🔋 Voltage of a supply
The energy given to each coulomb of charge that passes through the battery or power supply.
Energy and Voltage in Circuits » Voltage, Energy and Charge
What you'll learn this session
Study time: 30 minutes
Edexcel spec: 2.20, 2.21
- What voltage really measures: the energy transferred per unit charge passed
- Why one volt is the same as one joule per coulomb
- How to use energy transferred = charge × voltage, E = Q × V
- How E = Q × V links to the other electricity equations you know
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Unlock This CourseWhat does voltage actually measure?
You have used voltage in many calculations, and you have measured it with a voltmeter. Now it is time to say exactly what it is. The specification gives a definition that you must know:
Voltage is the energy transferred per unit charge passed.
Remember, charge is measured in coulombs. "Per unit charge" simply means "for each coulomb". So voltage tells you how many joules of energy are transferred for every coulomb of charge that passes.
This gives the volt its meaning:
The volt is a joule per coulomb. 1 V = 1 J/C.
A voltage of 1 V means 1 J of energy is transferred for each coulomb of charge that passes. A voltage of 5 V means 5 J for each coulomb.
Key terms:
- Voltage: the energy transferred per unit charge passed.
- Per unit charge: for each coulomb of charge.
- Joule per coulomb (J/C): another way of writing the volt. 1 V = 1 J/C.
What a 12 V battery means
A car battery is labelled 12 V. You can now read that label like a physicist: each coulomb of charge that passes through the battery is given 12 J of energy. The charge then moves around the circuit and transfers that energy in the components, for example in a lamp or a motor.
A helpful picture is a fleet of delivery vans. Each van is one coulomb of charge. The battery is the depot, where every van is loaded with energy. The voltage is the size of the load on each van. The vans drive round the circuit, deliver their energy to the components and return to the depot to be loaded again. The vans are not used up. Only the energy is delivered.
| Supply | Voltage | Energy transferred for each coulomb |
|---|---|---|
| One cell | 1.5 V | 1.5 J |
| Small rectangular battery | 9 V | 9 J |
| Car battery | 12 V | 12 J |
| Mains supply | 230 V | 230 J |
💡 Voltage across a component
The energy transferred by each coulomb of charge as it passes through the component. A lamp with 8 V across it receives 8 J from every coulomb.
This is why a higher voltage matters. The same amount of charge delivers more energy when the voltage is higher, because every coulomb carries a bigger load.
The equation: energy transferred = charge × voltage
If each coulomb transfers 12 J, then 2 C transfer 24 J and 10 C transfer 120 J. You multiply the charge by the voltage. This is the equation:
energy transferred = charge × voltage
E = Q × V
- E is the energy transferred, in joules (J)
- Q is the charge, in coulombs (C)
- V is the voltage, in volts (V)
The specification says "know and use" for this equation. That means it is not given on the formulae page of the exam paper. You must learn it.
Worked example 1: finding the energy
A 12 V car battery is connected to a windscreen wiper motor. A charge of 30 C passes through the motor. Calculate the energy transferred.
E = Q × V
E = 30 × 12
E = 360 J
Rearranging the equation
You can rearrange E = Q × V to find the voltage or the charge:
- V = E ÷ Q (voltage = energy transferred ÷ charge)
- Q = E ÷ V (charge = energy transferred ÷ voltage)
The first of these is the definition of voltage written in symbols: energy divided by charge, or joules per coulomb.
Worked example 2: finding the voltage
A charge of 50 C passes through the motor of a radio-controlled car. The energy transferred is 450 J. Calculate the voltage across the motor.
V = E ÷ Q
V = 450 ÷ 50
V = 9 V
Check: 9 V means 9 J for each coulomb, and 50 × 9 = 450 J.
Worked example 3: finding the charge
A convector heater is connected to the 230 V mains supply. It transfers 4.6 kJ of energy. Calculate the charge that passes through the heater.
First change kilojoules to joules: 4.6 kJ = 4600 J
Q = E ÷ V
Q = 4600 ÷ 230
Q = 20 C
Linking the equations together
Exam questions often give you a current and a time instead of a charge. Remember, charge = current × time, Q = I × t. Find the charge first, then use E = Q × V.
Worked example 4: two steps
A camping lantern has a 6 V battery. The current in its lamp is 0.3 A. Calculate the energy transferred when the lantern is switched on for 5 minutes.
First change the time to seconds: 5 × 60 = 300 s
Step 1, charge: Q = I × t = 0.3 × 300 = 90 C
Step 2, energy: E = Q × V = 90 × 6 = 540 J
The two steps can be joined into one. Start with E = Q × V and replace Q with I × t:
E = Q × V = (I × t) × V, so E = I × V × t
This is the equation you used in Energy Transferred by Appliances. Now you can see where it comes from. Check it with the lantern: 0.3 × 6 × 300 = 540 J, the same answer.
⚡ Use E = Q × V
When the question gives, or asks for, a charge in coulombs.
⏰ Use Q = I × t first
When the question gives a current and a time, and then asks about charge or energy.
Common mistakes
- Saying voltage is "the energy". Voltage is the energy transferred per unit charge. Leave out those three words and you lose the mark.
- Mixing up Q and I. Q is charge in coulombs. I is current in amperes. E = Q × V needs the charge, not the current.
- Dividing the wrong way round. Voltage is joules per coulomb, so it is energy ÷ charge, never charge ÷ energy.
- Forgetting to convert. Change kJ to J and minutes to seconds before you calculate.
- Thinking charge is used up. The charge flows all the way round the circuit. It is the energy that is transferred to the components.
- Leaving off the unit. Energy in J, charge in C, voltage in V.
Exam-style question
A cordless screwdriver has an 18 V battery connected to a motor.
(a) State what is meant by the term voltage. [1 mark]
(b) State how much energy is transferred when one coulomb of charge passes through the motor. Assume the voltage across the motor is 18 V. [1 mark]
(c) A charge of 40 C passes through the motor. Calculate the energy transferred. [3 marks]
(d) The current in the motor is 2.5 A. Calculate the energy transferred when the motor runs for 20 s. [4 marks]
(e) A different screwdriver has a 12 V battery. Explain how the energy transferred changes when the same charge of 40 C passes through its motor. [2 marks]
Model answer
(a) Voltage is the energy transferred per unit charge passed (1)
(b) 18 J (1)
(c) E = Q × V (1) = 40 × 18 (1) = 720 J (1)
(d) Q = I × t = 2.5 × 20 (1) = 50 C (1). E = Q × V = 50 × 18 (1) = 900 J (1)
(e) Less energy is transferred (1) because each coulomb now transfers only 12 J instead of 18 J (1). (40 × 12 = 480 J is also a good way to show this.)
Exam tip
In part (c) write the equation E = Q × V before you put in any numbers. It is not on the formulae page, so writing it correctly can earn a mark by itself. In part (d) the question gives a current and a time, not a charge, so find the charge first and then use E = Q × V.