S4.12.1 Chapter 1

Charge and current

Amina presses the switch of a torch and the lamp lights at once. What is moving in the wires, and how can we count it?

Your guess

Pick one before you read on. It is fine to be wrong.

Your guess

A Tiny particles that were already in the wire all start to move together.
You picked A. Read on. At the end, the chapter comes back to your guess.
B One electron races from the cell to the lamp, faster than light.
You picked B. Read on. At the end, the chapter comes back to your guess.
C The lamp uses up something from the wire, so less comes back to the cell.
You picked C. Read on. At the end, the chapter comes back to your guess.
D Light runs along the wire from the cell to the lamp.
You picked D. Read on. At the end, the chapter comes back to your guess.

By the end you can

Calculate charge from current and time
Explain current in metals as a flow of electrons

Press a torch switch and the lamp lights at once, even when the wires are long. So something must already be in the wire, ready to move. That something is electric charge.

Some particles carry charge. An electron carries a negative charge. A metal is made of atoms packed together. Each atom keeps most of its electrons, but one or two are loose. These free electrons wander between the atoms. The rest of each atom is a positive ion, and it stays in its place.

Inside a metal wire. The ions stay still. The free electrons move. The dashed line is an imagined cut across the wire.

With no cell joined, the free electrons wander in every direction, so nothing flows along the wire. Join a cell, and its push acts on every free electron at once. All of them now drift the same way along the wire. A flow of charge is an electric current.

The drift is slow. In an ordinary copper wire carrying 1 A, the electrons move at well under 1 mm each second. The lamp lights at once because the wire is already full of electrons. The cell pushes one end, and all the electrons start to move together, like beads in a full tube.

To count a current, count the charge that passes. Charge is measured in coulombs, written C. Current is the charge that passes a point each second. It is measured in amperes, called amps for short and written A. A current of 1 A means that 1 C of charge passes each second.

See it three ways

As a picture

In words

Current is the charge that passes each second. A bigger current means more charge each second.

In symbols

I = Q ÷ t. Charge Q is in C, time t is in s and current I is in A. So 1 A = 1 C ÷ 1 s.

A steady current gives the same charge every second. After 2 s, twice as much has passed. After 3 s, three times as much. So a graph of charge against time is a straight line through the origin. Look at a current of 2 A.

Draw it first

Charge against time for a steady current

1 Draw the line. A current of 2 A passes 2 C each second, so the line climbs 2 C for every 1 s.
2 At 3 s the line is at 6 C. The charge is the current times the time: 2 A × 3 s = 6 C.
3 At 5 s the line is at 10 C. The steeper the line, the bigger the current. The gradient of the line is the current.

Turn the equation round to find the charge: Q = It. Charge in coulombs is current in amps times time in seconds. The units agree: A × s = (C ÷ s) × s = C. You can also find the time: t = Q ÷ I.

The lamp loop of the next worked example. The ammeter reads 0.5 A.

Worked example

The ammeter in the loop reads 0.5 A. How much charge passes through the lamp in 20 s?

Write the equation: Q = It.
Put in the numbers: Q = 0.5 A × 20 s.
Q = 10 C.

Answer: 10 C

Worked example

A steady current of 0.4 A flows through a lamp. How long does it take 72 C of charge to pass through it? Give the time in minutes.

We want the time. Turn Q = It round to t = Q ÷ I.
Put in the numbers: t = 72 C ÷ 0.4 A = 180 s.
Change to minutes: 180 s ÷ 60 = 3 min.

Answer: 3 min

Before you put numbers in, change them to the base units: amps and seconds. A milliamp, mA, is one thousandth of an amp, so 1 mA = 0.001 A. A minute is 60 s. Skip this step and the answer is wrong by a factor of 1 000 or 60.

Worked example

A phone charger gives 250 mA for 3 minutes. How much charge passes through it?

Change the current to amps: 250 mA = 250 ÷ 1 000 = 0.25 A.
Change the time to seconds: 3 min = 3 × 60 = 180 s.
Put in the numbers: Q = 0.25 A × 180 s.
Q = 45 C.

Answer: 45 C

How big is a coulomb? One electron carries a charge of only 1.6 × 10⁻¹⁹ C. So 1 C is the charge of about 6.25 × 10¹⁸ electrons. That is about 6 million million million electrons. A small current moves a huge number of them.

Now the direction. Early scientists guessed that current was a flow of positive charge from the + end of a cell round to the − end. Later we found that the moving charges in a metal are electrons, and they go the other way. The old rule stayed. Conventional current is drawn from + round to −. Every rule and equation in this book uses it.

Conventional current leaves the + end of the battery and goes round to the − end.

The electrons go the other way, from the − end round to the + end. The same loop, the same lamp.

An ammeter measures the current. It goes in the loop, one part after another, which is called being in series. That way all the charge that goes round passes through it.

One ammeter on each side of the lamp. Both read 0.3 A. The lamp does not use up the current.

The current is the same everywhere in a loop with one path. The lamp does not use up charge. What the lamp changes is energy. The cell gives energy to the charges, and the lamp transfers it to its surroundings as heat and light. The next chapter shows how to measure that.

Try it

A tube of peas

You need: a clear plastic tube or a long drinking straw, about 30 cm, dried peas, lentils or small beads that just slide inside it, a thin stick or a pencil.

Be safe: Dried peas and beads are a choking danger. Keep them away from young children, and never put them in the mouth. Do this on a table, and pick up every pea afterwards.

Fill the tube with peas, so that they touch in a row from one end to the other.
Hold the tube level. Push one more pea into the left end with the stick.
Watch the right end. Notice how soon a pea comes out.
Now take out most of the peas and leave only two, far apart. Push one in at the left end and watch again.

What you will see: With a full tube, a pea falls out of the right end at the moment you push at the left. Each pea moved only a little. The push went along the whole row at once. A full wire of free electrons does the same, so the lamp lights at once.

If you cannot try it, this is what happens.

A wrong idea many people have

The lamp uses up the current, so less current comes back to the cell.

Why it feels right: The lamp gives out heat and light, so it seems to take something away. A battery goes flat, so it seems that something is used up.

The test that breaks it: Put an ammeter on each side of the lamp, as in the picture. Both read 0.3 A. If the lamp used up current, the second would read less.

What is true: Current is not used up. The same charge flows out of the lamp as flows in. The lamp changes energy: it takes energy from the charges and gives out heat and light.

A wrong idea many people have

The lamp lights at once because electrons race along the wire at the speed of light.

Why it feels right: Light and electricity both seem instant. Pictures often show an electron dashing round the loop.

The test that breaks it: Work out the drift speed. In a copper wire carrying 1 A, the electrons drift well under 1 mm each second. A 1 m wire would take hours for one electron. The lamp does not wait for that.

What is true: The wire is already full of free electrons. The push of the cell moves all of them together, so the current starts everywhere at once. Each electron drifts slowly.

A wrong idea many people have

Electrons flow from the + end of the cell to the − end, the same way as the arrows in a circuit drawing.

Why it feels right: We draw the current arrow from + to −, and we tend to think the moving things follow the arrow.

The test that breaks it: An electron has a negative charge. Opposite charges attract, so the + end of the cell pulls electrons towards it and the − end pushes them away. Look at the second loop picture.

What is true: Electrons move from the − end round to the + end. The arrows we draw show conventional current, which goes the other way. The maths gives the same answers either way.

Key words

charge: a property of some particles. It makes them feel electric forces. It is measured in coulombs.
electron: a tiny particle with a negative charge. Free electrons in a metal carry the current.
current: the flow of charge. It is the charge that passes a point each second. Its symbol is I.
coulombs: the unit of charge, written C.
amperes: the unit of current, written A. One ampere is one coulomb each second.
conventional current: current drawn from the + end of a cell round to the − end. The electrons go the other way.
ammeter: a meter that measures current. It goes in the loop, in series.
milliamp: one thousandth of an amp, written mA.

Back to your guess

The answer is A: Tiny particles that were already in the wire all start to move together.

A metal wire is full of free electrons. The cell pushes all of them along together, so the lamp lights at once. They drift slowly, and none is used up: the same charge passes every point of the loop each second.

Keep it

Copy this into your exercise book.

Current is charge each second. I = Q ÷ t, so Q = It. Charge in C, current in A, time in s. Conventional current goes + to −. Electrons go − to +. Current is not used up.

Draw: A loop with a battery, a lamp and an ammeter. Draw the current arrow from + round to −, and a second arrow for the electrons the other way. Write Q = It.