Electrical energy, power and domestic appliances

• Define electrical power as the rate of energy transfer per second, measured in watts.
• Calculate power utilizing the relationship between energy transferred and time taken.

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

• Explain the relationship between a device's power transfer, the potential difference across it, and the current flowing through it.
• Calculate electrical power using equations relating to current, potential difference, and resistance.

$P = I \times V$

$P = I^2 \times R$

• Describe the energy transformation pathways in various domestic appliances, from battery or mains sources to motors and heating elements.
• Contrast the properties and behaviors of direct voltage against alternating voltage.
• Define direct current (d.c.) as unidirectional charge movement and identify cells and batteries as primary d.c. sources.
• Define alternating current (a.c.) as the continuous directional reversal of charge movement.
• Recall the standard specifications of the UK domestic mains supply as an alternating current with a frequency of $50 \text{ Hz}$ and a voltage of approximately $230 \text{ V}$.
• Explain the distinct roles and functions of the live and neutral wires in a mains electricity input.
• Explain the critical safety functions of the earth wire, fuses, and circuit breakers in preventing electrical hazards.
• Understand the safety rationale for exclusively placing switches and fuses on the live wire within domestic circuits.
• Recall the standard potential differences maintained between the live, neutral, and earth wires in a mains supply.
• Analyze the severe hazards associated with establishing any accidental connection between the live wire and earth.
• Evaluate the relationship between the assigned power ratings of domestic appliances and the corresponding changes in stored energy during their operation.

Power tells us how quickly energy is transferred

Power is the energy transferred per second. It is a rate, rather than an amount of energy. A powerful appliance transfers energy quickly, but its total energy transfer also depends on how long it operates.

Power, $P$, is measured in watts (W). One watt means one joule transferred each second:

One kilowatt is $1000\text{ W}$. A $2\text{ kW}$ appliance therefore transfers $2000\text{ J}$ each second while operating at that power.

For example, a device transferring $600\text{ J}$ in $20\text{ s}$ has a power of $600\div20=30\text{ W}$. Its average rate of energy transfer is $30\text{ J}$ each second.

Rearranging the power equation gives two useful relationships:

These show why a lower-power device can transfer the same total energy as a higher-power device if it operates for longer.

Connecting power to current and potential difference

Since $E=IVt$ and $P=E/t$, dividing the energy transferred by the time gives:

This connects power directly to the flow of charge. Current tells us how much charge passes each second, and potential difference tells us how much energy each unit of charge transfers. Multiplying them gives energy transferred each second.

At a fixed potential difference, doubling the current doubles the power. At a fixed current, doubling the potential difference doubles the power.

For a motor with $12\text{ V}$ across it and a current of $3\text{ A}$, the electrical power input is $P=3\times12=36\text{ W}$. The motor receives $36\text{ J}$ electrically each second. Not all of this necessarily becomes useful movement: some energy is transferred to the surroundings by heating and sound.

Calculating power from resistance

Resistance describes how strongly a component opposes current. Using the circuit relationship $V=IR$, we can replace $V$ in $P=IV$:

Use this form when current and resistance are known. $R$ is resistance in ohms ($\Omega$), and the current must be squared.

For a resistor with resistance $5\,\Omega$ and current $2\text{ A}$, its power is $P=2^2\times5=20\text{ W}$. Energy is transferred to the resistor at a rate of $20\text{ J}$ each second, producing heating.

For a fixed resistance, doubling the current makes the power four times as large because the current is squared. This helps explain why a large current can produce substantial heating.

Motors and heating elements in domestic appliances

Domestic appliances use electrical energy transfers to produce different useful effects. A battery-powered remote control receives energy electrically from the battery's chemical store. Many larger household appliances receive energy electrically from the a.c. mains supply.

A motor produces movement. In a washing machine, a motor rotates the drum, transferring energy to its kinetic store and moving the clothes. A vacuum cleaner uses a motor to move air and create suction. Motors also transfer some energy to the surroundings through heating and sound.

A heating element becomes hot when current flows through it. In a kettle, energy is transferred electrically to the element's thermal store and then by heating to the water's thermal store. In a toaster, hot elements transfer energy to the bread, increasing its temperature and toasting it. Heating that escapes to other surroundings is not useful for these tasks.

These examples distinguish an energy store, such as a thermal or kinetic store, from a transfer pathway, such as electrical work or heating. Energy is transferred between stores; it is not used up.

What an appliance's power rating means

A power rating tells us the rate at which an appliance transfers energy under its intended operating conditions. A kettle rated at $2000\text{ W}$ transfers $2000\text{ J}$ electrically each second when operating at that rating. This leads to changes in the thermal stores of the element, water and surroundings.

For the same operating time, an appliance with twice the power transfers twice as much energy. For the same energy transfer, an appliance with twice the power needs half as much time.

For example, a $1\text{ kW}$ iron operating for one hour transfers the same total energy as a $2\text{ kW}$ iron operating for half an hour. Using seconds, both transfer $3\,600\,000\text{ J}$: $1000\times3600$ and $2000\times1800$ give the same result.

A higher power rating therefore means a faster total energy transfer, not automatically greater efficiency. When comparing how quickly two kettles heat the same amount of water, their useful heating rates matter as well as their electrical power inputs.

Units: $E$ in J, $P$ in W, $I$ in A, $V$ in V, $t$ in s and $R$ in $\Omega$.