Electrical appliances in our daily lives convert electrical energy into other forms of energy such as heat, light, and mechanical energy. Understanding the mathematical relationships between electrical energy, power, voltage, current, and resistance allows consumers to determine energy usage, calculate electrical consumption costs, and choose energy-efficient appliances to reduce household expenditure.
See how voltage, current, resistance and time connect to electrical energy, power and electricity cost.
\(1\text{ unit} = 1\text{ kWh}\)
\(\text{Energy (kWh)} = \text{Power (kW)} \times \text{Time (h)}\)
\(\text{Cost} = \text{Energy (units)} \times \text{Cost per unit}\)
An appliance labelled \(240\text{ V}, 700\text{ W}\) uses \(700\text{ J}\) of energy every second when supplied with \(240\text{ V}\).
Electrical energy is the work done by electric charges moving through a potential difference. It is given by \(E = VIt\), where \(V\) is potential difference, \(I\) is current and \(t\) is time.
Electrical power is the rate at which electrical energy is used. \(P = \dfrac{E}{t} = VI\). Using Ohm's law, it can also be written as \(P = I^2R\) or \(P = \dfrac{V^2}{R}\).
Working voltage is the potential difference required for an electrical appliance to operate under normal conditions. At this voltage, the appliance consumes its stated power rating.
Household electricity is billed in kilowatt-hours. \(1\text{ unit} = 1\text{ kWh}\). Energy used is calculated as power in kilowatts multiplied by time in hours.
Problem-solving framework
Close all windows and doors when using the air conditioner and keep the filter clean. Switch off appliances when not in use. Use only full loads of laundry in the washing machine. Use energy-saving lamps.
Answer in your mind, then press “Check Answer”.
An electric heater has an output power of \(80\text{ W}\). How much electrical energy does it supply in \(10\text{ seconds}\)?
A fluorescent lamp is rated \(240\text{ V}, 32\text{ W}\). What is its resistance under normal operating conditions?
If electricity costs \(30\text{ sen}\) per unit, what is the cost of operating a \(1\text{ kW}\) vacuum cleaner for half an hour?
1 kilowatt-hour (\(\text{kWh}\)) is a unit of electrical power.
Kilowatt-hour (\(\text{kWh}\)) is a unit of electrical energy, not power. It represents the energy consumed by a \(1\text{ kW}\) appliance running for \(1\text{ hour}\) (\(1\text{ kWh} = 1000\text{ W} \times 3600\text{ s} = 3.6 \times 10^6\text{ J}\)).
A higher power rating always means an appliance is more energy-saving.
A higher power rating means the appliance consumes more electrical energy per second. For the same output brightness or task, an appliance with a lower power rating (such as a \(12\text{ W}\) LED compared to a \(40\text{ W}\) CFL) consumes less energy and has higher efficiency.
Objective: Test your understanding of electrical energy, power, working voltage and electricity cost.
1 What is the electrical power of an appliance that operates with a potential difference of \(240\text{ V}\) and carries a current of \(0.5\text{ A}\)?
2 Which of the following defines 1 unit of electricity used in household billing?
3 The potential difference required for an electrical appliance to operate under normal conditions is known as the voltage.
4 The S.I. unit for electrical power is the , which is equivalent to \(\text{J s}^{-1}\).
Drag each term to the correct formula or description. If using a phone, tap the answer first, then tap the matching box.
There is something wrong with this question.
