Resistors, Resistivity and the Colour Code

Open any transceiver and count the components: there will be more resistors than anything else. They set the bias on every transistor, they divide the supply rail into the dozen different voltages a radio needs, they load an antenna analyser, they turn your volume control into a volume control. The exam repays this by asking about them more than any other single component — the unit of resistivity, what happens when a wire is made longer, what the last band means, and what two resistors come to when you put them side by side. This lesson covers all of it.

Resistance as a property

The first lesson divided materials into conductors, insulators and semiconductors. That division is really a spectrum, and resistance is where a particular object sits on it: the opposition it offers to the flow of current, measured in ohms (Ω), with the usual kilohm (1 kΩ = 1 000 Ω) and megohm (1 MΩ = 1 000 000 Ω) above it.

The distinction to hold on to is between a material and a component. Copper is a good conductor, but a long enough, thin enough piece of copper has plenty of resistance. Carbon is a mediocre conductor, which is precisely why it is useful for making resistors. What sets the resistance of an actual object is four things: what it is made of, how long it is, how thick it is, and how hot it is.

Resistivity

Strip out the shape and what is left is a property of the substance itself: resistivity, symbol ρ (rho). It is defined so that the resistance of a uniform piece of material is

Rearranging gives ρ = R × A ÷ L, whose units are ohms × metres² ÷ metres. That cancels to ohm-metres (Ω·m), and that is the SI unit of resistivity — not ohms per metre, which is the answer the paper offers alongside it.

Silver is the best conductor there is; copper is a whisker behind it and vastly cheaper, which is why the world is wired in copper. Aluminium is worse per metre but much lighter, which is why overhead transmission lines are aluminium.

The two consequences the exam wants

Read the formula as a shape rather than as algebra. L is on the top and A is on the bottom, so:

• Double the length and you double the resistance. Resistance is directly proportional to length. Twice as far to travel is twice as much jostling, and it is the same statement as two equal resistors in series adding up.
• Double the cross-sectional area and you halve the resistance. Resistance is inversely proportional to area. A thicker wire is a wider road carrying the same traffic with less congestion, which is why the DC lead to a 100 W transceiver is fat and the lead to an LED is not.

Worked example 1 — the supply lead to your rig

You run 5 metres of copper cable of 1.5 mm² cross-section from the power supply to the radio, and 5 metres back — 10 metres of copper in all. What is its resistance?

First the units: 1.5 mm² = 1.5 × 10⁻⁶ m². Then

R = ρL ÷ A = (1.7 × 10−8 × 10) ÷ (1.5 × 10−6) = 0.11 Ω

That sounds negligible until the rig draws 20 A on transmit, when it costs V = IR = 20 × 0.11 = 2.2 V — a 13.8 V supply arriving as 11.6 V. Doubling the cable to 3 mm² halves the loss. This is the single commonest reason a new station transmits at less power than it should.

Conductance, the other way of saying it

Resistance measures how hard it is for current to pass. Conductance measures how easy, and it is simply the reciprocal:

A 4 Ω resistor has a conductance of 0.25 S; a 10 Ω resistor, 0.1 S. The unit is the siemens, symbol S, and its older name — still the one the ASOC paper prints — is the mho, which is "ohm" spelt backwards. So conductance is proportional to the inverse of resistance, and the option saying it is proportional to resistance is exactly wrong.

The same reciprocal trick applies to the material property: conductivity, symbol σ (sigma), is 1 ÷ ρ, and since resistivity is in ohm-metres, conductivity is in siemens per metre, printed in the paper as mho/metre. Keep the pairs straight: ohm and siemens are properties of a component; ohm-metre and siemens per metre are properties of a substance.

Temperature

Resistance is not a fixed number; it moves with temperature, and which way it moves depends on the material.

• Metals have a positive temperature coefficient. Heat a copper wire and its atoms vibrate harder, obstructing the drifting electrons more, so its resistance rises. A filament lamp is the extreme case: cold, it is a near short circuit, which is why bulbs almost always fail at switch-on.
• Carbon and semiconductors have a negative temperature coefficient. Heat frees more charge carriers than the extra vibration obstructs, so resistance falls. A thermistor is a component built deliberately to do this, and it is what a rig uses to sense the temperature of its heatsink.

For a metal film resistor the coefficient is a few parts per million per degree — small enough to ignore in an amateur circuit, but it is the reason a precision five-band resistor sometimes carries a sixth band giving that figure.

Types of resistor

One warning matters more to an amateur than to anyone else. A wirewound resistor is a coil, and a coil has inductance. At DC and audio that is irrelevant; at radio frequency the inductance dominates and the component stops being a resistor at all. Never put a wirewound part in an RF path — not as a dummy load for an HF rig, not as a parasitic stopper, not across a tuned circuit. Use a non-inductive type, which is what a proper 50 Ω dummy load contains.

Power rating and derating

Every resistor turns the energy it opposes into heat, at P = I²R. The wattage marked on it, or implied by its physical size, is the maximum it can dissipate without damage — a ceiling, not a working figure. A quarter-watt resistor dissipating 3 mW is perfectly happy. Exceed the rating and the part gets hot, drifts in value, discolours, and eventually opens.

Carbon types run from about 1/8 W to 2 W; above that you are into wirewound. The value is colour coded but the wattage never is — you judge it by size. And in practice you derate: specify at least twice the calculated dissipation, because a component run at exactly its rating runs hot enough to shift value and to cook whatever is next to it on the board. In a sealed box in a Chennai summer, three times is better.

Preferred values

Beginners are puzzled by the shop having 2.2 kΩ, 3.3 kΩ, 4.7 kΩ and 6.8 kΩ but nothing in between. The reason is tolerance. If a resistor may be ±10 % out anyway, stocking 2.3, 2.4 and 2.5 kΩ is pointless — their tolerance bands overlap. So values are spaced logarithmically in preferred series, each value's spread just reaching the next:

E12 runs 10, 12, 15, 18, 22, 27, 33, 39, 47, 56, 68, 82 — and then repeats a decade up: 100, 120, 150 and so on. E24 interleaves 11, 13, 16, 20, 24, 30, 36, 43, 51, 62, 75 and 91 between them. If you need a value the series does not offer, combine two in series or parallel; that is what the last section of this lesson is for.

Variable resistors: potentiometer or rheostat

A variable resistor is a track of carbon or resistance wire with a fixed contact at each end and a wiper that slides along it. It has three terminals, and how you wire them decides what it is called — which is precisely what the exam asks.

Connected across a supply with the output taken from the wiper, it is a potentiometer or potential divider, and the voltage available at the wiper can be anything from zero up to the full supply. That is the volume control of every receiver ever built. Connected by one end and the wiper only, it sits in series with the load and controls the current through it; in that role it is called a rheostat. Same component, different job. A version adjusted once with a screwdriver and then left alone is a preset.

The colour code

Resistors are too small to print a value on, so the value is banded on in colour. Hold the resistor with the bands crowded to the left and read left to right; the tolerance band is the one set slightly apart at the other end.

The digit order is the one Indian students already learn as B.B. ROY of Great Britain had a Very Good Wife — Black, Brown, Red, Orange, Yellow, Green, Blue, Violet, Grey, White, for 0 to 9.

Four bands

Digit, digit, multiplier, tolerance. The third band is an instruction to multiply, not a third digit — for the whole-number multipliers it is simplest to read it as "that many zeros". Yellow, violet, orange, gold is 4, 7, three zeros: 47 000 Ω = 47 kΩ, ± 5 %.

Five bands

Digit, digit, digit, multiplier, tolerance. The precision form adds a third significant figure. Brown, green, black, brown, brown is 1, 5, 0, × 10 = 1 500 Ω = 1.5 kΩ, ± 1 %. If you count five bands, the first three are figures; on a four-band part only the first two are.

Work the widget below in both directions. Decode mode gives you bands and asks for the value; Identify mode gives you a value and asks for the bands, which is the direction the examiner prefers. Do a dozen of each and the code stops being something you look up.

Resistors in series

End to end, the current has to pass through every one of them in turn, so the oppositions simply add:

Sanity rule: a series total is always larger than the largest resistor in it. If your answer is smaller than one of the parts, you have used the wrong formula.

Resistors in parallel

Side by side, the current has a choice of paths, so the combination is easier to get through than any single branch. Conductances add, which is why the formula is written in reciprocals:

Two shortcuts save most of the arithmetic in the exam:

Four 100 Ω resistors in parallel are 100 ÷ 4 = 25 Ω. Sanity rule: a parallel total is always smaller than the smallest branch in it. That one check catches more mistakes than any other habit in this module.

Set up each of the worked examples below in the solver and watch the working. Note what happens when you switch the component type from resistors to capacitors with the same numbers: the two answers change places. Resistors and capacitors combine in opposite directions, and the solver is there to make that stick before you meet it in the capacitors lesson.

Worked example 2 — a mixed network

Two 10 Ω resistors are connected in series, and that pair is connected in parallel with a 20 Ω resistor. What is the total?

1. Innermost first: the series pair is 10 + 10 = 20 Ω.
2. That leaves two 20 Ω branches in parallel. They are equal, so 20 ÷ 2 = 10 Ω.
3. Check: 10 Ω is smaller than the smallest branch, 20 Ω. Correct.

Worked example 3 — three unequal branches

5 Ω, 10 Ω and 30 Ω are connected in parallel across 30 V. Find the total resistance and the total current.

Put everything over a common denominator of 30:

1 ÷ R = 1/5 + 1/10 + 1/30 = 6/30 + 3/30 + 1/30 = 10/30 = 1/3, so R = 3 Ω.

I = V ÷ R = 30 ÷ 3 = 10 A.

Check it branch by branch: 30/5 = 6 A, 30/10 = 3 A, 30/30 = 1 A, and 6 + 3 + 1 = 10 A. That the branch currents add to the total is Kirchhoff's current law, which the next lesson makes formal.