A-Level Electricity Revision: EMF, Internal Resistance, Potential Dividers, and Circuit Analysis

Overview

A-Level electricity becomes much easier when you stop seeing it as a list of disconnected equations and start seeing it as a small set of linked models. Most exam questions in this area come back to four core ideas:

• EMF as the energy supplied per unit charge by a source
• Potential difference as the energy transferred per unit charge between two points in a circuit
• Internal resistance as the resistance inside the power source itself
• Potential dividers as circuits that share voltage between components in predictable ways

These ideas then feed into wider circuit analysis A-Level questions involving series and parallel combinations, terminal potential difference, sensor circuits, graphs, and practical interpretation.

A useful starting point is to keep the definitions precise:

• EMF, ε: energy supplied by the source per coulomb of charge. Unit: volt, where 1 V = 1 J C^-1.
• Potential difference, V: energy transferred from electrical stores to other forms per coulomb between two points. Also measured in volts.
• Internal resistance, r: the resistance within the cell or power supply that causes some energy to be dissipated inside the source when current flows.
• Terminal potential difference: the p.d. across the external circuit, equal to the EMF only when no current is drawn.

The key relationship for internal resistance A-Level physics is:

ε = I(R + r)

where:

• R is the total external resistance
• r is the internal resistance
• I is the current

This is often rearranged to the more exam-friendly form:

V = ε - Ir

Here V is the terminal potential difference. This equation explains why terminal p.d. falls as current increases: more charge passes each second, so more energy is wasted inside the source each second.

That one equation appears in many disguises. A graph of terminal p.d. against current gives:

• y-intercept = ε
• gradient = -r

If you are revising for AQA, Edexcel, or OCR, the wording may vary slightly, but the physical model stays the same. The safest approach is to learn the meaning first, then the algebra.

If you want the wider order of topics around this area, see A-Level Physics Topics List with Best Revision Order and High-Value Skills. For a topic-by-topic formula bank, use A-Level Physics Equations List by Topic with Rearrangements and Unit Checks.

Topic map

Use this section as a revision route. If a question feels difficult, it usually breaks down into one of these smaller decisions.

1. Distinguish EMF from potential difference

This is one of the most common conceptual checks in A-Level electricity revision. Students often say EMF is “the voltage of the cell”, which is not quite enough. A better answer is:

EMF is the energy supplied per coulomb by the source to the whole circuit.

Potential difference is the energy transferred per coulomb between two points in a circuit.

Why this matters:

• It prevents confusion between what the source provides and what individual components receive.
• It helps with explanation questions about why terminal p.d. is less than EMF when current flows.
• It supports better six-mark answers because you are describing energy transfer, not just reciting symbols.

2. Use internal resistance consistently

A source with internal resistance behaves as though an extra resistor is in series with the external circuit. So the total resistance is:

R_total = R + r

Then current is:

I = ε / (R + r)

And terminal p.d. across the external resistor is:

V = IR

Combining these ideas gives:

V = ε - Ir

This is not a new law. It is just a compact way of expressing that some of the source energy is dissipated internally.

Common mistake: using ε in place of V across an external component even when internal resistance is present. In questions involving a real cell, the voltage across the load is usually the terminal p.d., not the EMF.

3. Read graphs carefully

Graph questions are common because they test both practical understanding and algebra. The standard relation is:

V = ε - Ir

Compare with y = c + mx:

• V is on the y-axis
• I is on the x-axis
• intercept = ε
• gradient = -r

If the graph is straight and slopes downward, that supports the model of a constant internal resistance. If the data curve or scatter badly, the question may be inviting discussion of uncertainty, heating, or limits of the simple model.

For practical analysis skills, especially uncertainty and graph use, see A-Level Physics Required Practicals Explained: Core Methods, Uncertainties, and Analysis.

4. Understand potential dividers as voltage-sharing circuits

A potential divider revision question usually starts with two resistors in series across a supply. In a series circuit, the same current flows through both resistors, so the p.d. across each resistor depends on its resistance.

For two resistors, R₁ and R₂, in series across supply voltage V_s, the output across R₂ is:

V_out = V_s × R₂ / (R₁ + R₂)

This equation is worth memorising, but it is even more useful to understand the pattern:

• a larger resistor gets a larger share of the total p.d.
• if one resistor changes, the output changes
• this makes potential dividers useful with sensors such as LDRs and thermistors

Example thinking: if the output is measured across an LDR, then brighter light causes the LDR resistance to decrease. If its resistance decreases, its share of the supply voltage decreases, so the output p.d. across it falls. If the output is taken across the fixed resistor instead, the trend reverses.

This is where many students lose marks: they remember “LDR resistance decreases in bright light” but do not trace through where the voltmeter is connected.

5. Build full circuit analysis in stages

Many harder questions are not difficult because of advanced maths. They are difficult because several basic steps must be linked in the right order. A dependable method is:

1. Identify whether components are in series, parallel, or mixed.
2. Find equivalent resistance where needed.
3. Decide whether to use EMF or terminal p.d.
4. Use current rules and p.d. rules correctly.
5. Check units and whether your answer is physically sensible.

For example, in a source with internal resistance connected to an external resistor:

1. Total resistance = R + r
2. Current = ε / (R + r)
3. Terminal p.d. = IR or ε - Ir
4. Power dissipated internally = I²r
5. Power delivered to load = I²R

That last pair is especially useful in explanation questions about efficiency and wasted energy.

Related subtopics

This hub sits at the centre of several nearby A-Level electricity ideas. Revising them together usually gives better results than learning them in isolation.

Resistivity and material behaviour

Questions about resistance are stronger when you also understand what sets resistance at a material level. Resistivity links microscopic material properties to macroscopic circuit behaviour:

R = ρL / A

Even when a question is mainly about internal resistance or current, this background helps you explain temperature effects, wire dimensions, and why a component’s resistance may change in use.

Power and energy in circuits

You should be comfortable moving between:

• P = IV
• P = I²R
• P = V² / R

In internal resistance questions, power is often the missing link that explains where energy goes. If current increases, internal power loss I²r can increase noticeably, causing heating in the source and a lower terminal p.d.

Sensor circuits and practical applications

Potential dividers are rarely examined as pure algebra only. They are often tied to:

• LDRs in lighting control
• thermistors in temperature sensing
• variable resistors for calibration
• comparator or switching circuits in broader electronics contexts

When revising, always ask:

• Which component changes resistance?
• Is its resistance increasing or decreasing?
• Across which component is the output measured?
• So does V_out rise or fall?

If you can answer those four questions calmly, many potential divider questions become routine.

Required practical links

This topic often connects to measuring EMF and internal resistance experimentally, or to plotting and interpreting current-voltage data. Practical questions may test:

• control of variables
• choice of meter placement
• reducing heating errors
• graph interpretation
• uncertainty in gradients and intercepts

That is why theoretical revision and practical revision should be combined rather than split into separate folders.

Exam technique for explanation questions

Electricity questions often look numerical, but a surprising number are really explanation tasks in disguise. You may be asked why current changes, why terminal p.d. falls, or why a sensor circuit behaves in a certain way. In these answers, do not jump straight to the final statement. Build a chain:

1. state what changes
2. state the effect on resistance, current, or p.d.
3. link to the equation or rule
4. state the final outcome

For extended responses, see How to Answer 6 Mark Physics Questions: A GCSE and A-Level Exam Technique Guide.

Bridging from GCSE to A-Level electricity

If you feel that A-Level circuit work is slipping because the basics are shaky, it helps to revisit core ideas such as series and parallel rules, resistance, power, and standard circuit symbols. A quick reset with GCSE Electricity Revision: Equations, Circuits, Power, and Resistance can save time.

How to use this hub

This page works best as a repeat-visit resource rather than a one-off read. A good revision routine is to return to it with different goals each time.

First pass: secure definitions and core equations

Make sure you can state, from memory:

• the difference between EMF and potential difference
• what internal resistance means physically
• why terminal p.d. falls when current increases
• the potential divider equation
• how to interpret a V against I graph

If your definitions are vague, numerical work becomes more fragile.

Second pass: practise worked steps

Take one question at a time and label the logic, not just the arithmetic. For example:

• real cell present → include internal resistance
• series circuit → same current
• find total resistance first
• use current to find terminal p.d.
• compare with EMF to identify lost volts

This kind of annotation trains decision-making, which is what most exam questions really test.

Third pass: mix question types

Do not revise only one format. Mix:

• definition questions
• short calculations
• graph interpretation
• sensor and potential divider questions
• practical method and uncertainty questions

That is the best way to build flexible understanding rather than pattern-matching.

A short self-test checklist

Before a class test or mock, check whether you can do the following without notes:

• Write down V = ε - Ir and explain each term.
• Explain why terminal p.d. equals EMF only when current is zero or negligible.
• Find current in a circuit containing external resistance and internal resistance.
• Determine EMF and internal resistance from a graph.
• Predict whether a potential divider output rises or falls when sensor resistance changes.
• Explain energy loss inside a source in terms of heating.

If two or more of these still feel uncertain, this topic deserves another focused session.

Useful supporting reads

To broaden or reinforce this area, these guides are worth keeping nearby:

• A-Level Physics Equations List by Topic with Rearrangements and Unit Checks
• A-Level Physics Required Practicals Explained: Core Methods, Uncertainties, and Analysis
• A-Level Physics Topics List with Best Revision Order and High-Value Skills

Although it is from a different topic area, the habit of careful model-building used in A-Level Waves Revision: Superposition, Stationary Waves, Diffraction, and Refraction is also useful here: define terms precisely, identify the governing relationship, and then apply it to unfamiliar contexts.

When to revisit

Revisit this hub whenever circuit questions start to feel procedural rather than understandable. In practice, there are a few clear moments when this topic needs another look:

• Before tests on electricity, especially if equations are blending together
• When starting required practical revision, because graph work and measurement method matter here
• After getting graph or sensor questions wrong, since these usually reveal a gap in underlying circuit thinking
• When revising mixed-topic papers, because electricity often appears in combination with energy, materials, and practical analysis
• When learning a new related subtopic, such as resistivity or electronics, because this model supports later work

A practical action plan for your next revision session:

1. Write the five key equations from memory.
2. Define EMF, terminal p.d., and internal resistance in full sentences.
3. Do one graph question, one potential divider question, and one mixed circuit calculation.
4. Mark where you made the first mistake, not just the final one.
5. Return to this hub and revise the exact weak point.

That last step matters. In physics revision, improvement usually comes faster from targeting the first gap in the chain than from repeating whole chapters passively.

If you want your electricity revision to hold under exam pressure, aim for this standard: you should be able to explain the energy story, set up the circuit model, choose the correct equation, and justify your answer in words as well as numbers. Once those pieces are in place, EMF, internal resistance, potential dividers, and wider circuit analysis stop feeling like separate topics and start behaving like one coherent part of A-Level physics.