Potentials on the wires

1. A potential difference is always measured between two points, so a single value quoted for one mains wire means the potential difference between that wire and the earth.
2. The earth is taken as the zero of potential, so earth potential is $0V$ and every other mains value is quoted relative to it.
3. The live wire is at an alternating potential of about $230V$ relative to earth, swinging one way and then the other $50$ times each second.
4. The neutral wire stays close to $0V$, because it is connected to the earth at the local substation.
5. The earth wire is at $0V$, since it is joined directly to the ground through a buried metal rod or through the earth conductor of the supply cable.
6. The potential difference across a working appliance is the difference between the two supply wires, about $230V-0V=230V$, and it is this potential difference that drives the current through the appliance.
7. Because the neutral and earth wires both sit near $0V$, there is almost no potential difference between them and a person standing on the ground, which is why the danger lies in the live wire.

Getting a shock

1. A person standing on the ground is in electrical contact with the earth, so their body sits at about $0V$.
2. If that person touches the live wire, the point of contact is raised to about $230V$ while their feet remain at $0V$.
3. A potential difference of about $230V$ therefore acts across the body, from the hand to the feet.
4. The human body is an electrical conductor, because body fluids contain dissolved ions that are free to move, so charge can pass through it.
5. That potential difference drives a current through the person and on into the ground, and this current through the body is an electric shock.
6. The size of the current follows from $I=\frac{V}{R}$, where $V$ is about $230V$ and $R$ is the total resistance of the whole path, including the skin at both points of contact.
7. It is the current that does the damage. It interferes with the electrical signals that control the heart and the muscles, and it dissipates energy in the tissue, which causes burns where the resistance is greatest.
8. A current whose path crosses the chest is the most dangerous of all, because it passes through the heart.

What makes a shock worse

1. Damp or sweaty skin lowers the resistance of the contact, because water carrying dissolved salts conducts far better than dry skin.
2. A smaller resistance gives a larger current for the same $230V$, from $I=\frac{V}{R}$, so wet hands can turn a survivable shock into a fatal one.
3. Bare feet on a damp floor make a good connection to the earth, which lowers the resistance of the return part of the path and raises the current again.
4. Dry shoes with rubber soles put a large resistance in series with the body, so the current driven by the same potential difference is much smaller.
5. A large area of contact, such as gripping a live conductor in the whole hand, gives a lower resistance than a brief touch with one fingertip.
6. The longer the contact lasts, the more energy is transferred into the body, which is why a protective device that cuts off the supply quickly reduces the harm done.
7. For these reasons mains sockets are not fitted in bathrooms, the supply is switched off at the consumer unit before any wiring is worked on, and an appliance is unplugged before it is opened.

Live wire when switched off

1. Switching an appliance off opens its switch, which puts a gap in the circuit so that no charge can flow round the loop.
2. Breaking the circuit stops the current, but it does not change the potential of the live wire on the supply side of the switch.
3. That length of live wire is still joined through the socket and the house wiring back to the substation, so it stays at about $230V$ relative to earth.
4. Anyone who touches it while standing on the ground still has about $230V$ across them, so a current is driven through them to earth and they receive a shock.
5. The current can flow because the person completes a new circuit from the live wire through their body to the earth, and that new path does not pass through the appliance's switch at all.
6. The appliance is only made safe by unplugging it, or by switching off the whole circuit at the consumer unit so that the house wiring is isolated from the supply.
7. A lamp with a broken switch or a damaged flex is dangerous for the same reason, because the live conductor inside it remains at about $230V$ whether the lamp is lit or not.

Short circuits

1. A short circuit is an unintended connection of very low resistance that lets charge bypass the path it was meant to follow.
2. It happens when the insulation between the live and neutral cores wears through, when a cable is crushed or pierced by a nail, or when water bridges two terminals.
3. The current then no longer passes through the appliance, so nearly all of the resistance is taken out of the circuit and only the small resistance of the wires is left.
4. From $I=\frac{V}{R}$, the same $230V$ across a very small resistance drives an extremely large current.
5. The rate at which energy is dissipated in that wire is $P=I^{2}R$, and because the current is squared, an enormous power is transferred in the cable even though its resistance is small.
6. The cable heats up within a fraction of a second, the insulation softens and melts, and the cable or the material around it can catch fire.
7. The very large current is also what makes the protective device act, since it melts the fuse or trips the circuit breaker in the live wire and disconnects the supply before the cable is destroyed.

Birds on overhead lines

1. A bird perched on a single overhead line is touching only one conductor.
2. Both feet rest on the same wire, and the short length of thick wire between them has an extremely small resistance, so there is almost no potential difference between one foot and the other.
3. With almost no potential difference across it, almost no current is driven through the bird, so it is unharmed even on a line at a very high potential.
4. The bird is also not connected to the earth, so there is no complete path from the line to any point at $0V$.
5. If the bird touched a second line, or an earthed pylon, at the same time, a large potential difference would appear across it and a large current would flow through it.
6. The contrast with a person is the connection to earth: standing on the ground holds the feet at $0V$, so touching a live conductor puts the whole supply potential difference across the body.