Electrical Power (Cambridge (CIE) O Level Physics): Revision Note

Electrical Power Equation

• 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:

$P=\frac{E}{t}=\frac{W}{t}$

• 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

$P=IV$

• Where:

  • P = power in watts (W)

  • I = current in amps (A)

  • V = potential difference in volts (V)

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

$E=VIt$

• Where:

  • E = energy transferred in joules (J)

  • V = potential difference in volts (V)

  • I = current in amps (A)

  • t = time in seconds (s)

Measuring Energy Usage

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:

$E=Pt$

• Where

  • E = energy (kWh)

  • P = power (kW)

  • t = time (h)

• This equation is unusual because SI units 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:

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

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

• To convert between Joules and kW h:

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

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

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