The full, readable lecture — what electric current really is, how a cell pumps charge round a loop, Ohm's law and resistance, how a wire's shape and material set its resistance, combining resistors in series and in parallel, the internal resistance of a real cell, and finally Kirchhoff's laws and electrical power. As you scroll, the panel on the right plays out each idea with an everyday picture you already know — water flowing in a pipe, a pump on a hill, a narrow constriction, a heating element glowing red.
1 — Electric current = flow of charge
Switch on a torch and electrons drift through the metal wire. Electric current is the rate of flow of electric charge — exactly like the litres of water flowing past a point in a pipe every second. The faster the charge streams past, the bigger the current.
- Current (I) — the charge passing a point per second: I = Q / t. Its unit is the ampere (A), and one ampere is one coulomb of charge per second.
- Conventional current — taken from + to − through the circuit (the way positive charge would move). It is the direction we draw on every circuit diagram.
- Electron flow — in a metal the actual carriers are electrons, which drift the opposite way, from − to +. Both descriptions give the same current.
Definition of currentI = Q / t · 1 A = 1 C / s · Q = I t
charge of one electron e = 1.6 × 10⁻¹⁹ C
worked — charge through a bulb
A bulb draws 0.5 A for 2 minutes. How much charge flows?
Q = I t = 0.5 × (2 × 60) = 0.5 × 120 = 60 C
Exam point: conventional current and electron flow point in opposite directions — but the value of I is identical. Always mark conventional current (+ to −) on a diagram unless told otherwise.
2 — Potential difference & EMF
Water will not climb a hill by itself — a pump must raise it. In a circuit the cell or battery is that pump: it lifts charge to a higher electrical potential, giving each coulomb the energy it needs to flow round the loop and do useful work in the components.
- Potential difference (V) — the energy delivered per coulomb as charge moves between two points: V = W / Q. Unit: the volt (V) = one joule per coulomb.
- Electromotive force (EMF, ε) — the total energy the cell supplies to each coulomb as it drives them right round the whole circuit. Also measured in volts. (Despite the name, EMF is an energy-per-charge, not a force.)
Potential difference & EMFV = W / Q · 1 V = 1 J / C
ε = energy supplied per coulomb by the cell (the "lift" of the pump)
worked — energy from charge
A 12 V battery moves 5 C through a motor. How much energy is delivered?
W = V × Q = 12 × 5 = 60 J
Voltmeter vs ammeter: a voltmeter connects across a component (in parallel) to read the potential difference; an ammeter connects in line (in series) to read the current through it.
3 — Resistance & Ohm's law
A narrow stretch of pipe fights the flow of water. In a wire, that opposition to current is the resistance, R, measured in ohms (Ω). Push harder — raise the potential difference — and the current rises in exact proportion, provided the temperature stays constant.
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 — a metal wire at fixed temperature: its V–I graph is a straight line through the origin, and R is found from the slope.
- Non-ohmic — a filament lamp or a diode: the line curves, because R changes as current (and temperature) change.
| Quantity | Symbol | Unit |
|---|
| Potential difference | V | volt (V) |
| Current | I | ampere (A) |
| Resistance | R | ohm (Ω) |
worked — find the resistance
6 V across a resistor drives a current of 0.3 A. Find R.
R = V / I = 6 / 0.3 = 20 Ω
4 — Resistivity
Why does a long, thin extension lead get warm while a short fat one stays cool? A wire's resistance depends on its shape and its material: a longer wire has more resistance, a thicker one (bigger cross-sectional area) has less — just as a long narrow pipe chokes water while a short wide pipe lets it gush.
Resistance & resistivityR = ρ L / A
ρ = resistivity (Ω·m) — a property of the material itself
L = length (m) · A = cross-sectional area (m²)
copper ρ ≈ 1.7 × 10⁻⁸ Ω·m
| Change made | Effect on R = ρL/A |
|---|
| Double the length (L × 2) | Resistance doubles |
| Double the area (A × 2) | Resistance halves |
| Change material (ρ) | copper conducts; nichrome resists (heaters) |
worked — a copper wire
L = 2 m, A = 1 × 10⁻⁶ m², ρ = 1.7 × 10⁻⁸ Ω·m. Find R.
R = ρL/A = (1.7 × 10⁻⁸ × 2) / (1 × 10⁻⁶) = 0.034 Ω
5 — Series circuits
Connect resistors end-to-end and there is only one path for the current. The same current must flow through each resistor in turn, and the supply voltage shares out between them in proportion to their resistances.
Series rulessame current everywhere: I is the same in each resistor
voltages add: V = V₁ + V₂ + …
total resistance: R = R₁ + R₂ + …
worked — two resistors in series
R₁ = 4 Ω and R₂ = 6 Ω across a 20 V supply. Find I and each voltage.
R = R₁ + R₂ = 10 Ω → I = V/R = 20/10 = 2 A
V₁ = I R₁ = 2 × 4 = 8 V · V₂ = I R₂ = 2 × 6 = 12 V (8 + 12 = 20 V ✓)
Old fairy lights: all the bulbs sit in series, so when a single bulb fails the one path is broken and the whole string goes dark.
6 — Parallel circuits
Give the current a choice of paths and it splits between them. Each branch is connected across the same two points, so each one 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 resistors in parallel
R₁ = 4 Ω and R₂ = 4 Ω across a 12 V supply. Find R and the total current.
1/R = 1/4 + 1/4 = 2/4 → R = 2 Ω
I = V/R = 12/2 = 6 A · I₁ = 12/4 = 3 A, I₂ = 3 A (3 + 3 = 6 A ✓)
Household wiring: the sockets in your home are in parallel — every appliance gets the full mains voltage, and you can switch one off without killing the rest.
7 — EMF & internal resistance
A real cell has its own small resistance, r, hidden inside it. As current flows, some of the EMF is "spent" pushing that current through the internal resistance — wasted as heat, which is why a hard-working battery warms up. So the voltage you actually measure at the terminals drops below the EMF as you draw more current.
Terminal voltageV = ε − I r
ε = EMF · r = internal resistance · I r = the "lost volts" inside the cell
- No load (I = 0) — no current, so nothing is lost on r: the voltmeter reads the full EMF, V = ε.
- On load — current flows, the lost volts Ir appear inside, and the terminal voltage sags.
worked — a torch cell
ε = 1.5 V, r = 0.5 Ω, drawing I = 0.6 A. Find the terminal voltage.
V = ε − I r = 1.5 − (0.6 × 0.5) = 1.5 − 0.3 = 1.2 V at the terminals
Car headlights dim for a moment when you start the engine: the starter motor draws a huge current, the large Ir drop briefly pulls the terminal voltage right down.
8 — Kirchhoff's laws, power & applications
Two simple bookkeeping rules — Kirchhoff's laws — let us analyse any circuit. The first counts charge at a junction; the second counts energy round a loop. And wherever current meets resistance, energy is converted: an electric heater, a kettle, a toaster all turn current into heat at a rate called the power, measured in watts (W).
Kirchhoff's lawsJunction (current) rule: ΣIin = ΣIout — charge is conserved
Loop (voltage) rule: Σε = ΣIR around any closed loop — energy is conserved
Electrical power & energyP = V I · P = I² R · P = V² / R
1 W = 1 J / s · energy E = P t (sold as kilowatt-hours on the bill)
- Heating effect — from P = I² R, doubling the current quadruples the heat. That is why heaters and toasters use high-resistance nichrome.
- Fuse — a thin wire that melts (P = I²R) if the current is too large, breaking the circuit before a fire can start.
worked — an electric kettle
230 V mains supplies a heating element of R = 26 Ω. Find the power.
P = V² / R = 230² / 26 = 52 900 / 26 ≈ 2034 W ≈ 2 kW
- 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 bill.