Electricity & Magnetism

Like charges repel and unlike charges attract. That single rule explains everything from a balloon sticking to a wall to the structure of the atom itself.

In a solid, the positive charges are the protons, locked inside nuclei that are fixed in the structure of the material. They cannot go anywhere. Only the electrons are free to move, and in a metal a few of them are very free indeed — detached from their parent atoms and able to drift through the whole lattice.

This is why an object becomes positively charged by losing electrons, never by gaining protons. Rub a polythene rod with a cloth and electrons transfer from cloth to rod: the rod becomes negative, the cloth positive. Saying that "positive charge moved to the cloth" describes the same outcome but scores nothing, because it is not what happened.

Charge is also quantised. Every charge you can measure is a whole-number multiple of the elementary charge e = 1.6 × 10⁻¹⁹ C. There is no such thing as half an electron of charge.

Current is the rate at which charge flows past a point. One ampere means one coulomb passing every second — roughly six million million million electrons.

Two things about current cause endless confusion, and both are worth settling now. First, current is not used up going round a circuit. The ammeter reading before a lamp and after it are identical. What the lamp takes is energy, not charge.

Second, conventional current is defined as flowing from the positive terminal of a supply to the negative. Electrons actually drift the opposite way, because they are negative. Every rule you will use — the motor rule, the right-hand grip rule, the direction arrows on a circuit diagram — is stated for conventional current. Use it consistently and the electrons' disagreement never matters.

I

currentA

Q

chargeC

t

times

Raise the resistance and watch the current fall for the same supply voltage. The relationship is I = V/R — halving the resistance doubles the current.

A battery does not supply charge — the charge is already in the wires. What it supplies is energy, and the measure of how much energy it gives each coulomb is its electromotive force or e.m.f., also measured in volts.

Potential difference is the same quantity measured the other way round: the energy each coulomb gives up in a component. A 12 V battery hands 12 joules to every coulomb; a 12 V lamp takes 12 joules back from every coulomb passing through it.

Because p.d. is a difference between two points, it is always measured across a component, never through it. A voltmeter therefore goes in parallel with whatever you are measuring, and must have a very high resistance so that it draws almost no current itself.

V

potential differenceV

E

energy transferredJ

Q

chargeC

Resistance measures how strongly a component opposes the flow of charge, and it is defined by R = V/I. That definition applies to every component without exception, whether or not its resistance stays constant.

Ohm's law is a narrower claim: for a metallic conductor at constant temperature, the current is directly proportional to the potential difference. The words "at constant temperature" are not decoration — leave them out and the statement is false, and the mark is lost.

The reason for the condition is that resistance rises with temperature in a metal. The metal ions vibrate more strongly when hot, so the drifting electrons collide with them more often, and each collision impedes the flow.

R

resistanceΩ

ρ

resistivityΩ m

L

lengthm

A

cross-sectional aream²

The four graphs you are asked to sketch, on one pair of axes. The orange line from the origin to the moving point is the thing to watch: R = V/I is the gradient of THAT line, not of the curve. On the fixed resistor it lies along the curve and never moves, which is what Ohm’s law looks like. On the lamp it tilts over as the filament heats and the resistance rises; on the thermistor it swings the other way as the resistance falls. On the diode there is nothing at all until about 0.7 V, and nothing ever in reverse.

Two instruments, two rules, and getting them the wrong way round is one of the most reliably penalised errors in the subject.

An ammeter measures current, so it must have the current flowing through it. It goes in series, and it must have very low resistance — otherwise it would reduce the very current it is supposed to be measuring.

A voltmeter measures potential difference, which is a difference between two points. It goes in parallel, connected across the component, and it must have very high resistance so that hardly any current is diverted through it.

When drawing a circuit diagram, use the standard symbols and keep the wires as straight lines with right-angled corners. A neat diagram is quicker to mark and quicker to check.