A guided, step-by-step walk through electric current — every idea comes alive in the live panel on the right. Scroll down; water flows through pipes, the cell pumps charge uphill, the V–I line draws itself and the heating element glows.
1 — Electric current = flow of charge
Turn on a torch and electrons drift through the wire. Electric current is the rate of flow of charge — exactly like litres of water per second flowing past a point in a pipe.
- Current (I) — charge passing a point per second: I = Q / t. Its unit is the ampere (A); one ampere is one coulomb per second.
- Conventional current — taken from + to − (the direction positive charge would move); electrons actually drift the opposite way.
Definition of currentI = Q / t · 1 A = 1 C / s · Q = I t
worked — charge through a bulb
A bulb draws 0.5 A for 2 minutes. How much charge?
Q = I t = 0.5 × 120 = 60 C
2 — Potential difference & EMF
Water won't flow uphill by itself — a pump must raise it. In a circuit the cell is that pump: it lifts charge to a higher potential so it can flow round and do work.
- Potential difference (V) — energy delivered per coulomb between two points: V = W / Q. Unit: the volt (V) = 1 joule per coulomb.
- EMF (ε) — the total energy the cell gives each coulomb as it drives them round the whole loop. Also in volts.
Potential difference & EMFV = W / Q · 1 V = 1 J / C · ε = energy per coulomb supplied by the cell
Voltmeter vs ammeter: a voltmeter goes across a component (parallel); an ammeter goes in line with it (series).
3 — Resistance & Ohm's law
A narrow stretch of pipe resists the flow. In a wire, that opposition to current is resistance (R), measured in ohms (Ω). Push harder — raise the voltage — and the current rises in proportion.
Ohm's lawV = I R · R = V / I · 1 Ω = 1 V / A
(at constant temperature, I ∝ V — a straight line through the origin)
- Ohmic conductor — metal wire at fixed temperature: V–I graph is a straight line; R is its slope.
- Non-ohmic — a filament lamp or diode: the line bends because R changes with current.
worked — resistor
6 V across a resistor drives 0.3 A. Find R.
R = V / I = 6 / 0.3 = 20 Ω
4 — Resistivity
Why do thin extension leads get warm? A wire's resistance depends on its shape and material: longer means more resistance, thicker (more area) means less — just like water through pipes.
Resistance & resistivityR = ρ L / A
ρ = resistivity (Ω·m, a property of the material)
copper ρ ≈ 1.7 × 10⁻⁸ Ω·m
- Length L — double the wire, double the resistance.
- Area A — double the cross-section, halve the resistance.
- Material ρ — copper conducts; nichrome resists (used in heaters).
worked — copper wire
L = 2 m, A = 1 × 10⁻⁶ m², ρ = 1.7 × 10⁻⁸ Ω·m?
R = ρL/A = (1.7e-8 × 2) / 1e-6 = 0.034 Ω
5 — Series circuits
Connect resistors end-to-end and there's only one path. The same current must flow through each in turn — and the supply voltage shares out between them.
Series rulessame current: I is the same everywhere
voltages add: V = V₁ + V₂
total resistance: R = R₁ + R₂ + …
worked — two in series
R₁ = 4 Ω, R₂ = 6 Ω across a 20 V supply.
R = 10 Ω → I = 20/10 = 2 A · V₁ = 8 V, V₂ = 12 V
Old fairy lights: all in series — one bulb fails and the whole string goes dark, because the single path is broken.
6 — Parallel circuits
Give the current a choice of paths and it splits between them. Each branch sees the full supply voltage, and the branch currents add up to the total drawn from the cell.
Parallel rulessame voltage: V is the same across every branch
currents add: I = I₁ + I₂
total resistance: 1/R = 1/R₁ + 1/R₂ + … (R is smaller than the smallest branch)
worked — two in parallel
R₁ = 4 Ω and R₂ = 4 Ω across 12 V.
1/R = 1/4 + 1/4 → R = 2 Ω · I = 12/2 = 6 A
Household wiring: sockets are in parallel — each appliance gets the full 230 V and you can switch one off without killing the rest.
7 — EMF & internal resistance
A real cell has its own small resistance r inside. Some of the EMF is "lost" pushing current through that internal resistance, so the voltage you actually get at the terminals drops as you draw more current.
Terminal voltageV = ε − I r
ε = EMF · r = internal resistance · I r = "lost volts"
- No load — I = 0, so V = ε: the voltmeter reads the full EMF.
- On load — current flows, I r is lost inside, and the terminal voltage sags.
worked — a torch cell
ε = 1.5 V, r = 0.5 Ω, drawing I = 0.6 A.
V = ε − Ir = 1.5 − 0.6×0.5 = 1.2 V at the terminals
Car headlights dim when you start the engine: the starter draws a huge current, the big Ir drops the terminal voltage for a moment.
8 — Electrical power & heating
An electric heater, a kettle, a toaster — all turn current into heat. The rate at which a component converts electrical energy is its power, measured in watts (W).
Electrical powerP = V I · P = I² R · P = V² / R
1 W = 1 J / s · energy: E = P t (kilowatt-hours on the bill)
- Heating effect — P = I²R: doubling the current quadruples the heat. This is why heaters use high-resistance nichrome.
worked — kettle
230 V mains, R = 26 Ω. Find the power.
P = V²/R = 230² / 26 ≈ 2034 W ≈ 2 kW
9 — Recap & applications
From the rate of charge flow to the heat in a kettle element, every formula in this chapter follows the same water-circuit logic.
Kirchhoff's lawsJunction rule: ΣIin = ΣIout (charge is conserved)
Loop rule: Σε = ΣIR around any loop (energy is conserved)
- Fuse — a thin wire that melts (P = I²R) if the current is too large, breaking the circuit before a fire starts.
- Household wiring — live, neutral and earth; appliances in parallel; earthing carries fault current safely away.
- Current I = Q/t, measured in amperes (coulombs per second).
- Potential difference V = W/Q and EMF are energy per coulomb (volts).
- Ohm's law V = IR; the V–I line is straight for an ohmic conductor.
- Resistance R = ρL/A — longer and thinner means more resistance.
- Series: same I, voltages add, R = R₁ + R₂. Parallel: same V, currents add, 1/R = 1/R₁ + 1/R₂.
- Real cell: V = ε − Ir; terminal voltage sags under load.
- Power P = VI = I²R = V²/R; the heating effect runs heaters, fuses and the electricity bill.