Voltage Does Not Flow

Across and through

Voltage is a difference in electric potential between two points: the energy transferred per coulomb of charge moved from one to the other. That is why a voltmeter has two probes and why "the voltage at this wire" is an incomplete sentence until you say what it is measured against.

Current is the rate at which charge passes through a cross-section. It is a flow; voltage is not. Nothing physically travels as voltage.

Getting this straight fixes a surprising amount at once, because almost every other error on this page is a version of it.

Current is not used up

Put two identical bulbs in series and both glow equally brightly. An ammeter before a lamp and an ammeter after it read the same. Charge is conserved and, in a single loop, it has nowhere else to go: every electron entering the filament leaves it.

What the lamp uses is energy. Charges arrive carrying electrical potential energy and leave with less, and that loss per coulomb is precisely the potential difference across the lamp — which is why a working component always has a voltage drop across it.

So the conserved thing and the consumed thing are different quantities. Current is conserved through the loop; energy is transferred out of it.

Current harms you, not voltage on its own

Scuffing across a carpet can charge you to twenty thousand volts, and the spark is startling but harmless. The 230 volts in a wall socket can kill. If voltage alone were the danger, this would make no sense.

Damage comes from current through the body — roughly ten to a hundred milliamps across the chest is the dangerous range — together with the path it takes and how long it lasts. Static electricity holds a minute amount of charge and dumps it in microseconds; mains can push tens of milliamps through you for as long as you are holding on.

Voltage matters because, with the resistance of your body and the contact, it sets that current. Wet skin can drop contact resistance by a factor of a hundred, which is why the same voltage is far more dangerous in a bathroom.

The bird on a bare 100,000-volt transmission line is the clean demonstration. Both feet sit on the same conductor, so the potential difference across the bird is almost nothing and almost no current flows through it. The absolute potential of the wire is irrelevant; the line carries hundreds of amps the whole time.

Electrons crawl, the signal does not

In a copper wire carrying a few amps, the average drift speed of the conduction electrons is around a tenth of a millimetre per second. It follows from I = nAvq and the sheer density of free electrons in a metal, about 10²⁹ per cubic metre. At that speed a single electron needs roughly ten thousand seconds — nearly three hours — to travel one metre of wire.

The lamp still lights instantly, because nothing waits for an individual electron to make the trip. Closing the switch establishes the electric field along the circuit at a large fraction of the speed of light, and the wire is already packed with mobile charges everywhere, including inside the filament. They all start drifting at once.

Two speeds, three orders of magnitude apart in opposite directions: the drift is glacial, the signal is nearly instantaneous, and the random thermal motion of the same electrons is faster than either.

A battery sets the voltage; the circuit sets the current

Connect a 9-volt battery to 90 ohms and it delivers 0.1 amps. Connect it to 900 ohms and it delivers 0.01 amps. The terminal voltage stayed near 9 volts in both cases while the current changed by a factor of ten.

A battery is a source of EMF with a small internal resistance, not a reservoir of current waiting to be handed out. Current cannot be stored in the first place — it is a rate of flow, not a substance.

The same idea explains short circuits: with almost no external resistance, the current is limited mainly by the battery’s internal resistance, which is why the wire and the battery get dangerously hot.

Parallel does not share out a fixed current

Add a second identical bulb in parallel across the same battery and the first bulb barely changes brightness. Each bulb still has the full battery voltage across it, so each still draws the same current as before, and the battery now supplies roughly twice as much in total.

The total resistance of the circuit went down, not up, because there are now two paths where there was one.

The intuition that the first bulb must dim is the constant-current battery again: a fixed ration of amps to be divided among whoever shows up. There is no such ration. The battery holds the voltage; the resistances decide how much current results.