Electricity and Circuits

Everything is made of atoms, and atoms contain protons, which carry a positive charge, and electrons, which carry a negative charge of exactly the same size. That size is the elementary charge, e = 1.602 × 10⁻¹⁹ C. An atom with as many electrons as protons is neutral: the charges cancel.

Charges of the same sign repel. Opposite charges attract. When you rub a balloon on a wool sweater, some electrons move from the wool to the balloon. The balloon ends up negative and the wool ends up equally positive. Protons stay put: they are locked in the atoms' nuclei.

Total charge before = total charge after

This is the law of conservation of charge. Rubbing, touching or chemistry can move charge from one object to another, but never create or destroy it overall.

Conductors, like copper, aluminum and other metals, have electrons that are free to move through the material. That's why wires are made of metal. Insulators, like plastic, rubber, glass and dry air, hold their electrons tightly, which is why wires are wrapped in plastic. (Pure water is a poor conductor, but tap water and the water on wet skin contain dissolved salts and conduct well enough to be dangerous.)

Static electricity is charge that builds up on an object and stays put. It builds up on insulators because the charge can't easily flow away. The spark when you touch a door handle after shuffling across a carpet is that charge suddenly jumping to a conductor. A charged balloon even sticks to a neutral wall: its negative charge pushes the wall's electrons slightly away, leaving the nearby surface slightly positive, and the attraction wins.

How strong is the push or pull between two charges? In 1785 the French engineer Charles-Augustin de Coulomb measured it with a delicate torsion balance, a twisting fiber that showed tiny forces. The result is Coulomb's law:

F = k q₁q₂ ÷ r²

Here q₁ and q₂ are the two charges in coulombs, r is the distance between them in meters, and k ≈ 8.99 × 10⁹ N·m²/C² is Coulomb's constant.

• Bigger charges, bigger force. Double one charge and the force doubles.
• Inverse square. Double the distance and the force drops to one quarter, just like gravity in Newton's law of gravitation.
• Direction. Like charges push apart; unlike charges pull together. The forces on the two charges are equal and opposite (Newton's third law).

That value of k is enormous, so a whole coulomb is a huge amount of static charge. Everyday static charges are usually measured in microcoulombs (µC, millionths of a coulomb) or less.

When charge flows, we have an electric current. Current I is the amount of charge Q that passes a point in a time t:

I = Q ÷ t

One ampere is one coulomb per second, which is about 6.24 × 10¹⁸ electrons every second. Current can only flow around a closed loop. Open a switch anywhere in the loop and the current stops everywhere in that loop.

Which way does it flow? By long-standing convention, conventional current flows out of the positive (+) terminal of a battery, around the circuit, and back into the negative (−) terminal. In a metal wire, though, the charges that actually move are electrons, and they drift the opposite way, from − to +. Both descriptions give the same answers. The convention is older than the discovery of the electron: Benjamin Franklin picked which kind of charge to call "positive" in the 1740s, and the electron wasn't identified until 1897. Physics and engineering use conventional current, and so does this page.

Slow drift, fast signal. Electrons in a wire wander randomly and drift along very slowly, typically around a tenth of a millimeter per second. A light still comes on the instant you flip the switch, because the wire is already full of electrons. The push travels through them at a large fraction of the speed of light, like water coming out of the end of a hose that is already full.

Circuit diagrams use standard symbols so anyone can read them. The ones on this page are shown on the right. A few things to notice:

• In a cell, the long thin line is the positive terminal and the short thick line is negative. A battery is two or more cells joined together, though people often call a single cell a battery too.
• A resistor is drawn as a zigzag in the US. Many other countries draw a small rectangle.
• Wires are drawn as straight lines with square corners. The length of a wire on a diagram doesn't matter: what matters is what it connects.

A battery doesn't supply charge: the charge is already in the wires. What a battery supplies is energy. Chemical reactions inside it give energy to each coulomb of charge that passes through, and that charge gives the energy up in the lamp, the motor or the speaker as it goes around the circuit.

Voltage, or potential difference, is the energy W transferred per unit of charge Q between two points:

V = W ÷ Q

So a 9 V battery gives each coulomb 9 joules of energy, and a 1.5 V cell gives each coulomb 1.5 J. Voltage is always measured between two points, which is why it is called a difference.

• An ammeter measures current. It goes in series, in the loop, so the current flows through it.
• A voltmeter measures voltage. It goes in parallel, across the part you're measuring, with one lead on each side.

A helpful picture: think of a closed loop of water pipe. The battery is a pump that raises the pressure, the current is the flow of water, and a narrow section of pipe is a resistor. Like every analogy it has limits, but it shows why the current is the same all around a single loop.

Push the same voltage across different objects and you get different currents. A thick copper wire lets a big current through; a lamp filament or a resistor lets much less through. Resistance R measures how strongly something opposes the current:

V = IR

Rearranged, I = V ÷ R and R = V ÷ I. This is Ohm's law, named after Georg Ohm, who published it in 1827. More voltage means more current; more resistance means less.

A wire's resistance depends on four things:

• Material: copper and silver are excellent conductors; nichrome, used in toasters and heaters, resists much more.
• Length: a longer wire has more resistance.
• Thickness: a thicker wire has less resistance, which is why heavy-duty cables are thick.
• Temperature: most metals resist more when they are hot.

Parts that follow V = IR with a fixed R are called ohmic: their current–voltage graph is a straight line through the origin. A lamp filament is not ohmic. As more current flows, it heats up to thousands of degrees and its resistance rises, so its graph curves over. R = V ÷ I still gives its resistance at any one moment.

In a series circuit, the parts are connected one after another in a single loop. There is only one path, so:

• The current is the same everywhere. Every coulomb that leaves the battery passes through every part in turn.
• The voltages add up to the battery voltage: V = V₁ + V₂ + … Each part takes its share of the energy.
• The resistances add up:

R_total = R₁ + R₂ + R₃ + …

Because V = IR and I is the same for each part, the part with the largest resistance takes the largest share of the voltage. Adding another lamp in series raises the total resistance, so the current drops and all the lamps get dimmer.

Series circuits have a big weakness: if one part breaks, the loop is open and everything stops. That's what happened with older strings of holiday lights, where one dead bulb could leave the whole string dark.

In a parallel circuit, each part is on its own branch, connected directly across the battery. The current splits at a junction and joins up again afterwards. So:

• Every branch gets the full battery voltage. V = V₁ = V₂ = …
• The branch currents add up to the total: I = I₁ + I₂ + … No charge is lost at a junction.
• The equivalent resistance comes from adding the reciprocals:

1 ÷ R_eq = 1 ÷ R₁ + 1 ÷ R₂ + …

For just two resistors there's a shortcut: R_eq = R₁R₂ ÷ (R₁ + R₂), "product over sum." The equivalent resistance is always smaller than the smallest branch, because every new branch is one more path for the current.

Homes are wired in parallel. Each lamp and appliance gets the full outlet voltage and can be switched on or off without affecting the others. But every appliance you switch on adds another branch, so the total current in the circuit goes up. Plug in too many and the wires could overheat, which is exactly what fuses and breakers are there to prevent (Idea 9).

It is current through the body that harms people, and Ohm's law explains why voltage and wet skin matter: the current is I = V ÷ R. Dry skin has a fairly high resistance, but wet skin has much less, so the same voltage can drive a far bigger, more dangerous current. That's why water and electricity are such a deadly mix.

Homes have three main protections:

• Fuses contain a thin strip of metal that melts and breaks the circuit if the current gets too big. A blown fuse must be replaced, and never with one of a higher rating.
• Circuit breakers do the same job with an automatic switch that "trips" open when the current is too large. After you fix the cause, you can reset it. Both fuses and breakers go on the hot wire, in series with the circuit they protect. They mainly protect the wiring from overheating and starting a fire.
• Grounding (called earthing in some countries): the third, round prong on a plug connects an appliance's metal case to the ground wire. If a loose hot wire touches the case, the fault current rushes through the ground wire instead of through you, and the breaker trips.

Kitchens and bathrooms in the US also use GFCI outlets (ground-fault circuit interrupters), the ones with Test and Reset buttons. They compare the current going out on the hot wire with the current coming back on the neutral. If more than about 5 mA is missing, which might be going through a person, they cut the power in a fraction of a second.

In the 1740s, electricity was a parlor wonder: glass tubes rubbed with silk, sparks, and "Leyden jars" that stored charge and gave nasty shocks. In Philadelphia, Benjamin Franklin (1706–1790) experimented with them. In a letter to the English merchant Peter Collinson dated 25 May 1747, he described objects as electrified "positively" or "negatively," "plus" or "minus," and argued that the electrical "fire" is never destroyed, only moved. Those are the signs we still use, and the idea is an early form of conservation of charge.

In 1785 Charles-Augustin de Coulomb used his torsion balance to show that the electric force follows an inverse-square law.

All of this was static electricity. A steady current needed something new. In a letter to Sir Joseph Banks of the Royal Society, dated 20 March 1800, the Italian physicist Alessandro Volta (1745–1827) described a stack of copper (or silver) and zinc discs, separated by pieces of cardboard or cloth soaked in salt water. His "pile" gave a continuous flow of electricity without being charged first. It was the first electric battery, and within months other scientists had used one to split water into hydrogen and oxygen. The unit of voltage, the volt, is named after him.

With steady currents to work with, the German schoolteacher Georg Simon Ohm (1789–1854) carefully measured how the current in a circuit depended on the wire and the source. He published his results in 1827 as Die galvanische Kette, mathematisch bearbeitet (The Galvanic Circuit Investigated Mathematically). The book got a cool reception at first, but recognition came, including the Royal Society's Copley Medal in 1841. The unit of resistance is the ohm. (Henry Cavendish had found the same relationship decades earlier, but never published it; his notes only became known in 1879.)