AQA A-Level Physics: Electricity — Complete Revision Guide
AQA A-Level Physics: Electricity — Complete Revision Guide
Electricity (Section 3.5 of AQA 7408) is the last major content unit of Paper 1 and the half of the course that most directly connects A-Level Physics to undergraduate engineering and applied science. The toolkit you build here — charge carriers, potential difference, resistance, network analysis, the EMF model of real sources — drives every subsequent electrical topic on the course. Paper 2 assumes you have it; the magnetic-fields work in AQA A-Level Physics: Magnetic Fields and Induction leans on it constantly; the optional electronics unit (AQA A-Level Physics: Electronics) extends it. Two of the twelve required practicals — RP5 (resistivity) and RP6 (EMF and internal resistance) — sit inside this unit.
This guide walks through the full content of AQA Section 3.5: charge, current and the I = nAvq model; potential difference and EMF; resistance, Ohm's law and resistivity; I–V characteristics of fixed resistors, filament lamps and diodes; series and parallel circuits; EMF and internal resistance; potential dividers; and Kirchhoff's two laws. It also unpacks RP5 and RP6 at the level of detail Paper 3 Section A demands. It is written for students who want to go beyond formula-substitution into genuine circuit reasoning — the level of fluency that makes Paper 1 question 9 (the longer circuit problem) feel like an easy mark.
Where Electricity Sits in the Specification
Section 3.5 carries roughly a sixth of Paper 1's 85 marks and is heavily synoptic with the earlier Paper 1 units. Mechanics-style energy reasoning (from AQA A-Level Physics: Mechanics and Materials) reappears in the work–energy framing of EMF and potential difference. The uncertainty toolkit (from AQA A-Level Physics: Measurements and Their Errors) is essential for RP5 and RP6. The ideas pivot directly into magnetic-flux problems on Paper 2. Our AQA A-Level Physics: Electricity course covers the topic in ten lessons.
Charge and Current
Charge is a fundamental property of matter. The elementary charge is e = 1.60 × 10⁻¹⁹ C. Electrons carry charge −e; protons carry +e.
Current is the rate of flow of charge: I = ΔQ/Δt. Units: amperes (A). 1 A = 1 C s⁻¹.
Conventional current is the direction in which positive charge would flow. In a metal wire, the actual charge carriers are electrons moving in the opposite direction — but circuit diagrams and equations use the conventional-current direction throughout. This is purely a historical convention from before the electron was discovered; you handle it by treating conventional current as your reference and remembering that electron flow is opposite.
The I = nAvq Model
For a conductor with cross-sectional area A, in which charge carriers of charge q each move with mean drift velocity v, the current is:
I = nAvq
where n is the number density of charge carriers (carriers per m³). This is the most physically informative equation in the topic — it links macroscopic current to microscopic motion.
For a copper wire of diameter 1 mm carrying 1 A, n (the conduction-electron density of copper) ≈ 8.5 × 10²⁸ m⁻³, A = π × (0.5 × 10⁻³)² ≈ 7.9 × 10⁻⁷ m², q = 1.6 × 10⁻¹⁹ C. Solving for v: v = I / (nAq) ≈ 9 × 10⁻⁵ m s⁻¹, or about 90 micrometres per second. The mean drift velocity is small — but the carrier density is enormous, which is why even tiny drift velocities produce useful currents.
The slowness of drift velocity is a frequent exam-question hook. Students sometimes (wrongly) conclude that switching on a light should take ages, since electrons drift slowly. The resolution: every electron in every part of the wire starts to drift essentially simultaneously when the field is applied — the signal travels at near-light speed; only the individual carriers drift slowly.
Potential Difference and EMF
Potential difference (pd) between two points is the work done per unit charge in moving charge from one point to the other through a passive component. V = W/Q. Units: volts (V); 1 V = 1 J C⁻¹.
Electromotive force (EMF) is the work done per unit charge by a source (battery, dynamo) in driving charge through the whole circuit, including the source itself. ε = W/Q. Units: also volts.
Both have units of volts but carry different physical meanings. Potential difference is what a load (a resistor, a lamp) takes; EMF is what a source provides. In an ideal source, the two are equal; in a real source, they differ by the voltage dropped across the source's own internal resistance — see EMF and internal resistance below.
The work delivered to or extracted from a circuit element is W = VIt. Power is P = VI. Using V = IR, this becomes P = I²R = V²/R — three equivalent forms for the power dissipated by a resistor.
Resistance, Ohm's Law and Resistivity
Resistance R = V/I. Units: ohms (Ω); 1 Ω = 1 V A⁻¹.
A component is ohmic if its resistance is constant — that is, its V–I graph is a straight line through the origin. A fixed-value resistor at constant temperature is ohmic. A filament lamp is not ohmic because its resistance increases with temperature; a diode is not ohmic because its resistance varies sharply with applied voltage.
Resistivity
The resistance of a wire depends on three things: its length, its cross-sectional area, and the material it's made of. The material property is resistivity ρ:
R = ρL / A
A long thin wire has high resistance; a short fat wire has low resistance. Resistivity has units of Ω m. Copper has ρ ≈ 1.7 × 10⁻⁸ Ω m. Aluminium has ρ ≈ 2.8 × 10⁻⁸ Ω m. Iron has ρ ≈ 1.0 × 10⁻⁷ Ω m. Glass has ρ ≈ 10¹⁰ Ω m — an insulator's resistivity is enormous.
Resistivity is temperature-dependent. For metals it increases with temperature (the metal's atoms vibrate more, scattering electrons more often). For semiconductors it decreases with temperature (thermal energy frees more charge carriers). For superconductors below a critical temperature, ρ drops to exactly zero.
I–V Characteristics
The current–voltage graph of a component reveals its electrical behaviour at a glance.
| Component | I–V graph | Notes |
|---|---|---|
| Fixed resistor (constant T) | Straight line through origin | Gradient = 1/R, slope is constant |
| Filament lamp | Curve, gradient decreases at high V | Resistance rises as the filament heats |
| Diode | Zero until threshold (~0.7 V for Si), then steeply rising | Conducts in one direction only |
| NTC thermistor | At fixed T, linear; over varying T, resistance falls as T rises | Used as temperature sensors |
| LDR | Linear at fixed light level; resistance falls as light intensity rises | Used as light sensors |
The three components a Paper 1 question is most likely to ask about are the fixed resistor, the filament lamp, and the diode. Be able to sketch the I–V characteristic for each and explain why it looks the way it does in terms of the physics inside the component.
Series and Parallel Circuits
Series
Components are in series if the same current flows through each. For n resistors in series:
R(total) = R₁ + R₂ + … + Rₙ
The total potential difference is the sum of the pd across each resistor; each takes a share proportional to its resistance.
Parallel
Components are in parallel if they have the same potential difference across each. For n resistors in parallel:
1/R(total) = 1/R₁ + 1/R₂ + … + 1/Rₙ
The total current is the sum of the current through each branch; each takes a share inversely proportional to its resistance. The parallel combination is always less than the smallest individual resistance.
Worked Example
A 6 Ω resistor in series with a parallel combination of 3 Ω and 6 Ω, driven by a 9 V ideal supply. Find the current from the supply.
Parallel combination: 1/R_p = 1/3 + 1/6 = 3/6, so R_p = 2 Ω. Total resistance: 6 + 2 = 8 Ω. Current from supply: 9/8 = 1.125 A.
Voltage across parallel combination: IR_p = 1.125 × 2 = 2.25 V. Current through 3 Ω branch: 2.25 / 3 = 0.75 A. Current through 6 Ω branch: 2.25 / 6 = 0.375 A.
The currents in the two parallel branches sum to 1.125 A — the current entering and leaving the parallel section. This is Kirchhoff's current law in action.
EMF and Internal Resistance
A real battery has not just an EMF but also an internal resistance r, which represents the resistive losses inside the source itself. The terminal pd (the voltage you measure across the battery's terminals when current is flowing) is:
V = ε − Ir
When the battery delivers no current (open circuit), the terminal pd equals the EMF. As the current rises, the terminal pd drops because of the Ir loss inside the cell.
If a battery of EMF ε and internal resistance r drives a load of external resistance R, the circuit current is:
I = ε / (R + r)
The power delivered to the external load is P = I²R = ε² R / (R + r)². This is maximised when R = r (the maximum power transfer condition). Beyond this, increasing R reduces the current faster than it boosts the voltage share; below it, the current is high but most of the power is dissipated internally.
Internal resistance is why a torch dims when you try to draw too much current, why a starter motor on a car can dim the headlights briefly, and why batteries warm up under heavy load (the dissipated I²r heats the cell).
Potential Dividers
A potential divider uses two resistors in series across a supply to produce a smaller, controllable output voltage. For resistors R₁ and R₂ in series across an EMF ε, the pd across R₂ is:
V_out = ε × R₂ / (R₁ + R₂)
The divider is the standard way to generate a fixed reference voltage from a higher supply. Replace one of the fixed resistors with a sensor (a thermistor, an LDR, a strain gauge) and you have a sensor circuit: as the sensor's resistance changes with the environmental variable, the output voltage changes too. This is the foundation of countless transducer circuits.
A rheostat uses a single variable resistor in series with the load to control current. A potentiometer uses a three-terminal variable resistor as a continuously variable potential divider — useful for full-range smooth control (e.g. a volume knob).
Kirchhoff's Laws
The two Kirchhoff laws formalise the conservation principles for circuits.
Kirchhoff's current law (junction rule): the algebraic sum of currents into any node is zero. Equivalently, current in = current out at every node. This is conservation of charge.
Kirchhoff's voltage law (loop rule): the algebraic sum of EMFs and pds around any closed loop is zero. This is conservation of energy.
For simple circuits, the series/parallel formulae suffice. For more complex networks (two-loop circuits, bridges), apply Kirchhoff's laws directly. Choose a current direction in each branch, write KCL at every node and KVL around every independent loop, and solve the simultaneous equations.
Required Practical 5: Measuring Resistivity
The setup: a thin uniform wire of known resistivity material (constantan or nichrome) is clamped at one end, runs over a pulley at the other, and is held taut by a small load. A power supply, ammeter and voltmeter are connected across a measured length of the wire.
The method:
- Measure the diameter of the wire d at three points along its length using a micrometer. Average. Calculate area A = π(d/2)².
- Set up a circuit with the wire, ammeter (in series) and voltmeter (across a known length L of the wire). Keep the current small to avoid heating.
- For each chosen length L, record the voltmeter and ammeter readings and calculate R = V/I.
- Plot R against L. The graph should be a straight line through the origin with gradient ρ/A. Multiply the gradient by A to extract ρ.
Sources of uncertainty: the diameter (small, and squared in A) dominates. The percentage uncertainty in d contributes 2 × %d to the total. See AQA A-Level Physics: Measurements and Uncertainties Guide for the full propagation.
Method improvements: keep the wire taut (a slack wire has an ill-defined cross-section), measure several diameters and check for taper, keep the current low to minimise heating, and use a long range of L to improve the gradient precision.
Required Practical 6: EMF and Internal Resistance
The setup: a cell of unknown EMF ε and internal resistance r is connected to a variable resistor (rheostat), a voltmeter across the cell terminals, and an ammeter in series.
The method:
- Vary the resistance to obtain a range of currents from near zero up to a chosen maximum (don't go too high, or the cell heats and parameters change).
- For each setting, record terminal pd V and current I.
- Plot V against I. The relationship V = ε − Ir predicts a straight line with y-intercept ε and gradient −r.
- Extract ε from the intercept and r from the magnitude of the gradient.
Sources of uncertainty: the gradient is small (internal resistances are typically a few tenths of an ohm) and so the percentage uncertainty in r is high — multiple repeats and a wide range of currents help. The intercept is taken at zero current, where the voltmeter measures essentially the open-circuit EMF.
Method improvements: switch the circuit off between readings to avoid the cell warming; use a high-resistance voltmeter (essentially zero current drawn) so the voltmeter doesn't load the cell; check by directly measuring V with no load (gives ε by definition).
Safety: old cells can leak. Discard any cell with visible corrosion. Heat is dissipated in the rheostat under high current — touch carefully.
How to Study This Topic
Three habits separate strong electricity performances from weak ones.
- Always redraw the circuit before solving. Tag every component with its value. Identify nodes. Distinguish series from parallel. A messy diagram produces messy reasoning; a clean diagram lets you see the network's structure at a glance.
- Practise both directions: forward (given component values, find I and V) and backward (given I and V, find component values). Paper 1 question 9 is often the backward kind — you're given readings and asked to deduce the network's hidden parameters. Forward practice gets the algebra fluent; backward practice gets your physical intuition sharp.
- For RP5 and RP6, learn the gradient–intercept extraction routine cold. RP5 plots R against L; RP6 plots V against I. Know which graph you'd draw, which axes go where, and how the gradient and intercept relate to the unknowns.
Common pitfalls to inoculate against:
- Treating a battery as ideal (ignoring internal resistance) when the question gives you r — almost always intentional, and the question wants you to use it.
- Computing parallel resistance as R₁ + R₂ (that's series) or as 1/(R₁ + R₂) (also wrong — it's 1/(1/R₁ + 1/R₂)).
- Treating the I in I = nAvq as the current in the source rather than the current through the conductor at the point under consideration.
- Confusing Ohm's law (V = IR, definition of resistance) with "Ohmic behaviour" (the special case of constant R).
- Forgetting to use cross-sectional area in resistivity — students sometimes use the diameter directly.
Related LearningBro Courses
- AQA A-Level Physics: Electricity — the ten-lesson home course for Section 3.5
- AQA A-Level Physics: Magnetic Fields and Induction — Paper 2 extension into magnetism and induced EMF
- AQA A-Level Physics: Electronics — optional unit building on potential dividers and I–V characteristics
- AQA A-Level Physics: Mechanics and Materials — the natural Paper 1 partner topic
- AQA A-Level Physics: Measurements and Their Errors — the toolkit for processing RP5 and RP6 data
Common Exam Pitfalls
Electricity questions tend to be lost in the same handful of ways every year. Recognising the trap before you start writing is worth several marks across Paper 1.
- Confusing emf with terminal pd. EMF epsilon is the work done per unit charge by the cell on charges passing through it. Terminal pd V is what the rest of the circuit sees: V = epsilon - I r. Under load the terminal pd is always smaller than the emf, and the difference I r is dissipated inside the cell. Many candidates write "the voltage of the cell is 1.5 V" without specifying which they mean.
- Internal resistance treated as zero by default. Unless the question explicitly says "a cell of negligible internal resistance", you must include r. Series-circuit current calculations that ignore r overestimate the current and the power dissipated externally.
- Forgetting that resistivity is a property of the material, not the wire. Resistance R = rho L / A depends on geometry; resistivity rho does not. A question that asks you to identify the material from a measured R, L and A requires you to compute rho and compare it with tabulated values, not just quote R.
- Mishandling parallel resistors. 1/R_total = sum(1/R_i) — not the sum of the resistances. For just two resistors in parallel a useful shortcut is R = R_1 R_2 / (R_1 + R_2). The total parallel resistance is always smaller than the smallest branch resistance; if your answer is larger, you have made an algebraic error.
- Power equations used carelessly. P = I V is always valid; P = I^2 R and P = V^2 / R are only valid for the component carrying that current I and dropping that voltage V. Plugging the supply emf into V^2 / R when R is one resistor of several in series will give a wildly wrong answer.
- Kirchhoff sign errors. When applying the voltage law around a loop, choose a direction of travel and keep it consistent. EMFs drive current from negative to positive terminal inside the cell; voltage drops across resistors are in the direction of current flow. Mark these on your circuit diagram before writing the equation.
- Forgetting to convert mm^2 to m^2 in resistivity questions. Cross-sectional area is almost always given in mm^2; resistivity tables are in ohm-metres. Failing to convert is a six-order-of-magnitude error that produces an answer the size of a galaxy.
Related Reading
- AQA A-Level Physics: Measurements and Uncertainties Guide — error propagation in resistivity and internal-resistance experiments
- AQA A-Level Physics: Mechanics and Materials Guide — the Paper 1 mechanics partner unit
- AQA A-Level Physics: Exam Strategy Guide — how electricity questions are structured on Paper 1 and Paper 3