Foundations

Nothing on this page is difficult. All of it is assumed, silently, in every class after the first, and a student who has not met it spends Class 5 fighting the arithmetic instead of learning the switching. Forty minutes, done once.

Prefixes, and reading a value out loud#

Every quantity in this course is written with a prefix. Knowing them is not memorisation, it is being able to read.

Each step is a factor of a thousand. That is the whole system.

The engineering shorthand#

You will see 4k7 and 2R2 and 1M0. The prefix letter replaces the decimal point, so 4k7 is 4.7 kΩ and 2R2 is 2.2 Ω. It exists because a printed decimal point disappears on a photocopy or a faded silkscreen, and a resistor value read as 47 kΩ instead of 4.7 kΩ is a factor of ten.

The conversions you will do constantly#

Use base units in every calculation. Volts, amps, ohms, farads, seconds. Mixing milliamps into a formula expecting amps is the single most common arithmetic error in this course, and it produces answers wrong by exactly a factor of a thousand, which is at least easy to spot once you are looking for it.

Powers of ten, without a calculator#

Multiplying and dividing by powers of ten is moving the decimal point. That is worth practising until it is automatic, because it is most of the arithmetic you will do at a bench.

0.02 × 150   →   2 × 150 = 300, then move two places   →   3
                 (0.02 is 2 × 10⁻², so the answer is 300 × 10⁻²)

12 ÷ 0.02    →   12 ÷ 2 = 6, then move two places the other way   →   600

The habit that makes this reliable: do the digits first, then count the zeros separately.

Sanity checking#

Before you accept any answer, ask whether it is roughly the right size. This catches nearly every mistake, and it takes a second.

Build the habit of stating the expected order of magnitude out loud before you calculate. It is the same discipline as predicting a measurement before you take it, and it works for the same reason.

The three formulae#

Everything electrical in this course sits on these.

V = I × R          Ohm's law
P = V × I          Power
P = I² × R         Power in a resistance

Rearranging without looking it up#

Ohm's law rearranges three ways. If you find yourself looking it up, cover the quantity you want with a finger on the triangle and read what is left.

I = V ÷ R          R = V ÷ I          V = I × R

The same for power. And the third formula follows from substituting the first into the second: since V = I × R, then P = V × I = (I × R) × I = I² × R.

The squared term is the one that matters most in practice. Double the current and the heating goes up four times. That single fact explains why undersized cable does not fail gently, why a loose connection runs away once it starts, and why a half-turned-on MOSFET destroys itself.

Worked examples, the ones you will actually do#

A 500 W lamp on 230 V. What current? I = P ÷ V = 500 ÷ 230 = 2.17 A

Six of those on one 16 A circuit. Is it acceptable? 6 × 2.17 = 13.0 A. Under 16 A, so yes on paper, and with about 19 per cent headroom, which is tight but workable. Seven would be 15.2 A and only 5 per cent under, which is not.

An LED needing 20 mA at 2 V, from a 5 V supply. The resistor drops 5 − 2 = 3 V at 0.02 A, so R = 3 ÷ 0.02 = 150 Ω. Its power is P = I² × R = 0.02² × 150 = 0.0004 × 150 = 0.06 W. A quarter-watt part is comfortable.

A MOSFET with 25 mΩ on-resistance carrying 8 A. P = I² × R = 64 × 0.025 = 1.6 W. Warm, and it wants some copper around it.

The same MOSFET half turned on, behaving like 2 Ω. P = 64 × 2 = 128 W. Destroyed in about a second. This is why gate drive matters.

Series and parallel arithmetic#

In series, resistances add: R = R₁ + R₂ + R₃

In parallel, the reciprocals add: 1/R = 1/R₁ + 1/R₂

For exactly two in parallel, the short form is easier: R = (R₁ × R₂) ÷ (R₁ + R₂)

Three shortcuts worth having:

• Two equal resistors in parallel give half the value. Ten equal ones give a tenth.
• A parallel combination is always smaller than the smallest resistor in it. If your answer is not, you have made an arithmetic error, and this check costs nothing.
• A very large resistor in parallel with a small one barely changes it. 1 MΩ across 100 Ω is 99.99 Ω, which is why a 10 MΩ meter can measure most circuits without disturbing them, and why the exceptions in Class 2 are exceptions.

Reading a schematic#

A schematic is a map of connections, not a picture of the object. Two wires crossing without a dot are not connected; with a dot, they are.

Read a schematic in the direction of the signal, left to right, and in the direction of the current, top to bottom. That convention is nearly universal, and once you know it a board's function is visible at a glance.

The two habits that make schematics readable: find the power rails first, and find the ground symbol. Everything else hangs off those two.

Practice#

The calculators all print their working, so you can check both the answer and the method. Do twenty LED resistor calculations by hand, then check them. Then do twenty power calculations for loads you can see around you.

The numbers drill has every examinable number in the course, and it schedules itself. Eight cards a night for a fortnight covers most of it.