Kilowatt-Hours (Oxford AQA IGCSE Physics): Revision Note

Units of Energy

Energy measured in joules

• Electrical energy transferred is often calculated with units of joules

  • One joule is equivalent to one-watt second

• Consider an average lightbulb with a power of 60 W, which is left on for 6 hours in a house

  • 1 hour is 3600 s

  • The electrical energy transferred over this time is 1.296 × 10⁶ J

• This number is large and that is one lightbulb for a single day

  • A household uses many appliances all year round – the energy transferred per month in joules would be inconveniently large

Energy measured in kilowatt-hours

• To make these large values more relatable to daily use:

  • Power can be measured in kilowatts (kW)

  • Time can be measured in hours (h)

• In this case, energy has units of kilowatt-hours (kW h)

  • The lightbulb from before receives 3.6 kW h of energy over the 6 hours

  • This value is much easier to understand for consumers and energy providers – thinking in terms of hours of use is more practical than seconds

Kilowatt-Hours

• As has been stated previously, the equation for energy transferred is:

$E=P\times t$

• But here we consider different units:

  • E = energy transferred measured in kilowatt-hours (kW h)

  • P = power of the appliance measured in kilowatts (kW)

  • t = time measured in hours (h)

• The usual unit of energy is joules (J), which is one watt-second

• To find the number of joules in 1 kW h, convert the power and time to watts and seconds

$1\mathrm{kW}\mathrm{h}=1000\mathrm{W}\times 3600\mathrm{s}=3.6\times {10}^6\mathrm{J}$

• 1000 watts multiplied by 3600 seconds is equal to 1000 multiplied by 3600, in watt-seconds

$1000\mathrm{W}\times 3600\mathrm{s}=1000\times 3600\mathrm{W}\mathrm{s}=3.6\times {10}^6\mathrm{J}$

• Therefore, 1 kWh = 3.6 × 10⁶ J

• To convert from kW h to J:

$E\left(\mathrm{kW}\mathrm{h}\right)\times (3.6\times {10}^6)=E\left(\mathrm{J}\right)$

• To convert from J to kW h:

$E\left(\mathrm{J}\right)÷(3.6\times {10}^6)=E\left(\mathrm{kW}\mathrm{h}\right)$

• The kW h is a large unit of energy, and is mostly used for energy in homes, businesses and factories