Module 14 · current electricity
Let the charges of Module 13 go and you have a current. This module is about what is actually moving inside a wire — which turns out to be far stranger and far slower than anyone expects — and about the handful of rules that will carry you through almost every circuit you meet, together with the places where those rules quietly stop working. It ends with the one that matters most: why a small current can kill you and a large voltage often cannot.
Current is the rate at which charge flows past a point: one ampere is one coulomb per second, which is about 6 × 10¹⁸ electrons going by every second. That much is bookkeeping. The interesting question is how fast each electron is going.
You flick a light switch and the bulb lights instantly. How fast is an individual electron travelling along the wire?
The picture to keep is a pipe already full of water. Push at one end and water comes out of the far end immediately — not because any molecule crossed the pipe, but because the pipe was already full. A wire is already full of free electrons, roughly one per copper atom, about 10²⁹ of them per cubic metre. Nudge them and the far end responds at once.
The picture stops there, though: in a real pipe the push travels along at the speed of sound in water, about 1,500 m/s, molecule shoving molecule. In a wire nothing is shoved along the line — the electric field arranges itself along the whole wire at nearly the speed of light. Take only the ‘already full’ part of the analogy with you.
So three quite different speeds live in the same wire, and confusing them is the standard mistake. The electrons' random jitter is about 1.6 million metres a second, going nowhere in particular — this is the Fermi speed, a quantum effect, and it barely changes when you heat the wire. Their drift along the wire is a fraction of a millimetre per second. The signal — the field itself establishing along the wire — moves at something close to the speed of light.
Conventional current is defined as flowing from + to −, which is the direction positive charge would move. In a metal wire the actual carriers are electrons, which are negative, so they go the other way. This is Benjamin Franklin's fault: in the 1750s he was the one who named the two kinds of charge positive and negative, and he had to guess which of the two was the one that actually moved. He guessed wrong, and by the time the electron was discovered in 1897 every textbook, instrument and convention in the world had been built on his choice. It is harmless: a flow of negative charge one way is electrically identical to a flow of positive charge the other. Still, worth remembering — a current arrow on a circuit diagram points the direction the electrons are not going.
As electrons drift along, they collide with the vibrating atoms of the metal and are knocked about, losing the speed the field gave them. That constant hindering is what we call resistance. The energy those collisions cost does not vanish: it ends up as heat in the wire. A kettle, a toaster and the filament of an old bulb are all resistance put there on purpose, in order to get exactly that heat.
For metals at a steady temperature, the current turns out to be simply proportional to the voltage across them:
How much resistance a particular piece of wire has depends on what it is made of and its shape:
Three quick words for the next bench. A battery's EMF is the energy it hands to each coulomb of charge, measured in volts. Its internal resistance is the small resistance of the battery's own chemical insides, which every coulomb has to cross on the way out. Its terminal voltage is what a meter across its two ends actually reads — and the last two sliders on Bench 2 are there to show you why the EMF and the terminal voltage are not the same number.
Your house wiring puts every appliance in parallel across the same 230 V. You switch on a second heater. The total resistance of the house and the total current drawn:
Everything at home is wired in parallel for two reasons. First, each appliance then gets very nearly the full 230 V whatever else is switched on — not exactly, for the reason in the next section, but close enough that the fan does not slow down when you put the kettle on. Second, switching one appliance off does not break the path for the others. Old Christmas-tree lights were in series, which is why one dead bulb killed the entire string.
A real battery is not a perfect source. Its chemistry gives it an EMF — the energy it supplies per coulomb — but the current also has to fight its way through the battery's own internals, so some of that energy is spent before it ever leaves. Write that internal resistance as a small r. The current I has to cross it too, and by V = IR that costs Ir volts. So what you measure across the terminals is always less than the EMF, by Ir, and the gap grows with the current drawn.
Slide the internal resistance up on the bench and watch the terminal voltage sag. This is why a battery too weak to turn a starter motor will still read a healthy voltage on a meter (which draws almost no current), why headlights dim when you crank an engine, and why a torch battery recovers a little if you let it rest.
The I²R form explains high-voltage transmission lines. Two different powers are in play here, so keep them apart. The power delivered to the town is P = VI, with V the voltage the line is run at. The power wasted as heat in the cable is I²R, where R is the cable's own resistance and the line voltage does not appear at all. To deliver a fixed P you may send a big I at a small V or a small I at a big V — and only the first roasts the cable. Step V up by a hundred and I falls by a hundred, so the waste falls by a hundred squared: ten thousand. That is the entire reason the tall steel transmission towers outside town carry 400,000 volts, and the reason transformers had to be invented before electricity could be sold at all. Module 17.
Every circuit so far settles instantly. Put a capacitor in one and it stops doing that: charge has to accumulate on the plates, and the resistor limits how fast it can arrive. The result is a circuit with a memory of how long it has been switched on — the first circuit in this course whose behaviour has to be drawn as a curve in time rather than settled with a single number.
At the first instant the capacitor is empty, so it puts up no opposition at all and the current is the largest it will ever be — a capacitor behaves like a plain wire the moment you connect it. As charge builds, its voltage grows and opposes the battery, so the current falls; and as the current falls, the charging slows further. The result is the exponential approach you see on the bench: fast at first, then a long lazy crawl, never quite arriving at the battery's own voltage. That is where the curve is headed — the capacitor stops taking charge only when its voltage exactly opposes the battery — and it is the battery that sets that destination, not the resistor.
You double the resistance in the charging circuit. The capacitor ends up:
What harms you is current, through a path, for long enough — and voltage is what sets that current once your body's impedance is fixed. At mains-frequency AC, roughly 1 mA through the body is just enough to feel, 10 mA makes muscles clamp so you cannot let go, and 100 mA through the chest can stop the heart; DC takes several times more current to reach each of those thresholds. How much current you get is V = IR again, with your own body as the resistor: I = V ÷ your resistance. That resistance is around 100,000 Ω if you measure it with a multimeter's few volts — but skin is not a resistor. Above about 50 V it breaks down, and at 230 V your hand-to-hand impedance collapses to roughly 1,000–2,000 Ω whether you are wet or dry. That is 100–200 mA: past the fibrillation threshold on the line above. Water does not create the danger, it only removes what little margin was left. This is why bathrooms have different wiring rules, and why a static spark of 20,000 volts from a car door is harmless — the voltage is enormous, but the duration is a microsecond and the charge is tiny, so almost no current has time to flow.
Find the power rating on three things in your house — a phone charger, a kettle, an LED bulb — and divide each by 230 V to get the current it draws. A 2 kW kettle pulls nearly 9 A; a 7 W bulb pulls 0.03 A. Now find the current rating stamped on the wall sockets — Indian sockets are marked 6 A or 16 A — and work out which of the three must go into the 16 A one. Then multiply the kettle's power by the hours it runs in a month, and check the result against the electricity bill: the unit on the bill, the kilowatt-hour, is just power × time, and it is 3.6 million joules.
1. Two identical bulbs are connected in series to a battery, then rewired in parallel across the same battery. In parallel they are:
2. A power station must deliver 1 MW to a town. Doubling the transmission voltage changes the heat wasted in the cables by a factor of:
3. A capacitor is charged through a resistor, with τ = 2 s. How charged is it after 6 seconds?