Power, Energy and Mains Electricity
Mains Electricity in the UK
The electricity supplied to UK homes and schools is alternating current (a.c.). It operates at approximately 230 V and completes 50 cycles every second — a frequency of 50 Hz. The current changes direction twice in each cycle, so it reverses 100 times every second. This is quite different from the direct current (d.c.) you get from a battery, which always flows the same way.
UK mains electricity: approximately 230 V, alternating current (a.c.), 50 Hz frequency. Batteries and cells supply direct current (d.c.).
The Three-Pin Plug
Most mains appliances connect to the supply via a three-pin plug. Understanding the role of each wire is essential for electrical safety.
Live wire (brown) — carries the alternating potential difference from the mains supply. It alternates between positive and negative peaks.
Neutral wire (blue) — completes the circuit and is kept close to 0 V (earth potential).
Earth wire (green and yellow stripes) — a safety wire connected to the metal casing of an appliance. If a fault causes the casing to become live, the earth wire carries the current safely to ground, blowing the fuse and breaking the circuit.
Even with an appliance switched off, the live wire remains at mains voltage relative to earth. If someone touches it, there is a large potential difference between their hand and the ground, which drives a current through the body. This is why switches must always be wired into the live wire — breaking the live side ensures no voltage reaches the appliance.
Fuses and Circuit Breakers
A fuse is wired into the live wire. If a fault causes excessive current to flow, the fuse wire heats up and melts, breaking the circuit before the appliance or cable can overheat and catch fire. Fuses are rated in amps (e.g. 3 A, 5 A, 13 A) — the correct fuse rating is just above the normal operating current of the appliance.
A circuit breaker performs the same protective function as a fuse but can be reset by flicking a switch. This makes circuit breakers more convenient — but both devices must be positioned in the live wire to be effective.
Electrical Power
The power of an appliance tells you how much energy it transfers every second. Two equations link power to current and potential difference:
$$P = IV$$
$$P = I^2 R$$
where \(P\) is power in watts (W), \(I\) is current in amps (A), \(V\) is potential difference in volts (V), and \(R\) is resistance in ohms (\(\Omega\)).
A hairdryer is rated at 1150 W and operates on a 230 V mains supply. Calculate the current it draws and select the correct fuse.
Rearrange \(P = IV\): \(I = \frac{P}{V} = \frac{1150}{230} = 5\) A
Since the normal current is 5 A, a 5 A fuse would blow under normal use. Select a 13 A fuse — the next standard rating above 5 A — to protect the cable while allowing normal operation.
Energy Transferred in a Circuit
The energy an appliance transfers depends on its power and how long it runs:
$$E = Pt$$
where \(E\) is energy in joules (J), \(P\) is power in watts (W), and \(t\) is time in seconds (s). You can also calculate energy transferred using charge: \(E = QV\), where \(Q\) is the charge in coulombs (C) that has flowed and \(V\) is the potential difference across the component.
A 60 W lamp is left on for 2 hours. Calculate the energy transferred.
Convert time to seconds: \(t = 2 \times 3600 = 7200\) s
\(E = Pt = 60 \times 7200 = 432{,}000\) J = 432 kJ
Using the charge equation: if the current is \(I = \frac{P}{V} = \frac{60}{230} \approx 0.26\) A, then charge \(Q = It = 0.26 \times 7200 \approx 1872\) C. Check: \(E = QV = 1872 \times 230 \approx 430{,}560\) J ✓ (rounding difference).
Transformers and the National Grid
The National Grid transmits electricity at very high voltages (hundreds of thousands of volts) and correspondingly low currents. The reason: power lost as heat in the cables equals \(P_{\text{loss}} = I^2 R\). A smaller current means far less wasted energy in the resistance of the cables.
A transformer changes the voltage of an a.c. supply. A step-up transformer at the power station increases voltage (and reduces current) before transmission. Step-down transformers near homes reduce the voltage back to a safe 230 V for domestic use.
Because energy is conserved in an ideal transformer, the power in equals the power out: \(V_p I_p = V_s I_s\). This is why stepping up voltage forces the current to decrease proportionally.