Electricity.

HookOne missed penalty, a million kettles, and twelve seconds to respond

ModelCharge, current, pd — three definitions that do real work

Current is the rate of flow of charge: \(I=\Delta Q/\Delta t\), so one ampere is one coulomb per second. Since each electron carries \(1.60\times 10^{-19}\ \text{C}\), a 1 A current is about \(6.2\times 10^{18}\) electrons passing per second — a number worth having felt once, because it explains why current is smooth and continuous on every human scale.

Potential difference is energy accounting per unit of charge: the work done per coulomb moved between two points, \(V=W/Q\), so one volt is one joule per coulomb. A 230 V supply gives each coulomb 230 J to spend in the element it passes through. Resistance is then defined as the ratio \(R=V/I\) — always calculable, for any component, at any point on its graph. Keep that separate from Ohm's law, which is the much stronger claim that current is proportional to pd at constant temperature. Every component has a resistance; only some obey Ohm's law, and the distinction is a favourite AQA one-marker.

ModelThree I-V characters — ohmic conductor, filament lamp, diode

To take an I-V characteristic you vary the pd across a component (a variable supply or potentiometer), record current and pd, then reverse the connections for the negative quadrant. Three shapes carry the marks.

An ohmic conductor — a metal wire at constant temperature — gives a straight line through the origin: constant gradient, constant resistance. A filament lamp starts straight but flattens: the current heats the filament towards 2,500 °C, the metal ions vibrate more violently, conduction electrons are scattered more often, so resistance climbs as pd rises. The curve is symmetric — reverse the pd and the heating is the same. A semiconductor diode is the deliberately lopsided one: negligible current in reverse bias and below the threshold of about 0.6 V forward, then a near-vertical rise as it switches on. When you sketch these, examiners look for the flattening of the lamp's curve (not a sharp corner), the diode's flat floor before 0.6 V, and axes labelled with quantities and units.

ModelResistivity — and the resistance that vanishes entirely

Resistance depends on the sample; resistivity \(\rho\) belongs to the material: \(R=\rho l/A\), so \(\rho=RA/l\) with units of \(\Omega\,\text{m}\) — ohm-metres, not ohms per metre, an error that costs a mark every session. Copper sits near \(1.7\times 10^{-8}\ \Omega\,\text{m}\); the nichrome in a kettle element is about sixty times higher, which is exactly why the element, not the flex, gets hot.

Temperature moves resistivity in opposite directions for the two materials AQA cares about. In metals, hotter ions vibrate more and scatter electrons more: resistance rises roughly linearly. In an NTC thermistor, extra thermal energy liberates more charge carriers, and that effect wins: resistance falls steeply as temperature rises — the basis of electronic thermometers and the sensing circuits in the potential-divider block below. Cool some metals and alloys the other way and something stranger happens: below a critical temperature, resistivity does not just get small, it becomes exactly zero — superconductivity. A current set up in a superconducting loop persists with no source. Niobium-titanium wire at about 10 K, bathed in liquid helium, winds the magnets of every MRI scanner; ceramic superconductors work above 77 K, cheap liquid-nitrogen territory, and carry lossless current in prototype grid cables and maglev track magnets. The catch, and the evaluation point examiners want, is the cooling bill.

DataRequired practical 5 — resistivity of a wire

The plan follows the equation \(\rho=RA/l\): you need an area, and resistance as a function of length. Measure the wire's diameter with a micrometer (checking its zero error first) at three or more positions and in two perpendicular orientations at each, because drawn wire is never perfectly circular; average, then \(A=\pi d^2/4\). Tape the wire straight along a metre rule. Clamp one connection at zero, touch a crocodile clip at a series of lengths, and for each length record V and I to get \(R=V/I\).

Plot R against l. The line should be straight with gradient \(\rho/A\), so \(\rho=\text{gradient}\times A\) — and the graph, not any single reading, is the result. Contact resistance where the clips grip the wire adds a constant to every measurement, and on the graph that constant lands harmlessly in the intercept while the gradient stays true; a one-length calculation would swallow it whole. Keep the current small and the readings brief, because current heats the wire and resistivity is temperature-dependent — you would be measuring a moving target. The dominant uncertainty is the diameter: it is squared in \(A\), so its percentage uncertainty counts double. That is why the micrometer, resolution 0.01 mm, is non-negotiable kit.

MechanismCircuit rules — two conservation laws in disguise

Series and parallel rules are not arbitrary recipes; they are conservation laws. Charge is conserved, so the current entering any junction equals the current leaving, and around a single series loop the current is the same everywhere. Energy is conserved, so the pds around any loop add up to the source pd. From those two facts: series resistors share the current and add their pds, giving \(R_T=R_1+R_2+\dots\); parallel resistors share the current and see the same pd, giving \(1/R_T=1/R_1+1/R_2+\dots\), always less than the smallest branch — every new branch is an extra route for charge.

Power comes in three interchangeable forms, \(P=VI=I^2R=V^2/R\); pick the one built from the quantities that are actually fixed in your problem. Mains sockets are wired in parallel precisely so each appliance gets the full 230 V and switches independently — which is what makes a national kettle surge possible in the first place.

MechanismThe potential divider — turning a resistance into a signal

Two resistors in series split the supply pd in the ratio of their resistances: the output across \(R_2\) is \[V_{out}=V_{in}\,\frac{R_2}{R_1+R_2}\] That one line is most of sensor electronics. Make \(R_1\) an NTC thermistor and watch the logic: temperature rises, thermistor resistance falls, so a larger share of the supply appears across the fixed resistor \(R_2\) — a rising voltage that can trip a transistor or comparator and switch a cooling fan. Swap the two components and the same rise in temperature produces a falling output that can fire a heater instead: which resistor you take the output across is a design decision, and AQA asks you to reason it, not memorise it. An LDR in place of the thermistor gives light-operated versions — the automatic streetlight is a divider whose output crosses a threshold at dusk.

For a continuously variable output, use a potentiometer: a single track with a sliding contact, dividing the supply anywhere from zero to the full pd. Unlike a variable resistor in series with a lamp, a potentiometer can take the output all the way down to genuinely zero volts — a standard 'explain the advantage' mark.

ModelEMF and internal resistance — the volts you never see

A source's EMF \(\varepsilon\) is the energy it gives each coulomb — chemical energy converted to electrical, per unit charge, measured across the terminals when no current flows. Real sources also have an internal resistance \(r\): the charge has to get through the cell's own chemistry, and that costs energy the moment current flows. The bookkeeping is one line: \(\varepsilon=I(R+r)\), or equivalently terminal pd \(V=\varepsilon-Ir\). The term \(Ir\) is the 'lost volts' — energy per coulomb spent heating the inside of the source, never available to the circuit.

Internal resistance explains a family of everyday effects. A car battery has \(r\) of order 0.01 Ω, so it can source the hundred-plus amps a starter motor demands; a 9 V PP3, with \(r\) around 1–2 Ω, could never — short-circuit current is capped at \(\varepsilon/r\). A phone battery's internal resistance climbs in the cold, so under load its terminal voltage dips below the cutoff and the phone dies showing 30% — carry it in a warm pocket and it revives. Maximum current, sagging terminal pd, warm batteries after use: all one equation.

DataRequired practical 6 — EMF and internal resistance of a cell

The circuit is minimal: cell, ammeter and variable resistor in series; voltmeter across the cell's terminals. Step the load resistance through six or so values and record terminal pd V and current I each time. The physics does the rest, because \(V=\varepsilon-Ir\) is already in straight-line form: plot V (y-axis) against I (x-axis) and the intercept on the V-axis is the EMF while the gradient is \(-r\). A fresh AA cell typically lands near \(\varepsilon\approx 1.6\ \text{V}\) with \(r\) of a few tenths of an ohm.

The error discipline is mostly about the cell misbehaving. Current heats the cell and runs it down, shifting both \(\varepsilon\) and \(r\) mid-experiment — so include a switch, close it only while reading, work quickly, and keep currents modest with a fixed protective resistor in series. Take the sweep twice (ascending and descending) and average to expose drift. The uncertainties in V and I come from the meters, but the systematic threat is a tired cell: with a nearly flat battery the 'constants' you are measuring genuinely are not constant, and the scatter about the line tells you so. Quote \(\varepsilon\) and \(r\) from the line of best fit, and estimate their uncertainty from steepest and shallowest acceptable lines through the error bars.

VocabularyKey terms the mark scheme pays for

TrapsMisconceptions that cost marks

ExamWhat examiners want