Practical Electricity

Every coulomb passing through a component gives up V joules, and I coulombs pass every second. Multiply the two and you have the energy transferred per second, which is the power. That is the whole derivation of P = VI, and it is worth understanding rather than memorising, because the other two forms follow from it in one line each.

Substituting V = IR gives P = I²R. Substituting I = V/R gives P = V²/R. All three are the same statement; you choose whichever one matches the quantities the question gives you.

The I² form matters more than it looks. Because power loss depends on the square of the current, halving the current cuts the heating to a quarter. That single fact is why electricity is transmitted across the country at hundreds of thousands of volts.

P

powerW

V

potential differenceV

I

currentA

R

resistanceΩ

E

energyJ

Change the supply voltage and watch the power reading. Doubling the voltage across a fixed resistance quadruples the power, because P = V²/R — the relationship is square, not proportional.

The joule is far too small a unit for a household bill. A single kettle boiling uses about half a million of them. So energy suppliers bill in kilowatt-hours, and the arithmetic becomes easy: power in kilowatts, multiplied by time in hours, multiplied by the price per unit.

The name causes trouble because it sounds like a rate. It is not. A kilowatt is a rate; a kilowatt-hour is a rate multiplied by a time, which is a quantity of energy. Examiners ask you to state this, and "a unit of energy" is often a mark on its own.

The practical lesson from any bill is that it is the heating appliances that cost money. Anything designed to warm something — kettle, iron, immersion heater, air conditioner — runs at kilowatts. Anything designed to process information runs at watts. A phone charger left plugged in all year costs less than one hot bath.

Mains wiring in a plug is not arbitrary. Each of the three wires does one job, and exam questions almost always ask you to explain that job rather than recite a colour.

The live wire carries the alternating supply voltage and is the dangerous one. The neutral completes the circuit and sits at roughly earth potential. The earth wire normally carries no current at all: it is a safety path, connected to the metal case of the appliance.

If a fault lets the live wire touch a metal case, the case becomes live. Without an earth wire, the next person to touch it becomes the path to ground. With an earth wire, a very large current flows instantly to earth instead, which blows the fuse and disconnects the appliance before anyone touches it.

A fuse is a deliberately weak link: a thin wire that melts when the current through it exceeds its rating, breaking the circuit. It is chosen to be just above the appliance's normal working current — near enough to react to a fault, far enough above to avoid blowing every time the appliance switches on.

Choosing a fuse is a two-step calculation that appears constantly. Work out the normal current from I = P/V, then pick the next standard fuse above it. The common ratings are 3 A, 5 A and 13 A.

A circuit breaker does the same job with an electromagnetic switch instead of a melting wire. It trips faster and, more usefully, can simply be reset instead of replaced.

Some appliances have no earth wire at all and are still safe. These are double insulated: the casing is plastic, and there is a second layer of insulation between the electrical parts and anything you can touch. With no metal case there is nothing to become live, so there is nothing to earth.