Ch 4 · 4.2.3 Electromotive Force and Potential Difference · O Level Physics 5054

Topic 4 of 17 in Electricity and Magnetism — O Level Physics 5054 — 59 lessons.

Introduction

A 9 V battery and a 1.5 V cell can both light a lamp, but the 9 V battery gives each coulomb of charge six times as much energy. Voltage tells you the energy per unit charge: given by the source (e.m.f.) or transferred in a component (p.d.). (Syllabus section 4.2.3.)

Key ideas — Electromotive force (e.m.f.)

The e.m.f. of a source (a cell, battery or generator) is the electrical work done by the source in moving a unit charge around a complete circuit:

🧑‍🏫 Teacher's explanation

Think of a battery like a pump in a water system. To keep water flowing in a loop, the pump has to provide energy to push the water molecules through the pipes and past obstacles. The electromotive force (e.m.f.) is the total 'push' or energy provided by the pump to get every bit of charge through the entire loop.

📖 Definitions

🔍 Worked example — Easy

A battery does 60 J of work to move a charge of 5 C around a complete circuit. Calculate the e.m.f. of the battery.

🔍 Worked example — Standard

A bulb has a potential difference of 4.5 V across it. If a charge of 0.2 C passes through the bulb, how much work was done on the charge by the bulb?

🔍 Worked example — Exam-style

A circuit contains two identical 1.5 V cells connected in parallel. A third identical cell is then added in series to the circuit. Calculate the total e.m.f. of the circuit.

⚠️ Common errors

🧠 Quick check 1

🧠 Quick check 2

🎯 Exam question

Key ideas — Potential difference (p.d.)

The p.d. across a component is the work done by a unit charge passing through the component (the energy each coulomb transfers to it, e.g. as light and heat in a lamp):

🧑‍🏫 Teacher's explanation

Imagine a water pump system. The electromotive force (e.m.f.) is like the pressure the pump provides to push water through the entire loop of pipes. It is the total energy 'boost' given to every bit of water. Potential difference (p.d.), however, is the pressure drop that occurs when water flows through a specific filter or narrow pipe. It represents how much energy is actually used up by that specific part of the system.

📖 Definitions

🔍 Worked example — Easy

A battery does 60 J of work to move a charge of 5 C around a complete circuit. Calculate the e.m.f. of the battery.

🔍 Worked example — Standard

A lamp uses 120 J of energy when a charge of 40 C passes through it. Calculate the potential difference across the lamp.

🔍 Worked example — Exam-style

Two identical 6 V cells are connected in parallel. What is the total e.m.f. of this combination?

⚠️ Common errors

🧠 Quick check 1

🧠 Quick check 2

🎯 Exam question

Key ideas — The volt

Both are measured in volts:

🧑‍🏫 Teacher's explanation

Imagine a water pump system. The electromotive force (e.m.f.) is like the pump's ability to add pressure to the water; it is the total energy 'boost' provided to every unit of water to get it moving through the whole system. Potential difference (p.d.) is like the pressure drop that occurs when water flows through a narrow pipe or a filter; it is the energy 'spent' by the water to get through that specific part.

📖 Definitions

🔍 Worked example — Easy

A battery does 60 J of work to move a charge of 50 C around a complete circuit. Calculate the e.m.f. of the battery.

🔍 Worked example — Standard

A lightbulb has a potential difference of 4.5 V across it. If 0.2 C of charge passes through the bulb, how much work is done by the charge on the bulb?

🔍 Worked example — Exam-style

A circuit contains three identical 1.5 V cells connected in series. A second circuit contains two of these identical 1.5 V cells connected in parallel. Calculate the total e.m.f. for both circuits.

⚠️ Common errors

🧠 Quick check 1

🧠 Quick check 2

🎯 Exam question

Key ideas — Voltmeters

🧑‍🏫 Teacher's explanation

Think of electricity like water flowing through a plumbing system. The electromotive force (e.m.f.) is like the pressure provided by a pump that pushes the water through the entire loop. The potential difference (p.d.) is the drop in pressure that occurs as water flows through a specific part of the pipe, like a narrow nozzle or a filter.

📖 Definitions

🔍 Worked example — Easy

A battery does 60 J of work to move 5 C of charge around a complete circuit. Calculate the e.m.f. of the battery.

🔍 Worked example — Standard

A 12 V cell is connected to a lamp. If the work done on the lamp is 4.8 J, calculate the charge that passed through the lamp.

🔍 Worked example — Exam-style

Two identical 4.5 V cells are connected in parallel. A third identical cell is then added in series to the parallel pair. What is the total e.m.f. of the circuit?

⚠️ Common errors

🧠 Quick check 1

🧠 Quick check 2

🎯 Exam question

(a) Define electromotive force (e.m.f.). [2] (b) Calculate the work done by the battery when 2 C of charge passes through the circuit. [2] [4 marks]

Key ideas — Cells in series and in parallel

In series (positive of one joined to negative of the next), the e.m.f.s add:

🧑‍🏫 Teacher's explanation

Think of electromotive force (e.m.f.) as the 'push' or the total energy a battery provides to every single unit of charge. Imagine a water pump in a circular pipe system. The e.m.f. is the total pressure the pump adds to the water to get it through the whole loop. Potential difference (p.d.), however, is the pressure drop that happens when the water has to fight through a narrow section of pipe (like a resistor).

📖 Definitions

🔍 Worked example — Easy

A battery provides 120 J of work to move a charge of 50 C around a complete circuit. Calculate the e.m.f. of the battery.

🔍 Worked example — Standard

Three cells, each with an e.m.f. of 1.5 V, are connected in series. One of the cells is accidentally connected with the positive terminal to the positive terminal of the next cell (reverse polarity). Calculate the total e.m.f. of the circuit.

🔍 Worked example — Exam-style

A circuit consists of two identical 4.5 V cells connected in parallel, and a resistor. A charge of 2 C passes through the resistor, and 9 J of work is done by the source on this charge. Calculate the total e.m.f. of the source and the p.d. across the resistor.

⚠️ Common errors

🧠 Quick check 1

🧠 Quick check 2

🎯 Exam question

Worked example

Example 1. A battery does 54 J of work moving 6.0 C of charge round a circuit. Find its e.m.f.

🔍 Worked example — Easy

A battery does 54 J of work moving 6.0 C of charge around a circuit. Calculate its e.m.f.

🔍 Worked example — Standard

The p.d. across a lamp is 6.0 V. How much energy is transferred when 15 C passes through it?

🔍 Worked example — Exam-style

Four 1.5 V cells are connected in series. Three are facing the same direction, but one is connected in reverse. Calculate the total e.m.f. of the battery.

⚠️ Common errors

Common mistakes

Practice

Answers: (1) The electrical work done by a source in moving a unit charge around a complete circuit. (2) One joule per coulomb. (3) V = 36 / 3.0 = 12 V. (4) (a) 6.0 V; (b) 2.0 V. (5) In parallel across the component; its high resistance means almost no current passes through it, so it does not change the circuit it is measuring.

Ch 4 · 4.2.3 Electromotive Force and Potential Difference · O Level Physics 5054

All chapters in Electricity and Magnetism