Electrical Power (Cambridge O Level Physics)

• In mechanics, power P is defined as the rate of doing work
  • The potential difference is the work done per unit charge
  • Current is the rate of flow of charge

• Therefore, the electrical power is defined as the rate of change of work done:

• Where:
  • P = power in watts (W)
  • E = energy in joules (J)
  • t = time in seconds (s)
  • W = work done in (J)

• The work done is the energy transferred so the power is the energy transferred per second in an electrical component

• The power dissipated (produced) by an electrical device can also be written as

• Where:
  • P = power in watts (W)
  • I = current in amps (A)
  • V = potential difference in volts (V)

• Using Ohm's Law V = IR to rearrange for either V or I and substituting into the power equation, means power can be written in terms of resistance R

• Where:
  • P = power in watts (W)
  • I = current in amps (A)
  • R = resistance in ohms (Ω)
  • V = potential difference in volts (V)

• This means for a given resistor if the current or voltage doubles the power will be four times as great.
  • Which equation to use will depend on whether the value of current or voltage has been given in the question

• Rearranging the energy and power equation, the energy can be written as:

• Where:
  • E = energy transferred in joules (J)
  • V = potential difference in volts (V)
  • I = current in amps (A)
  • t = time in seconds (s)

The Kilowatt Hour (kWh)

• Energy usage in homes and businesses is calculated and compared using the kilowatt hour
• The kilowatt hour is defined as:

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

• Appliances are given power ratings, which tell consumers:

The amount of energy transferred (by electrical work) to the device every second

Power Rating for a Kettle

This kettle uses between 2500 and 3000 W of electrical energy

• This energy is commonly measured in kilowatt-hour (kW h), which is then used to calculate the cost of energy used

Calculating with kWh

• The kilowatt hour can also be defined using an equation:

• Where
  • E = energy (kWh)
  • P = power (kW)
  • t = time (h)
    • This equation is unusual because S.I. unit are not used, both energy and power are × 10³, and time is in hours, not seconds

• Since the usual unit of energy is joules (J), this is the 1 W in 1 s
  • Therefore:

• • Since 1 kW = 1000 W and 1 h = 3600 s

• To convert between Joules and kW h:

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