Voltage as Energy per Charge

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.

• 2.20 — Voltage as energy transferred per unit charge; the volt as a joule per coulomb
• 2.21 — Use E = Q × V

Specification section 2(c) Energy and voltage in circuits — also taught in Charge and Current, Resistance and Ohm's Law, Series and Parallel Circuits, Current–Voltage Graphs, LDRs and Thermistors.

1 · Understand it

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

Most people meet voltage as 'the push' and never get further, which works until it does not. Here is the definition that actually explains things: VOLTAGE is the energy transferred per unit of charge. A volt is a JOULE PER COULOMB. When a battery is marked 9 V, it means that every coulomb of charge passing through it is given 9 joules of energy.

Read that again with the units in mind, because everything on this page follows from it. Charge carries energy around the circuit the way a conveyor carries parcels. The cell loads energy onto each coulomb; the components unload it. How much each coulomb is carrying, in joules, is what the voltmeter is reading.

Think of it like a wage rather than a wage bill

Suppose a factory pays every worker who passes through the gate exactly £9. Voltage is the £9 — the amount each individual receives, and it says nothing about how many there are. Current is how many workers pass per second. The total paid out each second — the wage bill, which is the power — is the two multiplied together. That is why P = I × V, and it also explains the two situations people find confusing. A high voltage with a tiny current is a generous wage paid to almost nobody: not much money leaves the building. A low voltage with a huge current is a small wage paid to an enormous crowd, and the bill can be enormous. Neither number tells you anything on its own.

Where the energy goes on one trip round the circuit

1. A coulomb of charge passes through the CELL and is given energy — 9 joules from a 9 V cell. This is a chemical store being emptied a little.
2. It travels round the circuit. The wires have very little resistance, so it gives up almost nothing on the way.
3. It passes through a COMPONENT — a lamp, a resistor, a motor — and transfers energy there. The voltage ACROSS that component is exactly how many joules it gives up.
4. It returns to the cell carrying no surplus energy, and is loaded again.
5. In a SERIES circuit it visits every component in turn, giving up some at each, which is why the voltages across the components add up to the supply voltage. Nothing else would balance the books.

That last step is a proof rather than a rule to memorise. If the voltages across the components did not add up to the supply voltage, a coulomb would either arrive back at the cell still carrying energy it had never given up, or would have given up more than it was ever given. Neither can happen, so they add up.

The equation for the total energy follows straight from the definition. If each coulomb carries V joules, then Q coulombs carry Q × V joules altogether: E = Q × V. It is the definition rearranged, and if you ever forget it you can rebuild it from the units — joules equals coulombs times joules per coulomb.

Energy transferred by a charge

A charge of 40 C passes through a lamp connected to a 12 V supply. How much energy is transferred to the lamp?

1. Each coulomb passing through the lamp transfers 12 J, because the voltage across it is 12 V.
2. E = Q × V = 40 × 12.
3. = 480 J.

Answer: 480 joules — and notice it can be checked in your head: forty lots of twelve.

One more use of the definition, and it is the one that settles arguments about safety. It is often said that 'it is the current that kills, not the voltage', which is true as far as it goes: what harms a person is the charge flowing through them each second. But the current through a body is decided by the voltage across it and the body's resistance, so a high enough voltage will always drive a dangerous current. The two are not rivals. The voltage is what makes the current possible.

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.

E = Q × V

E is energy transferred in joules (J), Q is charge in coulombs (C), V is voltage in volts (V)

Units: J, C, V. Rearranged: Q = E ÷ V and V = E ÷ Q. The last of those is the definition: a volt is a joule per coulomb.

Learn this definition · Voltage (potential difference)

The energy transferred per unit of charge. One volt is one joule of energy transferred per coulomb of charge passing.

What the definition explains, once you have it

• A VOLT IS A JOULE PER COULOMB — every other fact on this page follows from that
• A 9 V battery gives each coulomb 9 J; a 230 V supply gives each coulomb 230 J
• The voltage ACROSS a component is how many joules each coulomb gives up in it
• SERIES voltages add up to the supply voltage, because the energy given out must equal the energy given in
• PARALLEL branches each have the full supply voltage, because each coulomb goes down one branch and gives up all of its energy there

Voltage against current — two different questions

A. VOLTAGE is how much energy EACH COULOMB carries, in joules per coulomb. It says nothing about how many coulombs there are.

B. CURRENT is how many coulombs pass per second, in coulombs per second. It says nothing about how much energy each one carries.

Choosing between the electrical equations

1. If the question gives charge and voltage and asks for energy, use E = Q × V.
2. If it gives current and time, find the charge first with Q = I × t.
3. If it gives voltage and current and asks for a rate — energy per second — that is power, P = I × V.
4. Check by units at the end: joules for energy, watts for power, coulombs for charge.

Model answer [3 marks]

A charge of 25 C passes through a motor connected to a 6.0 V supply. Calculate the energy transferred. [3]

Each coulomb of charge transfers 6.0 J as it passes through the motor, because the voltage across it is 6.0 V. Using E = Q × V, the total energy transferred is 25 × 6.0 = 150 J.

Model answer [4 marks]

Explain, in terms of energy and charge, why the voltages across two components in series add up to the supply voltage. [4]

Voltage is the energy transferred per unit of charge, so the supply voltage is the energy given to each coulomb by the cell. In a series circuit the same charge passes through both components in turn, giving up some of its energy at each. The voltage across each component is the energy that each coulomb gives up in that component. Since all the energy given to a coulomb must be given up by the time it returns to the cell, the energies given up at the two components must add to the energy supplied, so the two voltages add to the supply voltage.

Not this: Voltage is the amount of electricity a battery contains.

This: Voltage is how much energy each coulomb of charge is given, in joules per coulomb. Two batteries of the same voltage give each coulomb the same energy, but one may be able to supply that energy for far longer than the other.

Mark-losing trap. A volt is a JOULE PER COULOMB. Quote that definition — it is often worth a mark on its own.

Mark-losing trap. Voltage is per coulomb; current is per second. They answer different questions.

Mark-losing trap. Find the charge with Q = I × t first if the question gives you a current and a time.

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 · State [1 mark] — One volt is equal to one what, per coulomb?
2. Grade 7 · Calculate [2 marks] — A charge of 15 C passes through a lamp with a voltage of 4.0 V across it. Calculate the energy transferred to the lamp.
3. Grade 8 · Calculate [4 marks] — A current of 0.50 A flows through a heater for 2.0 minutes. The voltage across the heater is 230 V. Calculate the energy transferred.
4. Grade 9 · Explain [5 marks] — Select every statement that belongs in a full-mark explanation of why the voltages across two components in series add up to the supply voltage.
5. 9+ · Analyse [6 marks] — A student says: 'It is the current that kills, not the voltage — so a 100 000 V supply is safe as long as the current is small.' Select every statement that belongs in a full-mark analysis.

The people behind this science

Two ways into the same idea — the one who measured what a joule is worth, and the one who admitted nobody knows what energy actually is. Inside Incandio each of them answers knowing exactly which lesson you have just finished.

James Prescott Joule — the one who measured what a joule is worth

The unit in the definition on this page is his, and he earned it by measurement rather than by theory. Joule spent years establishing that a fixed amount of mechanical work always yields a fixed amount of heat — most famously by letting weights fall to turn a paddle wheel in insulated water and measuring a temperature rise of a fraction of a degree. He also found, in 1841, that the heating in a wire depends on the resistance and on the SQUARE of the current, which is the reason the next page's calculations look the way they do.

• “How did you measure a temperature rise that small and expect anyone to believe it?”
• “What is the exchange rate between mechanical work and heat?”
• “Why does a wire carrying a current become warm at all?”
• “What convinced you heat was motion rather than a fluid?”
• “How long did it take before other scientists accepted your results?”

Richard Feynman — the one who admitted nobody knows what energy actually is

This page defines voltage in terms of energy, which invites the obvious question, and Feynman is almost the only physicist famous for answering it honestly: we have no knowledge of what energy is. He taught it with a parable about a child's building blocks that always number twenty-eight however cleverly they are hidden — energy is a number you can compute that comes out the same, and the fact that such a number exists is the discovery. For a learner being asked to picture joules riding on coulombs, that is the necessary corrective.

• “If energy is not a substance, what is it?”
• “Why is it useful to have a number that always comes out the same?”
• “What did you mean by the story about the blocks that are always twenty-eight?”
• “Is it wrong to picture energy as something carried by charge?”
• “How would you explain a volt to someone who has never met one?”

Carry on through the course

• Previous lesson: Current–Voltage Graphs, LDRs and Thermistors
• Next lesson: Electrical Power and Energy
• 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.
• Electrical Power and Energy — Why a wire carrying a current gets hot, how fast a device uses energy, and how to pick a fuse.
• All of Physics · Physics key terms · required practicals · equations · Incandio Science · The 4PH1 specification