Potential difference and e.m.f.

Physics· Unit 9: Current of electricity· 15 min read

1. Potential Difference: Definition and Calculation★★☆☆☆⏱ 4 min

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Potential difference (p.d.) is measured between two points in a circuit, and describes the amount of electrical energy converted to other usable or wasted forms of energy (like heat, light, or kinetic energy) when charge passes through a component.

📘 Definition

Potential Difference

V

Potential difference is defined as: $V = \frac{W}{Q}$ , where $W$ is work done (energy converted) by charge $Q$ moving through the component.

Example:

A 1.5 V torch bulb converts 1.5 J of electrical energy to heat and light per coulomb of charge passing through it.

📐 Worked Example

A 500 mA current flows through a lamp for 2 minutes, and 360 J of energy is dissipated as light and heat. Calculate the p.d. across the lamp.

1
First calculate total charge passing through the lamp using $Q = I t$ :
2
$Q = (500 \times 10^{-3} \text{ A}) \times (2 \times 60 \text{ s}) = 60 \text{ C}$
3
Substitute into the definition of p.d.:
4
$V = \frac{W}{Q} = \frac{360 \text{ J}}{60 \text{ C}} = 6 \text{ V}$
5
Final answer: p.d. across the lamp = 6 V

2. Electromotive Force: What It Actually Is★★☆☆☆⏱ 4 min

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Unlike p.d. (which describes energy leaving electrical form), e.m.f. describes energy being converted into electrical energy from other sources. Examples include chemical energy converted in a battery, or mechanical energy converted in a generator.

📘 Definition

Electromotive Force (e.m.f.)

\mathcal{E}

E.m.f. is the total energy transferred per unit charge by a source, given by: $E = \frac{W _{total}}{Q}$ , where $W_{total}$ is the total energy converted from non-electrical to electrical form.

Example:

A 12 V car battery converts 12 J of chemical energy to electrical energy per coulomb of charge that passes through it.

📐 Worked Example

A battery converts 1800 J of chemical energy to electrical energy when 150 C of charge flows through it. Calculate the e.m.f. of the battery.

1
Substitute directly into the definition of e.m.f.:
2
$\mathcal{E} = \frac{1800 \text{ J}}{150 \text{ C}} = 12 \text{ V}$
3
Final answer: e.m.f. of the battery = 12 V

3. E.m.f. and Terminal P.d. in Real Circuits★★★☆☆⏱ 5 min

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All real sources have internal resistance, meaning some energy is wasted as heat inside the source itself. By conservation of energy, the total e.m.f. of the source equals the sum of the useful terminal p.d. (across the external circuit) and the p.d. lost across the internal resistance: $E = V_{terminal} + v_{lost}$ .

📐 Worked Example

A cell of e.m.f. 1.5 V dissipates 0.2 J of energy as heat inside the cell when 1 C of charge flows through it. Calculate the terminal p.d. available to the external circuit.

1
First calculate the p.d. lost across the internal resistance, using $v_{lost} = \frac{W _{lost}}{Q}$ :
2
$v_{\text{lost}} = \frac{0.2 \text{ J}}{1 \text{ C}} = 0.2 \text{ V}$
3
Rearrange the energy conservation relationship to solve for terminal p.d.:
4
$V_{\text{terminal}} = \mathcal{E} - v_{\text{lost}} = 1.5 \text{ V} - 0.2 \text{ V} = 1.3 \text{ V}$
5
Final answer: terminal p.d. = 1.3 V

✓ Quick check

Test your understanding of the core difference between p.d. and e.m.f.:

Which statement correctly describes e.m.f.?
- Electrical energy is converted to heat per unit charge
- Chemical energy is converted to electrical energy per unit charge
- Kinetic energy is converted to heat per unit charge
- Electrical energy is converted to light per unit charge
Reveal answer
1 —
E.m.f. describes conversion of non-electrical energy to electrical energy, while p.d. describes the opposite conversion of electrical energy to other forms.

4. Common Pitfalls

Wrong move:

Calling e.m.f. a force and stating it has units of newtons.

Why:

The name 'electromotive force' is misleading, e.m.f. is not a force.

Correct move:

Always define e.m.f. as energy per unit charge with units of volts (J C⁻¹).

Wrong move:

Treating p.d. and e.m.f. as interchangeable terms because both are measured in volts.

Why:

They describe opposite directions of energy transfer in a circuit, so they are distinct concepts.

Correct move:

Always distinguish them: p.d. = energy out of electrical form, e.m.f. = energy into electrical form.

Wrong move:

Assuming terminal p.d. of a cell is always equal to its e.m.f.

Why:

All real cells have internal resistance, so energy is lost when current flows.

Correct move:

Only state e.m.f. equals terminal p.d. when the circuit is open (zero current) or internal resistance is explicitly neglected.

Wrong move:

Writing the definition of p.d. as $V = Q / W$ instead of $V = W / Q$ .

Why:

Mixing up the order, p.d. is work per unit charge, not charge per work.

Correct move:

Remember the phrase: 'work per unit charge' → work divided by charge.

5. Quick Reference Cheatsheet

Quantity	Symbol	Definition	Energy Transfer
Potential difference	$V$	$V = \frac{W}{Q}$	Electrical → other forms (heat/light)
E.m.f.	$E$	$E = \frac{W _{total}}{Q}$	Other forms → electrical (chemical/mechanical)
Circuit relationship		$E = V_{terminal} + v_{lost}$	For sources with internal resistance
Unit	V	$1 V = 1 J C^{- 1}$	Same for p.d. and e.m.f.

When this came up on past exams

AI-estimated based on syllabus patterns — cross-check with official past papers for accuracy. Use only as revision-focus signals.

2022 · 12
Compare e.m.f. and p.d.
2023 · 22
Calculate e.m.f. from energy data
2024 · 11
MCQ on energy transfer

What's Next

The distinction between potential difference and e.m.f. is the foundation for all circuit analysis in CIE A-Level Physics. This concept underpins calculations of resistance, power, internal resistance, and complex circuit problems using Kirchhoff's laws. You will apply these definitions to solve real-world circuit problems, from simple series-parallel combinations to potential divider circuits used in sensors and measurement systems.