What current, voltage and resistance really mean, how series and parallel circuits behave, how a lamp turns electricity into light, and how to calculate your way through every question in the topic. Work straight through it, or jump to the bit you are stuck on.
Almost everything in this topic is about three quantities and how they are linked. Learn what each one is measured in and how it is measured, and the rest follows.
The rate at which charge flows past a point in the circuit. 1 ampere is 1 coulomb of charge every second.
Measured with an ammeter, wired in series (in the loop) with the component.
The energy given to each unit of charge — the push that drives the current round the circuit. 1 volt = 1 joule per coulomb.
Measured with a voltmeter, wired in parallel (across) the component.
How much a component works against the current. For the same voltage, a bigger resistance means a smaller current.
Every component has resistance: wires have a little, a filament has a lot, an insulator has far too much for current to flow.
Charge will only flow if there is a complete, unbroken loop from one terminal of the supply, round through the components, and back to the other terminal. Break the loop anywhere — a switch, a loose wire, a blown lamp — and the current stops everywhere in that loop.
• A source of voltage — a cell, a battery or the mains supply.
• Conductors — wires, usually copper, with very low resistance.
• At least one component to use the energy — a lamp, a motor, a heater.
• A switch to open and close the loop.
• Conventional current flows from the + terminal, round the outside of the circuit, to the − terminal. (The electrons actually drift the other way.)
There is a single path, so the same current flows through every component.
• The supply voltage is shared between the components. • Resistances add up: R(total) = R1 + R2 + … • Add another lamp in series and the total resistance rises, the current falls, and every lamp gets dimmer. • If one lamp fails, the loop is broken and they all go out.
Each component sits on its own branch, so each one gets the full supply voltage.
• The voltage across every branch is the same. • The currents in the branches add up to the current from the supply. • Adding a branch lowers the total resistance and increases the total current. • Every lamp keeps full brightness, and one failing does not affect the others — which is why household lighting is wired this way.
A filament lamp works by getting hot. Charge is pushed through a very thin coil of tungsten wire — the filament — which has a high resistance. That resistance turns electrical energy into thermal energy, and the filament reaches roughly 2500 °C, hot enough to glow white-hot. Only a small fraction of the energy comes out as visible light; most of it leaves as heat, which is why an old bulb is too hot to touch.
• Emits light because the tungsten is white-hot. • Roughly 5% of the energy is light; about 95% is wasted as heat. • Typical life around 1,000 hours. • The glass bulb keeps oxygen out so the filament does not burn away, and the inert gas inside slows evaporation of the metal. • Resistance climbs as the filament heats up, so doubling the voltage does not quite double the current — the V–I graph curves instead of being a straight line.
• A semiconductor gives out light directly as charge crosses a junction, so the component barely warms up. • Far more efficient — much more of the energy becomes light rather than heat. • Typical life 15,000–25,000 hours, and it switches on instantly at full brightness. • It only conducts one way round, so it must be connected the right way, and it needs a resistor in series to limit the current — otherwise it destroys itself.
A 60 W filament lamp and a 9 W LED give out about the same amount of light. Left on for 5 hours a day, the filament lamp uses 0.3 kWh a day against 0.045 kWh for the LED — about six times less electricity for the same light.
Power is how fast a component transfers energy (watts). Energy is the total transferred (joules or kilowatt-hours).
A lamp takes 0.5 A from a 12 V supply and is left on for 3 hours. Find its power, the energy it uses, and the cost at $0.15 per kWh.
Power: P = V × I = 12 V × 0.5 A = 6 W Energy: convert first — 6 W = 0.006 kW. E = P × t = 0.006 kW × 3 h = 0.018 kWh Cost: 0.018 kWh × $0.15 = $0.0027, well under a cent.
A bigger appliance shows it better: a 2 kW kettle boiling for 0.2 hours (12 minutes) uses 2 × 0.2 = 0.4 kWh, which costs 0.4 × $0.15 = $0.06.
For a component whose resistance stays constant, the current is proportional to the voltage. Rearranged three ways, this one relationship answers most calculation questions:
Find resistance
6 V across a lamp, 0.5 A through it. R = V ÷ I = 6 ÷ 0.5 = 12 Ω
Find current
12 V battery, 3 Ω resistor in the loop. I = V ÷ R = 12 ÷ 3 = 4 A
Find voltage
2 A through a 5 Ω resistor. V = I × R = 2 × 5 = 10 V
Try each one with the answer covered, then check your working. Getting the method right matters more than the number.
1. A torch lamp has 3 V across it and a current of 0.2 A through it. What is its resistance?
Hint: you need the form of Ohm's law with R on its own.
R = V ÷ I = 3 V ÷ 0.2 A = 15 Ω
2. A 6 V battery is connected to a 20 Ω lamp. What current flows?
Hint: you know voltage and resistance, you want current.
I = V ÷ R = 6 V ÷ 20 Ω = 0.3 A (300 mA)
3. What voltage is needed to push 0.25 A through a 24 Ω resistor?
Hint: current and resistance known, voltage wanted.
V = I × R = 0.25 A × 24 Ω = 6 V
4. Three identical lamps are in series across a battery. What happens to their brightness when a fourth identical lamp is added in series?
Hint: the supply voltage has not changed, but the resistance in the loop has.
Total resistance rises, so the current falls (I = V ÷ R). The same smaller current flows through every lamp, so all four are dimmer than the three were.
5. A 60 W lamp is left on for 5 hours. How much energy does it use, and what does that cost at $0.15 per kWh?
Hint: convert watts to kilowatts before you multiply by hours.
60 W = 0.06 kW. E = P × t = 0.06 kW × 5 h = 0.3 kWh. Cost = 0.3 × $0.15 = $0.045 — about four and a half cents.
These five are the sort that turn up in tests, because they need an explanation as well as a number. Write your answers out first, then press the button.
1. A lamp is marked '12 V, 24 W'. Work out (a) the current through it at its rated voltage and (b) its resistance.
2. Each lamp in a parallel circuit is connected straight across the 6 V supply. Explain why adding a second lamp in parallel does not make the first one dimmer.
3. Two heating elements are connected first in series, then in parallel, across the same supply. Which arrangement gives the larger total current, and why?
4. An appliance draws 4 A from the 230 V mains. Would you fit a 3 A fuse or a 5 A fuse? Explain your choice.
5. The resistance of a filament lamp is much lower when it is cold than when it is lit. Explain why the current through a filament lamp is not simply proportional to the voltage across it.
• Battery circuits are safe to experiment with, but even a 1.5 V cell can push enough current through a bare wire to make it hot.
• Mains electricity is around 230 V (130 V in some countries) and can kill. Never open a plug or touch mains wiring with wet hands, and never work on a circuit that is still plugged in.
• A short circuit happens when a wire gives the current a low-resistance path straight back to the supply. Resistance collapses, current becomes very large, and the wires heat up enough to start a fire.
• A fuse contains a thin wire that melts when the current gets too high, breaking the circuit. A circuit breaker does the same job with a switch and can be reset.
• A three-pin plug has live, neutral and earth wires. The earth wire and the fuse work together: if the live wire touches the metal case, a big current flows to earth and the fuse blows before anyone touches the case.
• What matters to a body is the current through it, not just the voltage. Roughly 50 mA across the chest is enough to interfere with the heartbeat.
Charge (coulomb, C)
The quantity of electricity. Current is the rate at which charge flows.
Current (ampere, A)
Rate of flow of charge: 1 A = 1 C per second.
Voltage (volt, V)
Energy transferred per unit charge: 1 V = 1 J per coulomb.
Resistance (ohm, Ω)
How much a component opposes the current: R = V ÷ I.
Conductor
A material with low resistance, such as copper, so charge flows through it easily.
Insulator
A material with very high resistance — plastic, rubber, glass — used to keep current where it belongs.
Ammeter
Measures current. Wired in series, so the current passes through it.
Voltmeter
Measures voltage. Wired in parallel, across the component.
Power (watt, W)
The rate of energy transfer: P = V × I. 1 W = 1 J per second.
Energy (joule, J / kWh)
The total transferred: E = P × t. Electricity bills use the kilowatt-hour.
Short circuit
A low-resistance path across the supply, giving a dangerously large current.
Fuse / circuit breaker
Safety devices that break the circuit when the current gets too high.
Filament lamp
A thin tungsten wire heated white-hot by the current. Mostly a heater that happens to glow.
LED
A semiconductor that emits light directly, with very little waste heat. One-way only.
Non-ohmic
A component whose resistance changes, so its V–I graph is curved — a filament lamp or an LED.
Read a section, then close the page and try to write down the three key points before you check. The practice set has worked solutions under each question; the quiz hides them behind a button so you have to commit to an answer first.
For teachers: the quiz answers are held in the 'Show quiz answers' backend flow rather than in the page, and there is a grading endpoint at POST /api/quiz/grade. Send it a body like {"answers": {"1": "2 A, 6 Ω", "2": "…"}} and it marks each answer against keyword groups and returns a score with per-question feedback. Add "explain": true to get the model answers back with the marking.
Everything here is a normal page — change the wording, the colours, the numbers or the order and nothing breaks.