the source’s work done by the charge passing through it.

    Reason

    E.m.f. is energy supplied per unit charge by the source.

    Working

    ε = W/Q = 6.0/2.0 = 3.0 V

  2. Interpret the voltage

    Method

    State that the source supplies 3.0 J to each coulomb.

    Reason

    1 V = 1 J C⁻¹.

    Working

    3.0 V = 3.0 J C⁻¹.

Guided practice 2

Energy transferred in a component

About 4 min

Problem

A lamp has a p.d. of 6.0 V across it. How much energy is transferred when 2.0 C passes through the lamp?

Scale energy per coulomb by total charge

Unit: J

Hints

Hint 1: interpret the p.d.
6.0 V means 6.0 J transferred per coulomb.
Hint 2: use all the charge
Multiply by 2.0 C.
View solution step by step

  1. Calculate transferred energy

    Method

    Multiply charge by potential difference.

    Reason

    Potential difference gives energy transferred per coulomb in the component.

    Working

    W = QV = (2.0)(6.0) = 12 J

Common misconception 3

Using current to find charge first

Find and correct the mistake

Learner response

A lamp has 5.0 V across it while 2.0 A flows for 5.0 s. A student substitutes current directly as Q in W = QV. Diagnose the error and find the energy.

Bridge current and time to charge

Unit: J

View solution step by step

  1. Find the passing charge

    Method

    Multiply current by elapsed time.

    Reason

    Current is charge flow per second, not an amount of charge.

    Working

    Q = It = (2.0)(5.0) = 10 C

  2. Find the transferred energy

    Method

    Multiply the charge by the lamp’s p.d.

    Reason

    Each coulomb transfers 5.0 J in the lamp.

    Working

    W = QV = (10)(5.0) = 50 J

Examiner practice 4

Choosing e.m.f. vs p.d.

4 marks

Examination question

Name and define the quantity for (a) energy supplied per coulomb by a battery and (b) energy transferred per coulomb in a lamp. [4 marks]

Name each quantity and include its energy role

View solution step by step

  1. Define source e.m.f.

    2 marks

    Method

    Name e.m.f. and state work done or energy supplied per unit charge by the source around the complete circuit.

    Reason

    The battery raises the electrical energy carried by each coulomb.

    Working

    ε = W_supplied/Q

  2. Define component p.d.

    2 marks

    Method

    Name potential difference and state work done or energy transferred per unit charge through the component.

    Reason

    The lamp transfers electrical energy from each coulomb to other forms.

    Working

    V = W_transferred/Q

Challenge 5

Energy supplied by a source

Minimal support

Source-energy transfer

A cell has an e.m.f. of 1.5 V. Find the energy it supplies when 3.0 C passes through the cell.

Reverse the energy-per-charge definition

Hints

Hint 1: interpret the e.m.f.
The source supplies 1.5 J per coulomb.
Hint 2: scale by charge
Multiply by 3.0 C.
View solution step by step

  1. Calculate source work

    Method

    Multiply charge by source e.m.f.

    Reason

    E.m.f. gives the energy supplied to each coulomb.

    Working

    W = Qε = (3.0)(1.5) = 4.5 J

7. Mind Stretchers

Mind stretcher 1: Open circuit vs closed circuitExtension

A voltmeter reads 1.5 V across the terminals of a cell even when nothing is connected. Does this mean charges are flowing? Explain.

Show Answer

No. A voltmeter measures potential difference (energy per charge) between two points. A p.d. can exist without current. Current needs a closed circuit for charges to flow around the circuit.

Mind stretcher 2: “Voltage is used up?”Extension

Students sometimes say “voltage is used up in a lamp”. What is a better statement using p.d. and energy?

Show Answer

The potential difference across the lamp means charges transfer electrical energy to other forms (light/heat). The charges are not “used up”; energy is transferred per coulomb as charge passes through the lamp.

8. Practice and next step

Use the Current Electricity Quiz to distinguish source e.m.f. from component p.d., then complete the energy-per-charge questions in Structured Current Electricity. Continue to sources in series to combine source e.m.f.s with the correct orientation.

Continue with the next resource in this course.

Course and syllabus information
Course
SEC G3 Physics
Edition
SEC G3 Physics 2027