Chapter 3: Basic Electrical Concepts

A tiny nucleus of protons and neutrons in a cloud of electrons

The nucleus of protons and neutrons is tiny and central, and the electrons are smeared out around it as a cloud rather than orbiting like miniature planets.

Positive, none, negative

Protons are positive, neutrons carry no charge, as their name hints, and electrons are negative; 'none, positive, negative' swaps the proton and the neutron.

Neutron

Neutrons carry no charge, as their name hints; protons are positive and electrons negative, and the nucleus as a whole is positive because of its protons.

Electromagnetic attraction to the nucleus

The negative electrons and the positive nucleus attract each other, an electromagnetic effect; gravity between such tiny masses is far too weak to hold them.

The strong nuclear force

At the tiny distances inside a nucleus the strong nuclear force outweighs the electromagnetic force, which on its own would push the positive protons apart.

To bind the nucleus together

It binds the protons and neutrons of the nucleus together, overcoming the protons' electromagnetic repulsion; electrons are kept near the nucleus by electromagnetic attraction instead.

They push each other apart

Both electrons carry negative charge, and like charges repel, so the two push each other apart; only opposite charges, such as an electron and a proton, attract.

Ceramic

Ceramic is an insulator, its electrons all tightly bound; damp wood conducts through the impure water in it, and copper and solder are metals, which conduct.

Wet cloth

Water with impurities in it conducts, so a wet cloth can carry a current; rubber, ceramic and plexiglass are all good insulators.

They insulate the user from the current

Most plastics and rubber hold all their electrons tightly, so they insulate and keep current away from your hand; low weight and cost are side benefits only.

A steel paper clip

Steel is a metal, and most metals conduct through their loosely bound electrons; mica may look metallic, but like rubber and glass it is an insulator.

A positive charge builds up and pulls them back

Losing negative electrons leaves that part positive, and as opposite charges attract it pulls electrons back, so carriers must be replaced for a current to keep flowing.

Silver

No metal conducts better than silver, but it costs too much for most wiring; copper, very good and far cheaper, is the usual choice instead.

It costs too much

Silver conducts better than any other metal but costs far too much for most wiring; it does tarnish in air, but cost is the reason the manual gives.

Aluminium

Aluminium conducts well and is far lighter than copper, so it suits long overhead spans; copper conducts better but is over three times as dense.

Mercury

Mercury is a metal that stays liquid at room temperature, so it conducts; oil is a liquid too but insulates, and copper and rubber are solids.

A low-melting alloy, often tin and lead

Solder is a mix of metals, often tin and lead, though lead-free kinds are now common, that melts at a low temperature and so joins components easily.

Loosely bound electrons

In copper some electrons are only loosely bound, so they can drift through the metal as the current; tightly bound electrons, as in an insulator, cannot move.

Particles that move to make up a current

Charge carriers are whatever particles move to form a current, such as the loosely bound electrons in copper; a conductor is the material they move through.

It is a flow of charge

By definition a current is any flow of charge; in copper the carriers happen to be electrons, but other conductors can use other charged particles.

From Y to X, against the electrons

Unless stated otherwise, 'current' means conventional current, the way positive charge would go: negative electrons moving from X to Y amount to a current from Y to X.

Electrons drift steadily one way along a wire

A current needs charge moving in a fairly consistent direction; random jiggling carries nothing overall either way, and a static charge or a magnet at rest moves no charge.

The ampere

Current is measured in ampere, symbol A, after André-Marie Ampère; 'amp' is everyday slang, and the coulomb is the unit of charge, not of current.

Ampere

'Amp' is everyday shorthand for the ampere, the unit of current; 'amperage' means the size of a current, and an amplifier is a circuit.

The volt

Potential difference, often just called voltage, is measured in volt, one joule per coulomb; a voltmeter is the instrument that measures it, not the unit.

From the positive terminal to the negative terminal

Conventional current flows from the positive end of a circuit to the negative end, out of the battery's positive terminal; the electrons drift the other way, negative to positive.

Carry a unit positive charge from the lower potential to the higher

It is the energy per unit charge needed to carry a positive charge up from the lower potential to the higher; going downhill, energy is given out instead.

Volt

Energy per unit charge is potential difference, so one joule per coulomb is the volt; the farad is a coulomb per volt, the other way round.

750 V

Voltage is energy per unit charge: V = 1500 J ÷ 2 C = 750 V; forgetting that 1,5 kJ is 1500 J gives the 0,75 V slip.

14 V

Voltage is energy per unit charge: 54 J ÷ 4 C = 13,5 V exactly, so 14 V, 0,5 V away, is nearest; 12 V is 1,5 V away.

6 kJ

Energy is voltage times charge: E = 1200 V × 5 C = 6000 J = 6 kJ; reading 1,2 kV as 1,2 V gives the 6 J slip.

Water pressure and rate of flow

Voltage is like the pressure a pump creates, and current like the rate of flow it drives, such as litres per second; 'rate of flow and water pressure' swaps them.

Pressure

Voltage is like water pressure: the higher it is, the more flow it pushes through the pipe, and that rate of flow is what matches the current.

A voltage applied to it

A potential difference, or voltage, pushes the charge along, as a pump's pressure drives water; a thicker conductor only lets more current through, it does not make it flow.

Power = Current × Voltage

Power is voltage times current, P = V × I, so 12 V at 2 A gives 24 W; voltage divided by current gives the resistance, not the power.

Power

The watt measures power, the rate of using energy, one joule per second, so a 60 W lamp uses 60 J every second; energy itself is counted in joule.

Both take the same energy

Energy is power times time, and 100 W × 0,5 h = 50 W × 1 h, so the doubled power is exactly offset by half the time.

3 W

P = V × I = 12 V × 0,25 A = 3 W; dividing instead, 12 ÷ 0,25, gives the wrong 48 W, and adding volts to amperes means nothing.

250 W

P = V × I = 13,8 V × 18,5 A = 255,3 W, so 250 W, about 5 W away, is nearest; 300 W is about 45 W away.

1,84 kW

P = V × I = 230 V × 8 A = 1840 W, and a kilowatt is 1000 W, so that is 1,84 kW, not 18,4 kW.

4 A

From P = V × I, the current is I = P ÷ V = 48 W ÷ 12 V = 4 A; dividing the other way, 12 ÷ 48, gives the 0,25 A slip.

60 W

Power is energy per second: P = 3600 J ÷ 60 s = 60 W; 3,6 kW would mean using 3,6 kJ every second, not every minute.

1,5 A

Current is charge per second: 5000 C ÷ 3600 s ≈ 1,389 A, so 1,5 A, 0,11 A away, is nearest; 1 A is 0,39 A away.

60 C

Charge is current times time: Q = 0,5 A × 120 s = 60 C; using 2 instead of the 120 seconds in two minutes gives the 1 C slip.

Each turns energy of some other kind into electricity

Each turns another form of energy into electricity: motion in the dynamo, chemical energy in the battery and fuel burnt in the generator's engine; none stores power-station electricity.

The sun alone

The manual traces all energy used on earth to the sun, wind and rain included, since sunshine drives the weather; strictly, nuclear, geothermal and tidal energy are exceptions.

Coal burnt in a power station

Coal is a fossil fuel holding solar energy from ages ago; the water behind a hydro dam was lifted there by sun-driven weather only hours or days before.

Light falling on it

'Photo' means light, and photovoltaic cells turn light, usually sunlight, straight into electricity; heat warms a solar geyser but does not drive a photovoltaic cell.

Light

'Photo' means light, as in photograph, so photovoltaic cells turn light into electricity; 'solar' would mean 'of the sun'.

4,7 × 10⁻⁴ A

Micro is 10⁻⁶, so 470 µA = 470 × 10⁻⁶ A = 4,7 × 10⁻⁴ A, the comma moved two places; 4,7 × 10⁻⁵ A is only 47 µA.

3 µV

0,000 003 2 V = 3,2 × 10⁻⁶ V = 3,2 µV, so 3 µV, 0,2 µV away, is nearest; 0,3 µV is 2,9 µV away.

0,0005 A

Converted to µA: 0,0005 A = 500 µA, then 450 µA, 5 × 10⁻⁵ A = 50 µA and 40 µA, so 0,0005 A is the largest.

45 mV

Milli means one thousandth, so 0,045 V × 1000 = 45 mV; 4,5 mV would be only 0,0045 V, and the kV and MV answers are far too big.

One thousandth

Milli means one thousandth, as in 1 mA = 0,001 A; one hundredth is centi, a prefix the manual says not to use routinely.

× 1 000 000

Mega multiplies by a million, 10⁶, so 1 MHz is 1 000 000 Hz; × 100 000 is one zero short, and ÷ 1 000 000 is micro.

14,2 MHz

Mega means a million, 10⁶, so 14 200 000 Hz ÷ 1 000 000 = 14,2 MHz; 142 MHz has the decimal comma one place out.

145 500 kHz

A megahertz is 1000 kHz, so 145,5 MHz × 1000 = 145 500 kHz; 14 550 kHz has one zero too few, and 145 500 000 is the frequency in hertz.

2 400 000 000 Hz

Giga means 10⁹, a thousand million, so 2,4 GHz = 2,4 × 10⁹ Hz = 2 400 000 000 Hz; 240 000 000 Hz has one zero too few.

100 nF

Nano means 10⁻⁹, and 0,000 000 1 F = 1 × 10⁻⁷ F = 100 × 10⁻⁹ F = 100 nF; 10 nF would be 0,000 000 01 F.

3300 pF

A microfarad is 1 000 000 pF, so 0,0033 µF × 1 000 000 = 3300 pF; 330 pF has one zero too few.

T, × 10¹²

Tera is a capital T and means × 10¹², a million million; the small t is wrong, as prefix symbols keep their case, and M is mega.

hexa

Hexa is not an SI prefix; hecto (× 100) and centi (÷ 100) are, though the manual advises against using them routinely, and giga is a main one.

The siemens (conductance)

Unit symbols are case-sensitive: capital S is the siemens, the unit of conductance, while the second, the unit of time, is a small s, as in m/s.

pico, nano, micro, milli

Each step is a factor of 1000: pico is 10⁻¹², nano 10⁻⁹, micro 10⁻⁶ and milli 10⁻³; 'nano, pico, micro, milli' swaps the first two.

The unit of measurement

A number means little until its unit is given, such as 10 m or 10 mm; a prefix only scales a unit, so on its own it still says nothing.

625 000

Move the decimal comma five places to the right: 6,25 becomes 625 000; tacking five zeros onto 625 ignores the comma and gives 62 500 000.

5,2 × 10⁷

Moving the decimal comma seven places left turns 52 000 000 into 5,2, so it is 5,2 × 10⁷; 5,2 × 10⁶ is only 5 200 000.

0,0036

A negative power of ten moves the decimal comma left, here three places, so 3,6 × 10⁻³ = 0,0036, a small positive number; 0,036 moves it only two places.

2,5 × 10⁻⁴

Moving the decimal comma four places right turns 0,000 25 into 2,5, so the power of ten is 10⁻⁴; 2,5 × 10⁻³ is 0,0025, ten times too big.

5 × 10⁻³

Written out, 5 × 10⁻³ = 0,005, more than 0,002, 0,0009 and 3 × 10⁻⁴ = 0,0003; a more negative power of ten means a smaller number.

3,0 × 10⁸ m/s

299 792 km/s × 1000 = 299 792 000 m/s ≈ 2,998 × 10⁸ m/s, just 0,07 % below 3,0 × 10⁸; 2,9 × 10⁸ is about 3 % too low.

10²¹

Counting the places gives 1,4 × 10²¹, which is 0,4 × 10²¹ above 10²¹ but 1,3 × 10²¹ above 10²⁰, so 10²¹ is nearest; 10²² is further still.

1,6 × 10⁻¹⁹ C

An electron's charge is only 1,6 × 10⁻¹⁹ C in size, so a coulomb takes about 6,25 × 10¹⁸ electrons; 10¹⁹ C would be enormous.

Scientific notation

Scientific notation writes a number as a value times a power of ten, saving strings of zeros; a logarithm instead turns 3 × 10⁸ into the single power 8,48.

EXP

The E or EXP key, short for exponent, enters the power of ten directly, as in 8,2 EXP 6; with ^ you must key in the 10 and multiply.

The exponent

The power to which ten is raised, here 23, is the exponent; the base is the 10 itself, and 6 × 10²³ is 6 followed by 23 zeros.

4380

The rule writes numbers of up to four digits as one block, so 4380 has no space, though the prefix table slips into '1 000'; spaces start at five digits.

Twenty-five millionths

The comma starts the decimals and 0,000 025 has six decimal places, so it is 25 × 10⁻⁶, twenty-five millionths; twenty-five thousandths would be 0,025.

6,8 × 10⁻¹¹ F

Pico means 10⁻¹², so 68 pF = 68 × 10⁻¹² F = 6,8 × 10⁻¹¹ F; 6,8 × 10⁻¹⁰ F would be 680 pF.

7075 kHz

7074,968 kHz is only 0,032 kHz below 7075 kHz, so that is nearest; dropping the decimals gives 7074 kHz, almost a whole kilohertz out.