Charge and Current

Switch on a lamp and it lights at once. Something must be streaming round the wires the instant the switch closes — and that something has a name. Deep inside every metal wire sits a vast crowd of tiny particles called electrons, each carrying a scrap of electric charge. Ordinarily they jostle about at random and go nowhere. Connect a battery, and its push nudges the whole crowd to drift the same way round the loop. That organised drift of charge is an electric current — and it is what makes a bulb glow, a motor spin and a phone charge.

You already know a circuit only works when charge can flow round an unbroken loop. This page asks the next, sharper question: how much charge, and how fast? Getting those two ideas straight — the amount of charge and the rate it flows — is the key that unlocks the rest of electricity.

Charge, measured in coulombs

Charge is the "stuff" that flows. We give it the symbol Q and measure it in coulombs, written \text{C}. A coulomb is simply a fixed quantity of charge — a certain size of crowd — in the same way a litre is a fixed quantity of water. It happens to be a colossal number of electrons (about six million million million of them), but you never count electrons in a lab; you just talk in coulombs.

So charge answers the question "how much?". Two coulombs is twice as much charge as one coulomb — twice the crowd shuffled past. On its own, though, charge says nothing about speed: a coulomb dribbling past over an hour and a coulomb sweeping past in a flash are the same amount of charge but feel utterly different. To capture the difference, we need the idea of current.

Current is the rate of flow of charge

Current tells you how fast the charge is flowing — how much charge slides past a point each second. We give current the symbol I and measure it in amperes (or amps), written \text{A}.

The link to charge is beautifully simple. If a steady current I flows for a time t, the total charge that has passed is current multiplied by time:

Q = I\,t.

Read it aloud — "charge equals current times time". Turn it round and it defines what a current actually is: I = \dfrac{Q}{t}, the charge per second. And that gives the amp its plain-English meaning:

1\ \text{A} = 1\ \text{coulomb per second} = 1\ \tfrac{\text{C}}{\text{s}}.

A current of 3 A means three coulombs of charge march past every single second. Double the current and twice as much charge streams past in the same time; run it for twice as long and, again, twice the charge flows. Current is a rate; charge is the amount that rate builds up to.

Charge Q (coulombs, \text{C}) is the amount of electric charge that flows.
Current I (amperes, \text{A}) is the rate of flow of charge, and one amp is one coulomb per second.
They are linked by Q = I\,t, which rearranges to I = \dfrac{Q}{t} and t = \dfrac{Q}{I}.

Worked examples

The whole triangle Q = I\,t is really one relationship read three ways. Cover the quantity you want and the equation tells you what to do with the other two.

Example 1 — find the charge. A current of 4\ \text{A} flows through a lamp for 10\ \text{s}. How much charge passes through it?

Q = I\,t = 4\ \text{A} \times 10\ \text{s} = 40\ \text{C}.

Forty coulombs of charge have flowed through the lamp.

Example 2 — find the current. A charger pushes 60\ \text{C} of charge through a phone in 30\ \text{s}. What is the current?

I = \frac{Q}{t} = \frac{60\ \text{C}}{30\ \text{s}} = 2\ \text{A}.

Two coulombs pass every second, so the current is 2 A.

Example 3 — find the time. How long must a steady current of 5\ \text{A} flow to deliver 200\ \text{C} of charge?

t = \frac{Q}{I} = \frac{200\ \text{C}}{5\ \text{A}} = 40\ \text{s}.

Notice the units look after themselves: coulombs divided by amps (coulombs per second) leaves seconds. If your units don't tidy up like this, you've used the triangle the wrong way round.

See it flow: build up the charge

Here is a single loop with a battery at the bottom and charges drifting round it. Turn up the current slider and the loop fills with more charges sweeping past each second — a bigger current is a faster, heavier flow. Turn up the time slider and watch the running total: the charge Q = I \times t that has flowed past a point keeps climbing, because a steady stream simply adds up as the seconds tick by.

Two things to spot. First, the charges are spread all the way round the loop — the same current flows at every point, which is our next big idea. Second, at a fixed current, doubling the time doubles Q; at a fixed time, doubling the current also doubles Q. That is exactly what Q = I\,t says.

Same current all the way round

In a single loop — a series circuit — the current is the same at every point. Whatever streams out of the battery streams through the bulb and back in again, unchanged. The charge is not used up on the way round, and it does not pile up anywhere: for every electron that squeezes into the bulb, one squeezes out the far side at the same instant.

Think of a bicycle chain, or water in a full central-heating loop: push the chain at one place and the whole chain moves together at one speed. There is no "before" side that is faster and "after" side that is slower. So if an ammeter reads 2 A just after the battery, it reads 2 A just before it, and 2 A on either side of the bulb — everywhere on that single loop.

We measure current with an ammeter, and because it must count the charge actually passing through, it is wired in series — dropped straight into the loop so the whole current flows through it. (A voltmeter, which you will meet later, does the opposite job and goes across a component instead.)

A charming historical muddle. Long before anyone knew electrons existed, scientists guessed that current flowed out of the + terminal of a battery, round the circuit, and back into the − terminal. They drew all their diagrams that way, and this is still called conventional current: from plus to minus in the outside wires.

Then electrons were discovered — and it turned out the actual moving charges in a metal are negative, so they drift the opposite way, from minus to plus. Too late! Every book, rule and arrow already used the old direction. So we keep two pictures: conventional current (+ → −, the one on all the diagrams and the arrow in the animation above) and electron flow (− → +, what the electrons truly do). For GCSE, arrows show conventional current — just remember the electrons are quietly going the other way.

The classic trap is to muddle up charge and current, or to imagine the current getting "used up." Keep these straight:

Current is a flow, not a stuff. Charge (in coulombs) is the amount that flows; current (in amps) is how fast it flows. Amps measure a rate, not an amount — just as "litres per second" is not the same thing as "litres."
Current is not "used up" as it goes round. In a series loop the current is the same before and after the bulb. The bulb takes energy from the charge, but not the charge itself — the very same charge carries on round to the battery.
The bulb does not "eat" current, so it isn't weaker on the way back. A common wrong picture has more current leaving the battery than returning. Not so: what goes out comes back, coulomb for coulomb.