Electrical Power and Energy

What this lesson covers in the specification

Incandio is aligned to this specification. It is not published by, endorsed by or affiliated with Pearson, and it reproduces none of Pearson's wording — the statement numbers are given so you can check every lesson against your own copy.

• 2.3 — Why a current in a resistor transfers energy and raises temperature, and its domestic uses
• 2.4 — Use P = I × V, and apply it to choosing a fuse
• 2.5 — Use E = I × V × t

Specification section 2(b) Mains electricity — also taught in Resistance and Ohm's Law, Series and Parallel Circuits, Current–Voltage Graphs, LDRs and Thermistors, Mains Electricity and Safety.

1 · Understand it

No exam language yet. The only question this section answers is: do I actually understand what is happening?

Start with why anything gets hot at all. Electrons drifting through a resistor collide repeatedly with the vibrating positive ions of the lattice. At each collision the electron loses some of its energy to the ion, which vibrates more violently as a result — and more violent vibration of the particles IS a higher temperature. So the energy the cell gave to the charge ends up as thermal energy in the component. Nothing is lost; it has changed form and location.

In most of a circuit this is a nuisance: a cable that warms up is wasting energy and may become dangerous. But in a whole class of devices it is the entire purpose. An electric kettle, an immersion heater, a hair dryer, a toaster, an electric oven and the filament of an old-style light bulb are all built around a deliberately high-resistance element, precisely so that the collisions happen and the energy arrives as heat exactly where it is wanted.

POWER is the rate at which energy is transferred — joules per second, which is what a watt is. The equation for it comes straight out of the previous page and is worth deriving once rather than memorising. Current is coulombs per second. Voltage is joules per coulomb. Multiply them and the coulombs cancel, leaving joules per second: P = I × V.

Think of it like a delivery service billing by the parcel

If a courier delivers 20 parcels a second and each parcel is worth £5, the value being delivered is £100 a second. The number of parcels per second is the current, the value per parcel is the voltage, and the rate at which value arrives is the power. This makes the two ways of getting a high power obvious. You can send a great many cheap parcels — a huge current at a low voltage, which is how a car starter motor works — or a few very valuable ones, which is a high voltage at a small current, and is how electricity is sent across country. Both deliver the same value per second, and they need completely different cables.

The energy equation is then just power multiplied by time. E = I × V × t, because energy is the rate multiplied by how long it goes on for. And there is a check worth doing: if you already know Q = I × t and E = Q × V, then substituting one into the other gives E = I × V × t directly. It is not a new equation; it is two old ones joined together.

Power and energy for a kettle

A kettle draws 9.0 A from the 230 V mains and is on for 3.0 minutes. Find its power and the energy it transfers.

1. Power: P = I × V = 9.0 × 230 = 2070 W, or about 2.1 kW.
2. Time in seconds: 3.0 minutes = 180 s.
3. Energy: E = I × V × t = 9.0 × 230 × 180 — or more simply, E = P × t = 2070 × 180.
4. = 372 600 J, which is about 373 kJ.

Answer: About 2.1 kW, transferring roughly 373 kJ in three minutes.

Choosing a fuse — the reasoning, in order

1. A FUSE is a thin wire that MELTS if the current through it exceeds a set value, breaking the circuit before the appliance or its cable is damaged.
2. Work out the NORMAL OPERATING CURRENT of the appliance from its power rating and the mains voltage: I = P ÷ V.
3. Choose the fuse whose rating is the next one ABOVE that current. Standard fuses are 3 A, 5 A and 13 A.
4. It must be above, because a fuse rated below the normal current would melt in normal use and the appliance would never work.
5. But it must be only JUST above: a 13 A fuse in a 3 A lamp would allow four times the safe current to flow before it acted, by which time the flex could already be on fire.

Which fuse for a 500 W television?

A television is rated at 500 W and runs from the 230 V mains. Which of the 3 A, 5 A and 13 A fuses should be fitted?

1. Normal current: I = P ÷ V = 500 ÷ 230 = 2.17 A.
2. The fuse must be rated above 2.17 A, or it would blow in normal use.
3. The next standard rating above 2.17 A is 3 A.
4. A 5 A or 13 A fuse would work, in the sense that the television would run — but each would allow a dangerously large fault current before acting.

Answer: A 3 A fuse — the smallest standard rating above the normal operating current.

2 · Grade 9 Notes

A different job from the section above. You have already understood it; this is the precise set of things to LEARN — definitions to reproduce word for word, processes in order, equations with units, and the answers that score full marks.

P = I × V

P is power in watts (W), I is current in amperes (A), V is voltage in volts (V)

Units: W, A, V. Rearranged: I = P ÷ V and V = P ÷ I. A watt is a joule per second, and amperes × volts = coulombs per second × joules per coulomb = joules per second.

E = I × V × t

E is energy transferred in joules (J), I is current in amperes (A), V is voltage in volts (V), t is time in SECONDS (s)

Units: J, A, V, s. This is the same as E = P × t, and it comes from combining Q = I × t with E = Q × V.

Learn this definition · Power

The rate at which energy is transferred. One watt is one joule of energy transferred per second.

Taught in full in Power.

Statement 2.4 — choosing a fuse

1. Find the normal operating current of the appliance: I = P ÷ V.
2. Choose the smallest standard fuse rating ABOVE that current (3 A, 5 A or 13 A).
3. A rating below the normal current would blow in ordinary use.
4. A rating far above it would allow a large fault current to flow before the fuse melted.

Statement 2.3 — the heating effect, and where it is wanted

• Electrons COLLIDE with the vibrating ions of the lattice and lose energy to them at each collision
• The ions vibrate more violently, which IS a rise in temperature — so the component gets hot
• WANTED in: kettles, immersion heaters, hair dryers, toasters, ovens, electric fires and filament lamps
• UNWANTED in: cables and connecting wires, where it wastes energy and can start a fire
• This is why heating elements are made of high-resistance wire and connecting cables of low-resistance copper

Power against energy — a rate and a total

A. POWER is a RATE: joules per second, measured in watts. A 2 kW heater transfers 2000 J every second, whether it runs for a minute or a week.

B. ENERGY is a TOTAL: joules, and it depends on how long the device was on. The same 2 kW heater transfers far more energy in a week than in a minute.

Model answer [4 marks]

An electric heater is rated at 2.0 kW and runs from the 230 V mains. Calculate the current it draws, and state which fuse should be fitted. [4]

The power is 2.0 kW, which is 2000 W. Rearranging P = I × V gives I = P ÷ V, so the current is 2000 ÷ 230 = 8.7 A. The fuse must be rated above the normal operating current, and the smallest standard rating above 8.7 A is 13 A, so a 13 A fuse should be fitted.

Model answer [4 marks]

Explain why the element of an electric kettle becomes hot when a current passes through it. [4]

The element is made of wire with a high resistance. As electrons drift through it they collide frequently with the positive ions of the metal lattice, and at each collision an electron transfers some of its energy to an ion. The ions therefore vibrate more violently, and more violent vibration of the particles is a higher temperature, so the element gets hot. The energy transferred each second is given by P = I × V, and it is then transferred to the water by conduction and convection.

Not this: A bigger fuse is safer, because it is less likely to blow unexpectedly.

This: A fuse that is rated too high will let a dangerously large current flow before it melts, by which time the flex may already have overheated. The correct fuse is the smallest standard rating above the appliance's normal operating current.

Mark-losing trap. The fuse rating goes just ABOVE the normal current — the next standard size up, not the largest available.

Mark-losing trap. Convert kW to W and minutes to seconds before substituting. 2.0 kW is 2000 W.

Mark-losing trap. Power is a RATE in watts; energy is a TOTAL in joules. Read which one is asked for.

3 · Prove it — the five questions

The five questions climb Grade 6 → Grade 7 → Grade 8 → Grade 9 → Grade 9 challenge, and are marked inside Incandio on your own device, by rule, with an authored diagnosis of the mistake you actually made. The mark schemes stay in the app so that the practice is worth doing; the questions themselves are here.

1. Grade 6 · Calculate [2 marks] — A lamp draws a current of 0.30 A from a 12 V supply. Calculate its power.
2. Grade 7 · Explain [2 marks] — Explain why the connecting wires of a circuit are made of thick copper while a heating element is made of thin high-resistance wire.
3. Grade 8 · Calculate [3 marks] — A 1.5 kW hair dryer runs from the 230 V mains. Calculate the current it draws.
4. Grade 9 · Calculate [4 marks] — A 920 W microwave oven is connected to the 230 V mains and used for 5.0 minutes. Calculate the energy it transfers, in kilojoules.
5. 9+ · Analyse [6 marks] — A 700 W food mixer running from the 230 V mains is sold with a 13 A fuse already fitted. Select every statement that belongs in a full-mark analysis of whether this is the right fuse.

The people behind this science

Two ways into the same idea — the one who found the law that makes a kettle work, and the one who exploited the fact that power can be delivered two ways. Inside Incandio each of them answers knowing exactly which lesson you have just finished.

James Prescott Joule — the one who found the law that makes a kettle work

Statement 2.3 is Joule's own law, found in 1841: the heat produced in a conductor is proportional to its resistance and to the SQUARE of the current. That square is why a small increase in current in an overloaded cable is far more dangerous than it sounds, and why heating elements are made of high-resistance wire. He established it by measurement, in a private laboratory paid for by his family's brewery, at a time when heat was widely believed to be a fluid rather than a form of motion.

• “Why does doubling the current in a wire produce four times the heat?”
• “How did you measure the heat produced by a current?”
• “Why does the resistance of the wire matter as much as the current?”
• “Where exactly does the electrical energy go when a wire warms up?”
• “What made you think heat and mechanical work were the same thing?”

Nikola Tesla — the one who exploited the fact that power can be delivered two ways

The equation on this page has a consequence Tesla built a career on: the same power can be delivered as a large current at a low voltage or a small current at a high voltage, and since the heating in a cable depends on the square of the current, the second wastes vastly less. That is why transmission lines run at hundreds of thousands of volts, and it is the argument his alternating-current system won on — because a.c. can be transformed to a high voltage for transmission and back down again, and direct current at the time could not.

• “Why send electricity at a high voltage instead of a large current?”
• “How much energy is wasted heating the cables on a long transmission line?”
• “What made alternating current the practical choice for a national supply?”
• “Was the argument with your rivals about physics or about business?”
• “What did you imagine electricity would make possible?”

Carry on through the course

• Previous lesson: Voltage as Energy per Charge
• Next lesson: Mains Electricity and Safety
• Charge and Current — What is actually moving in a wire, how fast it is really going, and why the arrows on every circuit diagram point the wrong way.
• Resistance and Ohm's Law — What slows the electrons down, the one equation that ties the whole topic together, and when it stops being true.
• Series and Parallel Circuits — Two ways of joining components, and why every building in the world is wired one of them.
• Current–Voltage Graphs, LDRs and Thermistors — The shapes four components make on a graph, and two resistors that deliberately refuse to stay the same.
• Voltage as Energy per Charge — What a volt actually is — and why knowing that turns three separate equations into one idea.
• All of Physics · Physics key terms · required practicals · equations · Incandio Science · The 4PH1 specification