Domestic Electricity and Electrical Power
AC and DC
Direct current (DC) flows in one direction only — this is what batteries and solar cells produce. Alternating current (AC) constantly reverses direction, flowing back and forth through the circuit. The UK mains supply is AC at a frequency of 50 Hz (50 complete cycles per second) and a voltage of about 230 V.
On an oscilloscope trace, AC appears as a wave (typically a sine wave) that oscillates above and below zero. DC appears as a straight horizontal line. The key advantage of AC is that its voltage can be easily increased or decreased using transformers — this is essential for the efficient transmission of electricity through the National Grid.
The UK domestic supply is AC at 230 V and 50 Hz. Batteries supply DC. AC can be easily transformed to different voltages; DC cannot.
Mains Wiring and Safety
Scope note: the national grid, transformers and mains wiring are examined on Physics Paper 2 (topic P6), not Paper 1. They sit here because they follow on from domestic electricity.
A UK three-pin plug contains three wires, each with a specific colour and function:
• Live (brown) — carries the AC supply at about 230 V. This wire is always dangerous, even when the switch is open, because it remains connected to the mains supply.
• Neutral (blue) — completes the circuit and is normally at 0 V. Current flows in through the live wire and out through the neutral.
• Earth (green and yellow striped) — a safety wire connected to the metal casing of an appliance. It provides a low-resistance path to earth if a fault occurs, preventing the casing from becoming live.
A fuse is always connected in the live wire. If the current exceeds the fuse rating, the thin fuse wire melts and breaks the circuit, preventing overheating, fire or electrocution. The earth wire and fuse work together as a safety system: if the live wire touches the metal casing (a fault), a large current surges through the earth wire to ground, which immediately blows the fuse and disconnects the supply.
A residual current device (RCD) provides even faster protection. It compares the current in the live and neutral wires. If they differ (indicating current is leaking through a person or a fault), the RCD cuts the circuit within milliseconds.
The live wire alternates between approximately +325 V and -325 V (the 230 V rating is the root mean square value). Even when a switch is open (appliance turned off), the live wire is still connected to the mains supply and carries a potential of 230 V relative to earth. Touching it creates a large potential difference between your body and the ground, causing a dangerous current to flow through you. This is why you must never touch exposed wires or attempt to repair electrical appliances without disconnecting them from the mains.
Double insulation is an alternative safety feature used on appliances with plastic casings (such as hairdryers and power drills). The plastic casing cannot become live, so no earth wire is needed. These appliances are marked with a double-square symbol.
Electrical Power
Electrical power is the rate at which energy is transferred in a circuit. The key equations are:
$$P = V \times I$$
$$P = I^2 \times R$$
Where \(P\) is power (W), \(V\) is potential difference (V), \(I\) is current (A), and \(R\) is resistance (\(\Omega\)). The second equation is derived by substituting \(V = IR\) into the first. It is especially useful for calculating the power dissipated as heat in a resistor or in electrical cables.
Energy Transferred
The total energy transferred by an appliance depends on its power and how long it runs:
$$E = P \times t$$
Where \(E\) is energy (J), \(P\) is power (W) and \(t\) is time (s). Energy can also be calculated using charge: \(E = Q \times V\), where \(Q\) is charge (C) and \(V\) is potential difference (V). This tells you the energy transferred to each coulomb of charge as it passes through a component.
For domestic energy bills, energy is measured in kilowatt-hours (kWh) rather than joules. One kWh is the energy transferred by a 1 kW device running for 1 hour. To calculate the cost: \(\text{cost} = \text{energy (kWh)} \times \text{price per kWh}\). For example, a 3 kW oven running for 2 hours uses \(3 \times 2 = 6 \text{ kWh}\).
Power equations: \(P = VI\), \(P = I^2R\). Energy transferred: \(E = Pt\) or \(E = QV\). Domestic energy is measured in kWh. Cost = energy (kWh) × price per unit.
The National Grid
The National Grid is the nationwide system of cables and transformers that distributes electricity from power stations to consumers. Electricity is transmitted at very high voltages (up to 400,000 V) and correspondingly low currents to minimise energy losses in the cables.
The physics behind this is straightforward. Since \(P = V \times I\), transmitting the same power at higher voltage means a lower current. The power wasted as heat in the cables is \(P_{\text{loss}} = I^2 \times R\). Because current is squared, even a small reduction in current dramatically reduces heat losses. This is why the National Grid is efficient — only about 2% of energy is lost in transmission.
Step-up transformers at power stations increase the voltage (and reduce the current) for long-distance transmission. Step-down transformers at local substations reduce the voltage back to 230 V for safe domestic use.
For an ideal (100% efficient) transformer, the power input equals the power output:
$$V_p \times I_p = V_s \times I_s$$
Where \(V_p\) and \(I_p\) are the voltage and current in the primary coil, and \(V_s\) and \(I_s\) are those in the secondary coil. If voltage increases (step-up), current decreases proportionally — and vice versa for a step-down transformer. Transformers only work with AC because they rely on a changing magnetic field in the core to induce a voltage in the secondary coil.