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Calculating the Cost of Electricity (WJEC GCSE Science (Double Award)): Revision Note

Leander Oates

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WJEC Science (Double Award): PhysicsWJEC Physics

Units of Power & Energy

The Kilowatt 

  • The kilowatt (kW) is a unit of power 

  • Kilowatts are used mostly in the context of domestic power use

P space equals fraction numerator space E over denominator t end fraction

  • Therefore:

1 kW = 1000 W = 1000 J/s

The Kilowatt Hour 

  • The kilowatt hour (kWh) is a unit of energy

  • Kilowatt hours are the units of energy used by domestic energy providers

  • The kilowatt hour is defined as:

    A unit of energy equivalent to one kilowatt of power expended for one hour

E space equals space P t

  • Therefore:

1 kWh = 1 kW × 1 hour

  • Appliances are given power ratings, which tell consumers the amount of energy transferred to the device every second

Power Rating of a Kettle

power-rating, IGCSE & GCSE Physics revision notes

This kettle has a power rating of between 2500 and 3000 W, which means that 2500 - 3000 J of energy are transferred to the kettle every second

Calculating the Cost of Electricity

  • Energy suppliers calculate the cost of gas and electricity used by:

Units of energy used (kWh) = power used (kW) × time (hours)

  • Then the cost of that energy use can be calculated:

Cost (£) = units used (kWh) × cost per unit (£ per kWh)

  • Suppliers have different price plans called tariffs

  • Different tariffs will have slightly different prices for:

    • Cost of electricity per kWh

    • Cost of gas per kWh

    • Standing charges for electricity and gas

  • After the bill has been calculated, the total amount will be subject to the standard rate of VAT tax (approximately 20%)

Worked Example

In the month of January, a 3 bedroom household used 284 kWh of electricity, and 1366 kWh of gas.

The household's tariff details are listed below.

  • Electricity unit price: 26.47 p/kWh

  • Electricity standing charge: 51.38 p/day

  • Gas unit price: 7.00 p/kWh

  • Gas standing charge: 26.16 p/day

Calculate the total price of the energy bill for the month of January.

The month of January has 31 days. Ignore the cost of VAT tax. 

Answer:

Step 1: List the known quantities

  • Electricity used = 284 kWh

  • Electricity unit price = 26.47 p/kWh

  • Gas used = 1366 kWh

  • Gas unit price = 7.00 p/kWh

  • Electricity standing charge = 51.38 p/day

  • Gas standing charge = 26.16 p/day

Step 2: Write out the equation for calculating the cost of energy

Cost = units used × cost per unit

Step 3: Calculate the cost of the electricity used

cost space of space electricity space equals space 284 space cross times space 26.47

cost space of space electricity space equals space 7517.48 space straight p

  • Convert pence (p) to pounds (£) by dividing by 100 and rounding to the nearest pence

cost space of space electricity space equals fraction numerator space 7517.48 over denominator 100 end fraction space equals space £ 75.17

Step 4: Calculate the cost of the gas used

cost space of space gas space equals space 1366 space cross times space 7.00

cost space of space gas space equals space 9562 space straight p

cost space of space gas space equals space 9562 over 100 space equals space £ 95.62

Step 5: Calculate the total standing charge for electricity

total standing charge electricity = standing charge per day × number of days

total space standing space charge space electricity space equals space 51.38 space cross times space 31

total space standing space charge space electricity space equals space 1592.78 space straight p

total space standing space charge space electricity space equals fraction numerator space 1592.78 over denominator 100 end fraction space equals space £ 15.93

Step 6: Calculate the total standing charge for gas

total space standing space charge space gas space equals space 26.16 space cross times space 31

total space standing space charge space gas space equals space 810.96 space straight p

total space standing space charge space g a s space equals fraction numerator 810.96 over denominator 100 end fraction space equals space £ 8.11

Step 7: Add all the individual costs together to find the total cost of the bill

Total cost of bill = cost of electricity + cost of gas + total standing charge electricity + total standing charge gas

total space cost space equals space £ 75.17 space plus space £ 95.62 space plus space £ 15.93 space plus space £ 8.11 space

total space cost space equals space £ 195.47

Examiner Tips and Tricks

The price per unit is given in pence (p), but the total amounts are billed in pounds (£). Unless the exam question tells you otherwise, you should convert your answer into pounds and round to the nearest pence.

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    Leander Oates

    Author: Leander Oates

    Expertise: Physics

    Leander graduated with First-class honours in Science and Education from Sheffield Hallam University. She won the prestigious Lord Robert Winston Solomon Lipson Prize in recognition of her dedication to science and teaching excellence. After teaching and tutoring both science and maths students, Leander now brings this passion for helping young people reach their potential to her work at SME.