Mains Electricity, Power and the National Grid
Alternating Current and Direct Current
Alternating current (a.c.) changes direction repeatedly. The UK mains supply is a.c. at a frequency of 50 Hz, meaning it completes 50 full cycles per second. The peak voltage of UK mains is approximately 325 V, but the declared supply voltage is 230 V — this represents the equivalent d.c. voltage that would deliver the same power.
Direct current (d.c.) flows in one direction only. Batteries and cells supply d.c. Electronic devices (phones, laptops) typically require d.c. internally; their chargers convert mains a.c. to low-voltage d.c.
UK mains supply: alternating current (a.c.), declared voltage 230 V, frequency 50 Hz. Batteries supply direct current (d.c.). The mains frequency of 50 Hz means the current changes direction 100 times per second (two direction changes per cycle).
The Three-Pin Plug
Most UK appliances connect to the mains through a three-pin plug. The three wires have standard colours:
Live wire (brown) — carries the alternating potential difference from the supply, alternating between approximately +325 V and −325 V relative to earth.
Neutral wire (blue) — completes the circuit. It is at, or close to, 0 V (earth potential). Current returns to the supply via this wire.
Earth wire (green and yellow) — a safety wire connected to the metal casing of an appliance. It carries current safely to earth if a fault causes the casing to become live, tripping the fuse or circuit breaker.
The live wire is at a high potential difference (∼230 V) relative to earth at all times — even when the appliance switch is off. If you touch it, a large p.d. exists between your body and the ground, driving a current through you. Switches are therefore always placed in the live wire so that when open, the appliance and the neutral/earth wires are isolated from the high-voltage supply.
Fuses and Circuit Breakers
A fuse is connected in series in the live wire. If a fault causes an excessive current to flow, the fuse wire melts, breaking the circuit before the appliance or cable can overheat and cause a fire. Fuses are rated at 3 A, 5 A, or 13 A for most domestic appliances — the fuse rating should be just above the normal operating current.
A circuit breaker serves the same protective purpose but can be reset by pressing a switch — no replacement is needed. Residual current device (RCD) circuit breakers detect tiny imbalances between live and neutral currents (indicating a leakage to earth) and trip within milliseconds — faster than a fuse melts.
Electrical Power
Electrical power is the rate of energy transfer. The fundamental equation is:
$$P = IV$$
Where \(P\) is power in watts, \(I\) is current in amperes, and \(V\) is potential difference in volts. Combining with \(V = IR\) gives two further equations:
$$P = I^2R \quad \text{and} \quad P = \frac{V^2}{R}$$
\(P = I^2R\) is particularly useful for calculating power dissipated in a resistor when you know the current; \(P = V^2/R\) when you know the voltage. On a long transmission wire, power is wasted as heat — this dissipation follows \(P_{lost} = I^2R\), showing that reducing current dramatically reduces heat losses.
Three power equations: \(P = IV\) (use when both current and voltage are given); \(P = I^2R\) (use when current and resistance are given); \(P = V^2/R\) (use when voltage and resistance are given). \(P = V^2/R\) is not on the Edexcel equation list, so a question that needs it will give it to you. Power is always in watts; energy transferred is \(E = Pt\) in joules.
Energy Transferred
Energy transferred by an electrical device is given by:
$$E = Pt \quad \text{and also} \quad E = QV$$
Where \(E\) is energy in joules, \(P\) is power in watts, \(t\) is time in seconds, \(Q\) is charge in coulombs, and \(V\) is potential difference in volts. The equation \(E = QV\) links directly to the definition of potential difference as energy per unit charge.
A kettle operates at 230 V and draws a current of 9 A. Calculate (i) its power rating and (ii) the energy it transfers in 2 minutes.
(i) \(P = IV = 9 \times 230 = 2070\) W ≈ 2.1 kW
(ii) \(t = 2 \times 60 = 120\) s
\(E = Pt = 2070 \times 120 = 248\,400\) J ≈ 248 kJ
Check: the fuse should be rated just above 9 A — a 13 A fuse is appropriate. A 3 A fuse would melt immediately under normal operation.
The National Grid and Transformers
The National Grid transmits electricity from power stations to consumers. Because power loss in cables follows \(P = I^2R\), the key strategy is to transmit at very high voltage (and therefore very low current) to minimise energy waste as heat in the cables.
A transformer uses electromagnetic induction to change the voltage of an a.c. supply. Transformers work only with a.c. — this is one reason the National Grid uses a.c. rather than d.c.
A step-up transformer at the power station increases voltage from around 25 kV to 132 kV, 275 kV, or 400 kV for long-distance transmission. At the end of the transmission line, a series of step-down transformers reduce the voltage progressively to 33 kV, then 11 kV, then 230 V for domestic use.
High-voltage transmission keeps current low, which reduces power lost as heat in cables (\(P_{lost} = I^2R\)). A step-up transformer increases voltage at the power station; step-down transformers reduce it before it reaches homes.
A transformer works because the changing magnetic field produced by alternating current in the primary coil induces an alternating voltage in the secondary coil. A steady (d.c.) current produces a constant magnetic field — no change, no induction, no output voltage. This is why the National Grid must use a.c.: only a.c. allows transformers to step voltage up or down efficiently.