Electrical Power (CIE IGCSE Physics: Co-ordinated Sciences (Double Award))

• The power of an appliance is defined as: 

The rate at which energy is transferred by an appliance

• Power can be calculated in terms of energy:

• Where:
  • = power, measured in watts (W)
    • The watt is equivalent to joules per second (J/s)
  • = energy transferred, measured in joules (J)
  • = time, measured in seconds (s)
• Power can also be calculated in terms of work done:

• Where:
  • = work done, which is equivalent to energy transferred, measured in joules (J)

• The power of an electrical device is the energy transferred per second by the device

• The power dissipated by an electrical component can be calculated by:

• Where:
  • = dissipated power, measured in watts (W)
  • = current, measured in amps (A)
  • = potential difference, measured in volts (V)

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 energy transferred over this time is 1.296 × 10⁶ J
• This number is large and that is only 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

Calculating with kWh

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

• But here, different units are considered:
  
  •  = energy transferred, measured in kilowatt hours (kW h)
  • = power of the appliance, measured in kilowatts (kW)
  • = 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

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

• Therefore, 1 kWh = 3.6 × 106 J

• To convert from kW h to J:

• To convert from J to kW h:

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