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4. Volume 01

1.1 Charge and current

A current is charge on the move: the amount of charge that passes a point each second. The same current flows all the way round a loop, and none of it is used up.

Charge

Every atom holds tiny particles called electrons. Each one carries a small negative charge. In a metal, some electrons are free to wander between the atoms, and that is why metals conduct.

Charge is measured in coulombs (C). One electron's charge is so small that a coulomb is a huge crowd of them. Pushed through a wire at one coulomb per second, the crowd looks like this:

1 A carries 6.24 x 10^18 electrons past a point every second

That is about six billion billion electrons each second.

Current is charge per second

A current of one ampere (1 A) means one coulomb passing a point every second. Two coulombs a second is 2 A. In symbols, with I for current, Q for charge and t for time in seconds:

I = Q / t

Q = 2 C, t = 4 s: I = Q / t = 500 mA
Q = 30 C, t = 10 s: I = Q / t = 3 A
Q = 1 C, t = 1000 s: I = Q / t = 1 mA

Which way does current flow?

Schematics draw current flowing out of the battery's + end, round the loop and into its - end. That is conventional current. It was named before anyone knew about electrons.

Electrons are negative, so they actually drift the other way, from - to +. It makes no difference to any sum. Every formula and every datasheet uses conventional current, and so does this course.

Slow electrons, instant current

The electrons themselves drift surprisingly slowly:

1 A in a copper wire of 1 mm²: the electrons drift about 0.073 mm per second

Yet a lamp lights the instant you close the switch. The wire is already full of electrons. When the push starts, they all start moving together, all the way round the loop at once.

The same current all the way round

An ammeter measures current. Here are two of them in one loop: one before the resistor, and one after the lamp.

circuit loop-current: A1 reads 50 mA, A2 reads 50 mA

The two readings are equal. The resistor and the lamp take energy from the charge as it passes, but every coulomb that goes in comes out again. Current is never used up.

DC and AC

A battery pushes current one way only. That is direct current (DC). The mains supply pushes it one way and then the other, many times a second. That is alternating current (AC). Almost all electronics runs on DC, and so does this course. Volume 04 shows how AC is turned into DC.

1.2 Voltage

Voltage is the energy each coulomb of charge carries: one volt is one joule of energy per coulomb. It is always measured between two points.

Energy per charge

A battery gives energy to the charge it pushes out. Its voltage says how much energy each coulomb gets: a 9 V battery gives every coulomb 9 joules. Energy is measured in joules (J).

As the charge goes round, it hands that energy on. A lamp turns it into light and heat. A resistor turns it into heat. When the charge gets back to the battery, it has given all its energy away, and the battery gives it more.

energy = charge x voltage: 2 C x 9 V = 18 J

Always between two points

A voltage is a difference, like the height of a hill. A hill is not "100 metres high" on its own: it is 100 metres above something, such as the sea. In the same way, a point in a circuit is not "5 V" on its own. It is 5 V above some other point.

So circuits choose one point to call 0 V, and measure every other voltage from it. That point is called ground, drawn as a small stack of lines. When a lesson says "the voltage at a point", it means the voltage between that point and ground.

Cells in series

A single chemical cell makes a fixed voltage - 1.5 V for an ordinary AA cell. Stack cells end to end, + to -, and their voltages add:

circuit two-cells: 1.5 V + 1.5 V = 3 V across the lamp; lamp current 200 mA
the point between the cells is at 1.5 V; the top wire is at 3 V

That is how most batteries are made inside. A rectangular 9 V battery holds six small cells:

6 cells of 1.5 V in series: 9 V

Voltages you will meet

Chips run at low voltages too. Many use 3.3 V for their pins and less than 1 V deep inside. Volume 06 shows how a chip turns those voltages into 0s and 1s.

1.3 Resistance and resistors

Resistance is how hard a part makes it for current to flow, measured in ohms (Ω). A resistor is a component made to have one known resistance, so a designer can set exactly how much current flows.

What decides a resistance

A conductor such as copper has little resistance. An insulator such as plastic has so much that almost no current flows. Between them, three things decide the resistance of a piece of material:

1. The material. Each material has its own resistivity. Copper's is very low; nichrome, used in heaters, is much higher.
2. The length. A wire twice as long has twice the resistance.
3. The thickness. A wire with twice the cross-section area has half the resistance.

R = resistivity x length / area

Here is copper, with a resistivity of about 1.68 × 10^-8 ohm metres. The areas are in square millimetres (mm²):

1 m of 0.5 mm² copper: 33.6 mΩ
100 m of 0.5 mm² copper: 3.36 Ω
1 m of 0.05 mm² copper: 336 mΩ

A metre of ordinary wire has only a few hundredths of an ohm. That is why circuits treat wires as having no resistance at all. Only long or very thin wires need counting.

nichrome resists about 65 times as much as copper

Resistors

A resistor packs a chosen resistance into a small part. It is usually a thin film of carbon or metal on a ceramic rod, with a wire lead at each end. Resistors have no + or - end: they work either way round.

Circuits use resistors to limit a current - to protect an LED, for example - and to set voltages. Both jobs are in Volume 02. Each resistor also has a power rating, as Volume 00 showed. Small ones take a quarter of a watt.

A potentiometer is a resistor you can adjust. A sliding contact moves along the resistance, so turning a knob changes it. A volume knob is often a potentiometer.

1.4 Reading resistor values

Small resistors are marked with coloured bands: two digits, then a multiplier, then a tolerance band. Their values come from a fixed series such as E12, so a designer picks the nearest value in the series.

The colour code

Each colour stands for a digit:

On a four-band resistor, read from the end the bands are bunched towards:

1. Band 1 is the first digit.
2. Band 2 is the second digit.
3. Band 3 is the multiplier: how many zeros to write after the two digits.
4. Band 4, set a little apart, is the tolerance: gold for 5 percent, silver for 10 percent, brown for 1 percent.

So yellow, violet, red means 4, 7 and two zeros: 4700 Ω, written 4.7 kΩ.

yellow violet red = 4.7 kΩ
red red brown = 220 Ω
brown black orange = 10 kΩ
orange orange yellow = 330 kΩ
brown black green = 1 MΩ

A gold third band means divide by 10 instead, for values under 10 Ω. Resistors with five bands work the same way, with three digits before the multiplier.

Tolerance

No resistor is made exactly. The tolerance says how far off it may be:

4.7 kΩ at 5 percent: anything from 4.465 kΩ to 4.935 kΩ

Why the values look odd

Resistors are not sold in every value. They come in fixed series. The common E12 series has twelve values in each tenfold step:

E12 values: 10, 12, 15, 18, 22, 27, 33, 39, 47, 56, 68, 82

Multiply them by 1, 10, 100 and so on to get 47 Ω, 470 Ω, 4.7 kΩ, 47 kΩ. Each value is about a fifth bigger than the one before. With a tolerance of 10 percent, the ranges of neighbouring values nearly touch, so every resistance is covered.

When a sum asks for a value that is not in the series, pick a neighbour:

nearest E12 values to 5 kΩ: 4.7 kΩ below, 5.6 kΩ above

Tiny resistors

Surface-mount resistors are too small for bands. They carry a three-digit code instead: two digits and then the number of zeros.

472 = 4.7 kΩ
103 = 10 kΩ
221 = 220 Ω

1.5 Measuring with a multimeter

A voltmeter goes across a part, an ammeter goes into the loop, and an ohmmeter measures a part with the power off. A good meter barely changes what it measures - but only barely.

The multimeter

A multimeter is several meters in one box. A dial chooses what it measures: volts, amps or ohms. It has two leads. The black one plugs into the socket marked COM, and the red one into the socket for what you are measuring.

Volts: across the part

A voltmeter measures the voltage between its two leads. Touch them to the two ends of a part, and it shows the voltage across that part. Nothing needs to be broken or unplugged.

Inside, a voltmeter has a very high resistance, often 10 MΩ. So it takes almost no current, and the circuit carries on as before.

Amps: in the loop

An ammeter measures the current flowing through it. So the current has to go through the meter: you break the loop and put the meter into the gap. Inside, an ammeter has almost no resistance, so it does not hold the current back.

circuit measure: A1 reads 5 mA; V1 reads 9 V

The ammeter's reading includes the tiny current through the voltmeter. At 10 MΩ that is under a microamp - a millionth of an amp - far too small to change the reading.

The ammeter mistake

Never put an ammeter across a part, the way a voltmeter goes. An ammeter has almost no resistance, so across a battery it is a short circuit:

an ammeter straight across a 9 V battery with 2 Ω inside reads 4.5 A - a short circuit

Most multimeters have a fuse on the amps socket for exactly this mistake. After measuring current, move the red lead back to the volts socket, or the next voltage you measure becomes a short.

Ohms: power off

An ohmmeter measures resistance by pushing its own small current through the part. So the circuit must be switched off, or the circuit's own voltages confuse the reading. Take the part out of the circuit if you can. Otherwise, other paths through the circuit are measured along with it.

Meters change what they measure

A meter is part of the circuit while it is connected. Usually that makes no difference, but not always. Here a voltmeter measures across one of two equal resistors of 1 MΩ each:

circuit loaded: two 1 MΩ resistors should give 4.5 V; the meter reads 4.29 V
with two 1 kΩ resistors instead, it reads 4.5 V
with two 100 kΩ resistors instead, it reads 4.48 V

With resistors of a few kilohms, the meter's 10 MΩ makes no visible difference. With resistors of a megohm, it pulls the reading down by about a fifth of a volt. The rule of thumb: a voltmeter is only trustworthy when its resistance is far bigger than the resistances it measures across. This effect is called meter loading.

What you learned

• Current is charge per second: I = Q / t. One amp is one coulomb a second, about 6.24 × 10¹⁸ electrons.
• Conventional current flows from + to -; electrons drift the other way, slowly.
• The same current flows all the way round a loop; parts use energy, not current.
• Voltage is energy per coulomb, always between two points. Ground is the 0 V reference.
• Cells in series add their voltages.
• Resistance grows with length and shrinks with thickness: R = resistivity x length / area.
• The colour code gives two digits and a multiplier; values come from series such as E12.
• A voltmeter goes across a part, an ammeter goes in the loop, and an ohmmeter needs the power off.
• A voltmeter's own resistance can pull its reading down when the circuit's resistances are high.

Key words from this volume

Every word below has a plain-English entry in the glossary.

• Current
• Electron
• Electric charge
• Coulomb (C)
• Conventional current
• Direct current (DC)
• Alternating current (AC)
• Voltage
• Joule (J)
• Ground (0 V)
• Resistance
• Resistor
• Conductor
• Insulator
• Resistivity
• Power rating
• Potentiometer
• Tolerance
• E12 series
• Multimeter
• Voltmeter
• Ammeter
• Ohmmeter
• Meter loading

Practice

Q = 12 C, t = 3 s: I = Q / t = 4 A

3 cells of 1.5 V in series: 4.5 V

green blue red = 5.6 kΩ
5.6 kΩ at 5 percent: anything from 5.32 kΩ to 5.88 kΩ

a 1 MΩ meter across R2 reads 3 V

Interview corner

Volume 02 puts voltage, current and resistance together in Ohm's law, and works out series and parallel circuits by hand.