Electricity

When charge flows through a conductor there is an electric current in it. In a torch the cells make charge flow and the bulb glows. A switch makes a conducting link between the cell and the bulb. A continuous and closed path of current is an electric circuit. If the path breaks anywhere, or the switch opens, the current stops and the bulb goes out.

In a metal wire the electrons carry the charge. Current was first thought of as a flow of positive charge. So in a circuit the direction of current is taken opposite to the direction of the electrons — from the positive terminal of the cell towards the negative terminal.

Water does not flow by itself in a level tube. If one end is joined to a tank at a height, the pressure difference pushes the water. Electrons in a metal wire move only when there is a potential difference along the wire. A battery of one or more cells produces that difference. Chemical action inside a cell keeps the potential difference across the terminals even when no current is drawn. To keep the current going, the cell spends its chemical energy.

The potential difference between two points is the work done to move a unit charge from one point to the other. V = W/Q. The SI unit is the volt. One volt is the potential difference when 1 joule of work moves 1 coulomb: 1 V = 1 J/C. Potential difference is measured with a voltmeter, connected in parallel across the two points.

In 1827 Georg Simon Ohm found that the potential difference across a metal wire is proportional to the current through it, provided the temperature does not change. This is Ohm law. V ∝ I, or V = IR. R is the resistance of that wire.

Resistance is the opposition to the flow of charge. The unit is the ohm (Ω). 1 Ω = 1 V/1 A. Since I = V/R, doubling the resistance halves the current. A component that changes the current without changing the source voltage is a variable resistance. A rheostat is often used for this in a circuit.

The resistance of a uniform metal wire is proportional to its length l and inversely proportional to its area of cross-section A. R = ρl/A. ρ (rho) is the resistivity. Its SI unit is Ω m. Metals and alloys have resistivity from about 10⁻⁸ Ω m to 10⁻⁶ Ω m. Insulators such as rubber and glass are of order 10¹² to 10¹⁷ Ω m. Both resistance and resistivity change with temperature.

The resistivity of an alloy is usually higher than that of its metals, and alloys do not oxidise readily at a high temperature. That is why the coils of irons and toasters are alloys. Tungsten is used for a bulb filament. Copper and aluminium are used for transmission lines. The table values need not be memorised. For a comparison, silver has the lowest resistivity, then copper. Iron has a lower resistivity than mercury, so iron is a better conductor than mercury.

In series the current is the same everywhere. A bulb and a heater need different currents, so joining them in series is not practical. If one bulb fuses, the whole string goes out — finding the dead bulb in festival series lights takes a long time.

In a parallel connection each appliance gets the full potential difference of the source and each draws the current it needs. If one appliance is switched off, the others keep working. The total resistance falls, so the total current from the source can rise.

A cell spends energy to keep the current going. In a fan some of it becomes useful work and the rest becomes heat. In a circuit of resistors only, all the energy becomes heat. This is the heating effect of current. A heater, an iron, a toaster and a kettle work on it.

If a current I flows for time t through a resistance R at potential difference V, the energy supplied by the source is VIt. That energy is the heat. Putting V = IR from Ohm law gives H = I²Rt. This is Joule law of heating. The heat is proportional to the square of the current, to R when I is fixed, and to the time. The unit is the joule.

Power is the rate of energy. P = VI = I²R = V²/R. The unit is the watt. 1 W = 1 V × 1 A. The commercial unit is the kilowatt hour. 1 kWh = 1000 W × 3600 s = 3.6 × 10⁶ J. We pay the board for energy, not for electrons. Electrons are not used up in the circuit.

The filament of a bulb is tungsten. Its melting point is 3380 °C, so it becomes hot enough to give light without melting. The filament is held on insulating supports. The bulb is filled with inactive nitrogen and argon so that the filament lasts longer. Most of the power of the filament becomes heat and a small part becomes light.

A fuse protects the circuit. It is placed in series with the appliance. The wire is a metal or alloy that melts at a suitable temperature, such as aluminium, copper, iron or lead. If the current rises above the rated value the wire melts and the circuit breaks. Household fuses are rated 1 A, 2 A, 3 A, 5 A and 10 A.

The cord of a heater does not glow while the heating element does, because the current is the same in both but the resistance of the element is much larger. In H = I²Rt a larger R gives more heat.