Electricity
Electricity is the movement of electric charge, and the energy that moving charge carries. It runs lights, motors, heaters, phones, computers and the whole power grid, and a typical European home uses about 10 kWh of it a day. Electricity is useful because it carries energy almost instantly, through a thin wire, over hundreds of kilometres. At the far end it turns back into motion, heat or light with very little lost. The same flow of charge can also carry information, which is what every computer and network does.
All of it comes from one property of particles, electric charge, and from the electrons that are free to move inside metals and semiconductors.
Charge
Electrons carry a negative charge and protons an equal positive one. Opposite charges attract and like charges repel, and the force between two charges gets weaker with the square of the distance between them, which is Coulomb's law:
Charge is measured in coulombs (C), and k is 8.99 × 10⁹ N·m²/C². One coulomb is the charge of 6.24 × 10¹⁸ electrons. Charge can't be created or destroyed, only moved, so whenever one object becomes negative by gaining electrons, another becomes equally positive by losing them. Rubbing a balloon on your hair moves electrons from your hair to the balloon, and the opposite charges then make your hair stand up toward it.
Ordinary matter has exactly as many electrons as protons, so its charges cancel and it feels no electric force overall. That cancellation hides how strong the force is. If the electrons in a 1 kg block of copper could all be moved onto a second block a metre away, the two blocks would pull on each other with about 2 × 10²⁵ N. That is 100,000 times the force of gravity holding the Moon in orbit.
The electric field
A charge affects the space around it whether or not another charge is there to feel it. That influence is the electric field: at every point, the force a positive charge of one coulomb would feel there. The field is what one charge uses to push another, and it carries the push from place to place at the speed of light.
The field is measured in volts per metre. In a chip, 1 V across a transistor's insulating layer, about a nanometre thick, makes a field of a billion volts per metre. In dry air, about 3 million volts per metre tears electrons off air molecules, and the air sparks.
Voltage
Voltage is energy per unit of charge. A charge moved against the field gains energy, the way a ball gains energy when lifted, and voltage measures how much energy each coulomb gains or loses between two points. One volt is one joule per coulomb, so a 1.5 V battery gives each coulomb that passes through it 1.5 J of energy, and a 230 V socket gives each coulomb 230 J.
Voltage is always between two points. A bird can sit on a 400,000 V power line unharmed, because both its feet are on the same wire at the same voltage, so no charge flows through it.
Current
Current is the amount of charge passing a point each second, measured in amperes (A). One ampere is one coulomb per second, 6.24 × 10¹⁸ electrons. A phone charger supplies about 2 A, and a kettle about 9 A.
In a metal wire the current is carried by its free electrons, and they move surprisingly slowly. A current I flowing through a wire of cross-section A, with n free electrons per cubic metre each carrying charge e, needs those electrons to move at an average drift velocity of:
Copper has 8.5 × 10²⁸ free electrons per cubic metre. Push 10 A through a 1.5 mm² household wire and each electron drifts along at about 0.5 mm per second, so it would take more than half an hour to move a metre.
A light still comes on the moment you flip the switch, because the wire is already full of electrons. The switch doesn't send electrons from the switch to the bulb. It starts a push that travels along the wire as a change in the electric field, at a large fraction of the speed of light. That push sets every electron in the circuit drifting at almost the same instant, including the ones already inside the bulb's filament.
Resistance and Ohm's law
As the electrons drift, they keep colliding with the vibrating ions of the metal and with impurities, and each collision hands some of their energy to the metal as heat. That opposition to current is resistance, measured in ohms (Ω). For most conductors at a fixed temperature, the current is proportional to the voltage, which is Ohm's law:
Every coulomb passing through a resistance R gives up V joules, and I coulombs pass each second, so the power turned into heat is:
A 2 kW kettle on a 230 V supply draws 2,000 / 230 = 8.7 A, so its element has a resistance of 230 / 8.7 = 26 Ω. The same heating that boils the kettle is a loss everywhere else, warming wires, motors and chips.
How much a piece of material resists depends on its shape as well as what it is made of. A longer wire has more collisions along the way, and a thicker wire has more electrons sharing the current, so the resistance is the material's resistivity ρ times the length over the cross-section:
A 10 m run of 1.5 mm² copper wire has a resistance of 1.68 × 10⁻⁸ × 10 / 1.5 × 10⁻⁶ = 0.11 Ω.
Resistivity spans about 31 powers of ten, a wider range than almost any other property of materials. Metals have a resistivity around 10⁻⁸ Ω·m, and their resistance rises as they warm, because hotter ions vibrate more and scatter electrons more often. A tungsten filament has about 15 times as much resistance glowing as it does cold.
Circuits
A circuit is a closed loop that current can flow around. Every circuit obeys a rule for current and a rule for voltage, both coming from things that can't be created or lost:
- Current in equals current out at every junction, because charge is conserved. If 3 A flows into a junction, 3 A flows out.
- The voltages around any loop add up to zero, because energy is conserved. The energy each coulomb gains in the battery it gives up in the components around the loop.
Components can be connected in series or in parallel. In series they sit one after another on a single path, so the same current flows through each, their resistances add, and the battery's voltage is shared between them. In parallel they sit side by side across the same two points, so each gets the full voltage, their currents add, and each works independently.
The sockets in a house are wired in parallel, so every appliance gets the full mains voltage and switching one off leaves the others running. The currents of everything switched on add up in the supply cable, and a fuse or circuit breaker in series with each circuit cuts it off if that total gets high enough to overheat the wiring.
Why copper conducts and glass doesn't
In a single atom an electron can only have certain energies. When billions of atoms pack into a solid, each of those allowed energies spreads into a band of very closely spaced energies, with gaps between the bands where no electron can be. Electrons fill the bands from the bottom up, two to a state, and only electrons with empty states just above them can conduct. To speed up along the wire, an electron needs a slightly higher-energy state to move into.
- Metals have a top band that is only partly filled, so their outermost electrons always have empty states right next to them and conduct easily.
- Insulators like glass have a completely filled band with a large gap above it, around 9 eV in quartz. At room temperature, heat gives electrons about 0.025 eV, far too little to cross, so nothing conducts.
- Semiconductors like silicon have the same filled band, but with a small gap, 1.1 eV in silicon. A few electrons get enough heat to jump it, and each leaves behind a hole, an empty place in the lower band that acts like a positive charge and conducts too.
Pure silicon has about 10¹⁰ free electrons per cubic centimetre at room temperature. That is ten trillion times fewer than copper, but the number grows steeply with temperature, so silicon conducts better as it warms, the opposite of a metal.
Semiconductors
Silicon becomes useful when it is doped with a tiny trace of another element. Phosphorus has one more outer electron than silicon, so each phosphorus atom added gives a spare electron that is free to conduct. That makes n-type silicon, carrying current with negative electrons. Boron has one fewer, so each boron atom leaves a hole and makes p-type silicon, carrying current with positive holes. One impurity atom per million silicon atoms raises the conductivity by a few million times.
The useful devices come from putting the two types side by side. Where p-type meets n-type, electrons from the n side fill the holes nearby and leave a thin depletion zone with no free carriers, which blocks current.
A voltage one way pushes carriers into the zone and current flows, and the other way widens it and current stops, so a p–n junction lets current through in one direction only. That one-way valve is a diode, and it is used to turn AC into DC in every power adapter. When electrons and holes meet and cancel at the junction, they give off their energy, and in materials like gallium nitride it comes out as light of a colour set by the gap: that is an LED. A solar cell runs the process backwards: light knocks electrons loose near the junction, and the junction's built-in field pushes them out through the circuit.
Transistors
A transistor is a switch with no moving parts, in which a small voltage turns a much larger current on and off. The type in nearly every chip is the MOSFET.
It has two n-type regions, the source and the drain, in a block of p-type silicon. With no voltage on the gate there is no path between them. A positive gate voltage pulls electrons up into a thin channel under the gate, joining source to drain, and current flows. The gate sits on a layer of insulating oxide, so it draws almost no current itself, and one transistor's output can drive the gates of the next ones.
Wiring transistors so they switch each other gives logic: a circuit whose output is on only when both inputs are on, or when either is. From those, a chip builds adders, memory and whole processors. A modern processor has tens of billions of transistors, each switching billions of times a second. The same device can also amplify, because a small change in gate voltage makes a large change in current, which is how a radio or an audio amplifier boosts a weak signal.
Capacitors
A capacitor stores charge on two conducting plates separated by a thin insulator. Push charge onto it and a voltage builds between the plates in proportion: the charge stored is Q = C·V, where C, the capacitance, is measured in farads. The energy stored is:
A capacitor charged through a resistor fills quickly at first and then more slowly, because the voltage building on its plates pushes back against the supply. The time scale is the resistance times the capacitance, RC: after one RC it reaches 63% of the supply voltage, and after five it is effectively full. A 1 kΩ resistor charging a 100 µF capacitor gives an RC of 0.1 s.
Capacitors deliver their energy far faster than a battery can, but store far less of it. A camera flash charges one over a few seconds and dumps it into the bulb in a thousandth of a second. Power supplies use them to smooth out ripple, and every bit in a computer's main memory (DRAM) is a tiny capacitor that is either charged or not.
AC, DC and the grid
Batteries give direct current (DC), always flowing the same way. The mains gives alternating current (AC), which reverses 50 times a second in Europe and 60 times a second in North America. The grid runs on AC because AC voltage can be raised and lowered efficiently by a transformer, two coils on an iron core, and raising the voltage is what makes long-distance power lines possible.
A power line wastes energy as heat in proportion to the current squared, I²R. Sending the same power at ten times the voltage needs a tenth of the current, so it loses a hundredth as much. That is why transmission lines run at 400,000 V or more, and transformers step it down near your home to 230 V or 120 V, which is safer to use. For very long links and undersea cables, modern electronics can now convert power to high-voltage DC and back efficiently, so some of the longest lines use DC instead.
Other ways to carry charge
Moving electrons in a metal are only one way to carry a current:
- Ions carry current in liquids. In a battery's electrolyte, ions flow between the electrodes while electrons go round the outside circuit, as in Molecules and chemistry. Your nerves signal the same way, with sodium and potassium ions crossing the cell membrane, at up to 120 m/s.
- Plasmas carry current with both free electrons and ions, as in lightning and neon lights.
- Superconductors carry current with no resistance at all once they are cooled below a critical temperature. A current set flowing in a superconducting loop keeps flowing for years with no power supply. MRI scanners use coils of niobium-titanium wire cooled to 4 K with liquid helium to make their strong, steady magnetic fields.
Moving charge also makes magnetic fields, and changing magnetic fields push on charge, and those two effects together are how electric motors turn current into motion.