Mains Electricity & Electrical Power

Alternating and Direct Current

Electric current can flow in two ways. In direct current (d.c.) the current flows in one direction only and keeps a steady value. Cells and batteries supply d.c. — electrons drift steadily from the negative terminal round to the positive terminal.

In alternating current (a.c.) the direction of the current reverses back and forth many times each second, and its value rises and falls smoothly. The mains supply that comes out of the wall sockets in your home is a.c.

Key terms

Direct current (d.c.) — current that flows in one direction only, with a constant value.

Alternating current (a.c.) — current that repeatedly reverses direction.

Frequency — the number of complete cycles per second, measured in hertz (Hz).

In the UK, the mains supply has a voltage of about 230 V and a frequency of 50 Hz. A frequency of 50 Hz means the current completes 50 full cycles (and so changes direction 100 times) every second.

The Three-Pin Plug

Mains appliances connect to the supply through a three-pin plug. Inside the plug there are three wires, each with its own job and its own colour. Knowing the colours is a common exam question.

The current flows in through the live wire and back out through the neutral wire. The earth wire carries no current in normal use — it only does its job if a fault occurs.

Exam tip

Remember the colours with BLue = neutraL, brown = live (both start with the "b" sound), and the stripy green-and-yellow wire is always earth. The fuse is always fitted on the live side.

Safety Features

Mains electricity is dangerous, so several features protect both the user and the appliance.

The fuse is a thin piece of wire fitted in the live side of the circuit. If the current rises above the fuse's rating, the fuse wire heats up and melts, breaking the circuit. This stops the wires overheating and starting a fire.

Earthing protects appliances with a metal case. The earth wire connects the case to the ground. If the live wire works loose and touches the case, a very large current flows straight to earth. This surge of current blows the fuse, disconnecting the appliance so the case can never become live and give the user a shock.

Circuit breakers do the same job as a fuse but use an electromagnetic switch instead of a melting wire. When the current gets too large, the switch trips and breaks the circuit. They act faster than fuses and can simply be reset rather than replaced.

Double insulation is used in appliances such as hairdryers and kettles that have a plastic outer case. The case cannot become live because it does not conduct, so these appliances have no earth wire — only live and neutral. They are marked with a square-inside-a-square symbol.

Key terms

Fuse — a thin wire that melts and breaks the circuit if the current exceeds a set value.

Earthing — connecting an appliance's metal case to the ground so a fault current blows the fuse instead of leaving the case live.

Double insulation — an appliance built with an insulating case so no earth wire is needed.

Electrical Power

Power is the rate at which an appliance transfers electrical energy. It is measured in watts (W), where 1 W = 1 joule per second. For a mains appliance the power is given by:

$$P = V \times I$$

where $P$ is power in watts, $V$ is potential difference in volts and $I$ is current in amperes.

Because $V = IR$, we can also write power in terms of current and resistance:

$$P = I^2 R$$

This second form is useful for working out the heat produced in a resistor or in a cable.

Worked example

A 2300 W electric heater is plugged into the 230 V mains.

Find the current it draws.

Rearrange $P = VI$ to give $I = \dfrac{P}{V} = \dfrac{2300}{230} = 10\ \text{A}$.

So the heater draws a current of 10 A.

Choosing the Right Fuse

A fuse should have a rating just above the normal operating current of the appliance — high enough that it does not blow in normal use, but low enough to protect the circuit. Common ratings are 3 A, 5 A and 13 A.

For the heater above, the current is 10 A, so a 13 A fuse would be chosen. A low-power device such as a 460 W television draws $I = 460 \div 230 = 2\ \text{A}$, so a 3 A fuse is suitable.

Watch out

Never pick a fuse rating below the working current — it would blow straight away. And never fit one far too high — it would not protect the appliance. Choose the standard fuse just above the normal current.

Energy and the Cost of Electricity

The energy transferred by an appliance depends on its power and how long it runs:

$$E = P \times t$$

If $P$ is in watts and $t$ in seconds, the energy $E$ is in joules.

Energy companies do not charge in joules — the numbers would be huge. Instead they use the kilowatt-hour (kWh), the energy used by a 1 kW appliance running for 1 hour.

Key terms

Kilowatt-hour (kWh) — the energy transferred by a 1 kW appliance in 1 hour; the "unit" of electricity on your bill.

To find the cost of running an appliance:

$$\text{cost} = \text{power (kW)} \times \text{time (h)} \times \text{cost per kWh}$$

Worked example

Electricity costs 30p per kWh. How much does it cost to run a 2 kW kettle for 15 minutes?

Time in hours: $15\ \text{min} = 0.25\ \text{h}$.

Energy used: $E = 2 \times 0.25 = 0.5\ \text{kWh}$.

Cost: $0.5 \times 30 = \mathbf{15p}$.

The Heating Effect of Current

When a current flows through a wire, the moving electrons collide with the metal ions and make them vibrate more. This raises the wire's temperature — current always has a heating effect. The power dissipated as heat is given by $P = I^2 R$.

This effect is useful in devices designed to get hot: kettles, toasters, electric heaters, hair straighteners and the filament of an old light bulb all rely on it.

It can also be a danger. Cables carrying too much current overheat, which can melt the insulation and start fires. This is why we use correctly rated fuses, avoid overloading sockets, and use thick wires for high-current appliances to keep their resistance — and therefore their heating — low.

Real world

The thin wires in a phone charger feel warm because of the $I^2R$ heating effect. A coiled-up extension lead carrying a heater can overheat badly — uncoiling it lets the heat escape and keeps it safe.