# Potential Difference

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## Key Stage 2

### Meaning

Voltage is how much push electricity has.

The bigger the voltage the more push the electricity has to go around the circuit.
Adding another cell to the circuit in series will increase the voltage.
With a bigger voltage a lamp will be brighter and a buzzer will be louder.
 A series circuit with one cell and one bulb. A bulb will be brighter if the voltage is higher.

## Key Stage 3

### Meaning

Potential Difference is how much energy is transferred by a current.

Potential Difference is measured using a Voltmeter.
The units of potential difference are Volts (V).
Potential Difference is sometimes described as the 'push' that moves a current around a circuit.

## Key Stage 4

### Meaning

Potential Difference is the amount of energy transferred per unit charge between two points in a circuit.

Potential Difference is measured using a Voltmeter.
The units of potential difference are Volts (V).
Potential difference is the difference in potential between two points in a circuit.
Potential difference can be measured between two points in a circuit and is measured across a component.
If two points in a circuit are at the same potential there is no potential difference between them so no energy is transferred between those two points.

### Equation

NB: You should remember this equation with energy transferred as the subject of the formula.

Charge = (Energy Transferred)/(Potential Difference)

$$V=\frac{E}{Q}$$

Where

$$V$$ = The potential difference between two points.

$$Q$$ = The amount of charge that move between two points.

$$E$$ = The Energy Transferred by the charge.

### Example Calculations

#### Finding Potential Difference from Charge and Energy Transferred

 A charge of 84C transfers an energy of 20kJ. Calculate the potential difference correct to two significant figures. 170J of energy is transferred by a charge of 92mC. Calculate the potential difference correct to two significant figures. 1. State the known quantities in correct units. Q = 84C E = 20kJ = 20x103J 1. State the known quantities in correct units. Q = 92mC = 92x10-3C E = 170J 2. Substitute the numbers into the equation and solve. $$V=\frac{E}{Q}$$ $$V=\frac{20 \times 10^3}{84}$$ $$V=238.0952V$$ $$V\approx 240V$$ 2. Substitute the numbers into the equation and solve. $$V=\frac{E}{Q}$$ $$V=\frac{170}{92 \times 10^{-3}}$$ $$V=1847.826V$$ $$V\approx 1800V$$

#### Finding Charge from Potential Difference and Energy Transferred

 The potential difference of 12V is placed across a resistor increasing its thermal energy store by 3.7J as a result. Calculate the charge that has flowed through the resistor in this time correct to two significant figures. A circuit transfers 2.8kJ of energy electrically to a motor. The potential difference across the motor is 1.5V. Calculate thecharge that has flowed through the motor in this time correct to two significant figures. 1. State the known quantities in correct units. V = 12V E = 3.7J 1. State the known quantities in correct units. V = 1.5V E = 2.8kJ = 2.8x103J 2. Substitute the numbers and evaluate. $$V=\frac{E}{Q}$$ $$12=\frac{3.7}{Q}$$ 2. Substitute the numbers and evaluate. $$V=\frac{E}{Q}$$ $$1.5=\frac{2.8 \times 10^3}{Q}$$ 3. Rearrange the equation and solve. $$Q=\frac{3.7}{12}$$ $$Q=0.3083C$$ $$Q\approx0.31C$$ 3. Rearrange the equation and solve. $$Q=\frac{2.8 \times 10^3}{1.5}$$ $$Q=1866.7C$$ $$Q\approx1900C$$

#### Finding Energy Transferred from Charge and Potential Difference

 A bolt of lightning with a potential difference 31,000kV transfers a charge of 15C. Calculate the energy transferred by this bolt of lightning correct to two significant figures. A 9V battery is able to mobilise a charge of 4.3kC during its operation. Calculate the total amount of energy stored in this battery correct to two significant figures. 1. State the known quantities in correct units. V = 31,000kV = 3.1x107V Q = 15C 1. State the known quantities in correct units. V = 9V Q = 4.3kC = 4.3x103 2. Substitute the numbers and evaluate. $$V=\frac{E}{Q}$$ $$3.1 \times 10^7=\frac{E}{15}$$ 2. Substitute the numbers and evaluate. $$V=\frac{E}{Q}$$ $$9 =\frac{E}{4.3 \times 10^3}$$ 3. Rearrange the equation and solve. $$E = 15 \times 3.1 \times 10^7$$ $$E = 4.65\times10^8 J$$ $$E\approx4.7\times10^8 J$$ 3. Rearrange the equation and solve. $$E = 4.3 \times 10^3 \times 9$$ $$E = 38700J$$ $$E \approx 39000 \times 10^4J$$

### References

#### AQA

Potential difference (p.d), page 294, GCSE Combined Science Trilogy 1, Hodder, AQA
Potential difference (p.d); current-potential difference graphs, pages 43-5, GCSE Physics, Hodder, AQA
Potential difference (p.d); direct and alternating, page 50, GCSE Physics, Hodder, AQA
Potential difference (p.d); in transformers, page 237, GCSE Physics, Hodder, AQA
Potential difference (p.d); induced, pages 232-3, GCSE Physics, Hodder, AQA
Potential difference (p.d.), page 39, GCSE Physics, Hodder, AQA
Potential difference (p.d.); in series and parallel circuits, pages 46-7, GCSE Physics, Hodder, AQA
Potential difference, page 185, GCSE Chemistry; Student Book, Collins, AQA
Potential difference, pages 180, 181, GCSE Combined Science; The Revision Guide, CGP, AQA
Potential difference, pages 24, 25, 96-98, GCSE Physics; The Revision Guide, CGP, AQA
Potential difference, pages 52-69, 71-77, 264-5, GCSE Physics; Student Book, Collins, AQA
Potential difference, pages 54-55, 58-61, 64-65, 67-70, 224-229, GCSE Physics; Third Edition, Oxford University Press, AQA
Potential difference, pages 62-67, 89, 90, GCSE Combined Science Trilogy; Physics, CGP, AQA
Potential difference, pages 64-69, 92, 93, GCSE Physics; The Complete 9-1 Course for AQA, CGP, AQA
Potential difference; alternating, page 188, GCSE Combined Science; The Revision Guide, CGP, AQA
Potential difference; direct, page 188, GCSE Combined Science; The Revision Guide, CGP, AQA
Potential difference; energy transferred, page 190, GCSE Combined Science; The Revision Guide, CGP, AQA
Potential difference; energy transferred, page 33, GCSE Physics; The Revision Guide, CGP, AQA
Potential difference; in parallel circuits, page 186, GCSE Combined Science; The Revision Guide, CGP, AQA
Potential difference; in parallel circuits, page 29, GCSE Physics; The Revision Guide, CGP, AQA
Potential difference; in parallel, pages 72, 73, GCSE Combined Science Trilogy; Physics, CGP, AQA
Potential difference; in parallel, pages 74, 75, GCSE Physics; The Complete 9-1 Course for AQA, CGP, AQA
Potential difference; in series circuits, page 185, GCSE Combined Science; The Revision Guide, CGP, AQA
Potential difference; in series circuits, page 28, GCSE Physics; The Revision Guide, CGP, AQA
Potential difference; in series, pages 68, 69, GCSE Combined Science Trilogy; Physics, CGP, AQA
Potential difference; in series, pages 70, 71, GCSE Physics; The Complete 9-1 Course for AQA, CGP, AQA
Potential difference; induced, pages 258-60, GCSE Physics; Student Book, Collins, AQA
Potential difference; induced, pages 303-306, GCSE Physics; The Complete 9-1 Course for AQA, CGP, AQA
Potential difference; induced, pages 96-98, GCSE Physics; The Revision Guide, CGP, AQA
Potential difference; I-V characteristics, page 183, GCSE Combined Science; The Revision Guide, CGP, AQA
Potential difference; I-V characteristics, page 26, GCSE Physics; The Revision Guide, CGP, AQA
Potential difference; measuring, page 106, GCSE Physics; The Revision Guide, CGP, AQA
Potential difference; measuring, page 239, GCSE Combined Science; The Revision Guide, CGP, AQA
Potential difference; measuring, pages 235, 236, GCSE Combined Science Trilogy; Physics, CGP, AQA
Potential difference; measuring, pages 331, 332, GCSE Physics; The Complete 9-1 Course for AQA, CGP, AQA
Potential difference; national grid, page 191, GCSE Combined Science; The Revision Guide, CGP, AQA
Potential difference; national grid, page 34, GCSE Physics; The Revision Guide, CGP, AQA
Potential difference; transformers, page 98, GCSE Physics; The Revision Guide, CGP, AQA

#### Edexcel

Potential difference (p.d.), pages 142-143, 174, GCSE Physics, Pearson Edexcel
Potential difference, pages 184-187, GCSE Combined Science; The Revision Guide, CGP, Edexcel
Potential difference, pages 221, 222, GCSE Physics, CGP, Edexcel
Potential difference, pages 71-74, GCSE Physics; The Revision Guide, CGP, Edexcel
Potential difference; in parallel circuits, pages 235, 236, GCSE Physics, CGP, Edexcel
Potential difference; induced, pages 280-283, GCSE Physics, CGP, Edexcel

#### OCR

Potential difference (p.d.), p ages 100-101, 130-134, 136-137, Gateway GCSE Physics, Oxford, OCR
Potential difference (p.d.); Calculations, pages 113, Gateway GCSE Physics, Oxford, OCR
Potential difference (p.d.); Graphs, pages 106-107, Gateway GCSE Physics, Oxford, OCR
Potential difference (p.d.); In series circuit, pages 102-103, Gateway GCSE Physics, Oxford, OCR
Potential difference (p.d.); Measurement, pages 101, 259-260, 262, Gateway GCSE Physics, Oxford, OCR
Potential difference, page 95, Gateway GCSE Chemistry; The Revision Guide, CGP, OCR
Potential difference, pages 176-182, Gateway GCSE Combined Science; The Revision Guide, CGP, OCR
Potential difference, pages 44-50, Gateway GCSE Physics; The Revision Guide, CGP, OCR