Electricity & Magnetism Notes

Last reviewed 30 Sept 2026 · 8 min read

Electric charge

Matter contains positive charges (protons), negative charges (electrons) and neutral particles (neutrons). Charge is quantised: the smallest free charge is that of the electron, $e = 1.6 \times 1 0^{- 19}$ C. The SI unit of charge is the coulomb (C).
Like charges repel; unlike charges attract. Charge is conserved.
Coulomb's law: $F = k \frac{q _{1} q _{2}}{r ^{2}}$ , with $k = 9 \times 1 0^{9} N m^{2} C^{- 2}$ .
Conductors (metals, graphite, acids, salt solutions, the human body) allow charge to flow; insulators (rubber, glass, plastic, dry wood, air) do not; semiconductors (silicon, germanium) lie in between.
Charging: by friction (glass rod rubbed with silk becomes positive, ebonite/plastic rubbed with fur becomes negative), by conduction and by induction.
The gold-leaf electroscope detects charge. Lightning is a huge electric discharge between clouds or between a cloud and the ground; a lightning conductor (arrester) on tall buildings safely conducts the charge to earth (Benjamin Franklin).

Electric current and potential difference

Electric current is the rate of flow of charge: $I = \frac{Q}{t}$ . The SI unit is the ampere (A): 1 A = 1 C/s. By convention the direction of current is from the positive to the negative terminal (opposite to the flow of electrons).
Ammeter measures current; it is connected in series and has a very low resistance.
Potential difference (voltage) between two points is the work done per unit charge: $V = \frac{W}{Q}$ . SI unit: volt (V). Voltmeter measures it; it is connected in parallel and has a very high resistance.
A cell is a source of EMF; a battery is a combination of cells. The EMF is the potential difference across the terminals when no current is drawn.

Ohm's law

At constant temperature, the current through a conductor is proportional to the potential difference across it:

V = I R

$R$ is the resistance (unit: ohm, Ω). Conductors that obey Ohm's law are ohmic (metals at constant temperature); a diode and a filament lamp are non-ohmic.

Resistance and resistivity

R = ρ \frac{l}{A}

Resistance is directly proportional to length and inversely proportional to the cross-section area, and depends on the material ( $ρ$ = resistivity, unit Ω·m) and temperature. For metals, resistance increases with temperature; for semiconductors and insulators it decreases.

Good conductors: silver (best), copper, gold, aluminium. Nichrome, constantan and manganin have high resistivity (used in heaters, resistance boxes). Tungsten has a high melting point (3422 °C) and is used for bulb filaments. Superconductors have zero resistance below a critical temperature.
Conductance $G = 1/ R$ (unit siemens).

Combination of resistors

Series	Parallel
$R = R_{1} + R_{2} + \dots$	$\frac{1}{R} = \frac{1}{R _{1}} + \frac{1}{R _{2}} + \dots$
same current through all; voltages add	same voltage across all; currents add
total resistance is more than the largest	total resistance is less than the smallest
if one fails, the circuit breaks (Christmas lights)	if one fails, others work (household wiring)

Worked ExampleExample — combination

Resistors of 6 Ω and 3 Ω are connected in parallel across a 12 V battery.

Solution. $\frac{1}{R} = \frac{1}{6} + \frac{1}{3} = \frac{1}{2} \Rightarrow R = 2 Ω$ . Total current $I = \frac{12}{2} = 6 A$ (4 A through the 3 Ω resistor and 2 A through the 6 Ω resistor).

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