Chapter 5: The Resistor and Potentiometer

A conductor with known resistance

A resistor is a conductor made to have a known resistance: it lets current through, only less of it. An insulator would block current altogether, and storing charge is a capacitor's job.

As a simple rectangle

The manual draws a resistor as a rectangle, with a connecting line at each end. The zigzag is an older symbol, still common in American diagrams, which the manual does not use.

Maximum power it can safely dissipate

The power rating is the most power the resistor can turn into heat without damage, about 125 mW up to 5 W and beyond. The power it actually uses depends on the current and voltage in the circuit.

The current through it and voltage across it

The heat produced depends on the current through the resistor and the voltage across it (P = V × I, chapter 3). One resistor can dissipate very different powers, so its value alone does not decide it.

1 W

0,4 W is 400 mW, more than 250 mW or 125 mW, so those resistors would be overloaded; 1 W is the smallest rating offered that covers it, with room to spare.

The wires joining it to other components

A plain line in a schematic is a connection, so the lines at each end join the resistor to the rest of the circuit. They do not show which way the current flows.

From under 1 Ω to several hundred MΩ

The manual says resistors run from a small fraction of an ohm up to several hundred megohms. 0,1 Ω to 10 MΩ covers the everyday values but stops far short of the top of the range.

1350 to 1650 Ω

10% of 1500 Ω is 150 Ω, so the value may be anywhere from 1500 − 150 = 1350 Ω to 1500 + 150 = 1650 Ω. 1485 to 1515 Ω takes 15 Ω, which is only 1%.

446,5 to 493,5 Ω

5% of 470 Ω is 0,05 × 470 = 23,5 Ω, giving 446,5 Ω to 493,5 Ω. 467,65 to 472,35 Ω uses 2,35 Ω, only 0,5%, and 458,25 to 481,75 Ω halves the tolerance.

99 kΩ to 101 kΩ

1% of 100 kΩ is 1 kΩ, so the value may lie from 99 kΩ to 101 kΩ. 90 to 110 kΩ would be ±10%, 98 to 102 kΩ ±2% and 99,9 to 100,1 kΩ ±0,1%.

50,4 to 61,6 Ω

10% of 56 Ω is 5,6 Ω, so the value may lie from 56 − 5,6 = 50,4 Ω to 56 + 5,6 = 61,6 Ω. 55,44 to 56,56 Ω takes only 0,56 Ω, which is 1%.

5,9 kΩ

5% of 5600 Ω is 280 Ω, so the highest value is 5600 + 280 = 5880 Ω, nearest 5,9 kΩ. 5,3 kΩ is near the lowest value, 5320 Ω, the wrong end of the range.

No: ±2% allows at most 2754 Ω

2% of 2700 Ω is 54 Ω, so the value may be 2646 Ω to 2754 Ω, and 2770 Ω is 16 Ω too high. Within 5% would do for a gold-band (±5%) resistor, not a ±2% one.

70 Ω

Each may be 2% (36 Ω) either side of 1800 Ω, so one could be 1764 Ω and the other 1836 Ω: 72 Ω apart, nearest 70 Ω. 35 Ω allows for only one being off; 1840 Ω is a value, not a difference.

41 kΩ

5% of 820 kΩ is 0,05 × 820 = 41 kΩ, so the value may be up to 41 kΩ above or below 820 kΩ. 4,1 kΩ is only 0,5%, and 861 kΩ is the highest value itself, not the difference.

39 kΩ ±10%

The nominal value is the middle, (35,1 + 42,9) ÷ 2 = 39 kΩ, and each limit is 3,9 kΩ from it: 3,9 ÷ 39 = 0,1 = 10%. ±1% would allow only 0,39 kΩ either side.

±2%

It is 18 Ω low, 1,5% of 1200 Ω. ±1% allows only 12 Ω, so it fails that; ±2% allows 24 Ω, so ±2% is the tightest it meets.

Wirewound resistor

Wirewound resistors are made for high power ratings in DC circuits, from about 2,5 W up to 20 W and beyond. Carbon film resistors stop at about 2 W, and metal film and network resistors are low-power parts.

They have high inductance

The wire is wound like a coil, which gives it high inductance, and that upsets radio-frequency circuits. Their ±5% or ±10% tolerance is no reason: carbon film resistors are ±5% and work well at RF.

Wirewound

The manual rules out wirewound resistors for RF because their coiled wire gives them high inductance. It raises no such objection to carbon film, metal film or network resistors.

2,5 W to 20 W and above

Wirewound resistors are the high-power type, rated from about 2,5 W up to 20 W and beyond. Up to 2 W is the range of carbon film resistors, and metal film stops at about 500 mW.

Metal film resistor

Metal film resistors are made to ±1% or better, so their actual value stays close to the marked one. Carbon film, the cheap everyday type, is typically only ±5%.

A tight tolerance

A precision circuit needs values close to those marked, and metal film resistors are made to ±1% or better. Their power ratings reach only about 500 mW, so high power is not the reason.

125 mW to 500 mW

The manual gives metal film resistors 125 mW to 500 mW (larger ones exist, but are less common). Up to 2 W is the range of carbon film resistors, and high ratings belong to wirewound ones.

Carbon film

Carbon film resistors are the everyday, low-cost kind, typically ±5% and 125 mW to 2 W. Metal film costs more and is chosen when a tighter tolerance is needed.

They pack many resistors into one small part

A resistor network packs many resistors, often all of one value, into a single package like an integrated circuit. Networks are meant for low-power use, so they do not raise the power rating.

A resistor network

A resistor network holds many resistors, often all of one value, in a single package, which is just what is needed here. A potentiometer is one variable resistance, not eight fixed ones.

Integrated circuits

A resistor network holds several resistors in one package shaped like an integrated circuit, with a row or two of pins. It is a single part, not a small board of separate resistors.

They are too small for printed values

Most resistors are only a few millimetres long, so a printed value would be hard to read; the bands give the value and the tolerance instead. Cost is not the reason the manual gives.

With the gold band on the right

The code is read from left to right, with the tolerance band, here gold, at the right-hand end, so the far-left band is the first digit. Held the other way, the value would come out wrong.

A third digit of the value

The extra band gives a third digit, so the value can be stated more precisely; the multiplier and the tolerance band follow as before, so there is still only one tolerance band.

121 kΩ

Five bands give three digits, 1, 2, 1, then the multiplier, orange × 1000: 121 × 1000 = 121 kΩ. Read as a four-band code, 12 × 10, it would wrongly give 120 Ω.

±5%

A gold tolerance band means ±5%: the actual value may be up to 5% above or below the marked value. Silver, the other metallic colour, means ±10%.

Silver

Silver in the tolerance band means ±10%. Gold, the other metallic colour, means ±5%, and brown and red mean ±1% and ±2% on precision resistors.

220 Ω ±5%

Red 2, red 2, brown × 10: 22 × 10 = 220 Ω, and a gold band means ±5%. ±10% would need a silver band.

11 400 to 12 600 Ω

Gold means ±5%, and 5% of 12 000 Ω is 600 Ω, so the value lies from 11 400 Ω to 12 600 Ω. 10 800 to 13 200 Ω is ±10%, which a silver band would mean.

19,5 Ω

Gold means ±5%, and 5% of 390 Ω is 0,05 × 390 = 19,5 Ω, so it may be up to 19,5 Ω high (409,5 Ω). 39 Ω would be 10%, the tolerance of a silver band.

610 Ω

Silver means ±10%: 10% of 680 Ω is 68 Ω, so the lowest value is 680 − 68 = 612 Ω, nearest 610 Ω. 650 Ω comes from ±5%, the tolerance of a gold band.

From its colour code

The tolerance is given by a colour band, such as gold for ±5% or silver for ±10%. Body size gives a rough idea of the power rating, not of how accurate the value is.

270 kΩ

Red 2, violet 7, then yellow, the multiplier, × 10 000: 27 × 10 000 = 270 000 Ω = 270 kΩ. 2,7 MΩ would need × 100 000, a green third band.

Yellow, violet, red

4,7 kΩ = 4700 Ω = 47 × 100: yellow 4, violet 7, then red, × 100. Violet, yellow, red has the two digits the wrong way round: 74 × 100 = 7400 Ω.

47 kΩ

Yellow 4, violet 7, orange × 1000: 47 × 1000 = 47 000 Ω = 47 kΩ. 74 kΩ reads the two digit bands the wrong way round.

Blue

Blue stands for 6. The digit colours run black 0, brown 1, red 2, orange 3, yellow 4, green 5, blue 6, violet 7, grey 8, white 9, so violet, next to blue, is 7.

Green

Green stands for 5, with yellow (4) and blue (6) on either side of it in the table, which runs from black, 0, to white, 9.

Blue

Blue stands for 6, so as a multiplier it adds six zeros: × 1 000 000. Green, 5, adds only five zeros, × 100 000.

× 100 000

Green stands for 5, so as a multiplier it adds five zeros: × 100 000. × 10 000 belongs to yellow, 4.

5,6 MΩ

Green 5, blue 6, then green as the multiplier, × 100 000: 56 × 100 000 = 5 600 000 Ω = 5,6 MΩ. 560 kΩ uses × 10 000, which is yellow.

8,2 kΩ

Grey 8, red 2, red × 100: 82 × 100 = 8200 Ω = 8,2 kΩ. 9,2 kΩ takes grey for white, which is 9; the two pale bands are easily confused.

8

The digit colours run from black, 0, to white, 9. Grey is 8, just before white, the other pale colour that is often confused with it.

White

White is 9, the last digit colour in the table, and grey is 8. Black is 0, and gold appears only as a tolerance in the manual's table.

White, brown, brown

910 Ω = 91 × 10: white 9, brown 1, then brown, × 10. Grey, brown, brown would be 810 Ω, as grey is 8, and a red third band would make it 9,1 kΩ.

Brown, grey, black

18 Ω = 18 × 1: brown 1, grey 8, then black, × 1 (no zeros). Brown, white, black would be 19 Ω, as white is 9, and a brown third band would make it 180 Ω.

Grey, brown, red

8,2 kΩ is 8200 Ω. Grey, brown, red is 81 × 100 = 8100 Ω, only 100 Ω away; white, red, red is 9200 Ω, 1000 Ω away, and grey, red, orange is 82 kΩ.

3,3 kΩ

The k means kilo and stands where the decimal comma would be, with the Ω left out: 3k3 = 3,3 kΩ = 3300 Ω. 33 kΩ would be written 33k.

6k8

Write the k where the decimal comma is and leave out the Ω: 6,8 kΩ becomes 6k8. 68k would mean 68 kΩ, ten times as much.

2k0

2k0 is 2,0 kΩ = 2000 Ω, only 50 Ω from 2050 Ω. 2k2 is 2200 Ω, 150 Ω away, three times as far; 200R and 20k are ten times too small and too big.

18k

18k is 18 kΩ = 18 000 Ω. 1k8 is only 1,8 kΩ, as the k marks the decimal comma; 180R is 180 Ω and 1R8 is 1,8 Ω.

1R2

With no k or M, the letter R takes the place of the decimal comma: 1,2 Ω is written 1R2. 12R means 12 Ω, and 0R12 means 0,12 Ω.

0,47 Ω

With no k or M, R marks the decimal comma, so R47 is 0,47 Ω, a typical low-value power-supply resistor. 47 Ω would be written 47R.

0R22

With no k or M, R takes the place of the decimal comma: 0,22 Ω is written 0R22. 22R would be 22 Ω, a hundred times as much, and 2R2 is 2,2 Ω.

A resistance of 2,2 MΩ

This shorthand is used for resistor values: M means mega and stands at the decimal comma, so 2M2 = 2,2 MΩ. 22 MΩ would be 22M, and milli is a small m.

Means mega and marks the decimal comma

M stands for mega, × 1 000 000, and takes the place of the decimal comma: 1M8 = 1,8 MΩ. Milli would be a small m, and the label says nothing about the type.

Word processors and spreadsheets

The manual says ordinary word processors and spreadsheets handle Ω easily, so no special software is needed, and values can be written out in full.

Yes, though it takes a little more effort

The manual says writing values in full, such as 3,3 kΩ, does no harm; it is just a little more work. The shorthand is a convenience, not a rule.

To vary resistance

A potentiometer is a variable resistor: moving its wiper changes the resistance between the wiper and each end. Despite its name it is not a measuring instrument, and it neither stores energy nor amplifies.

The resistance from it to each end of the track

Moving the wiper changes the resistance from the wiper to each end, but the two always add up to the fixed end-to-end value, which the wiper cannot change.

110 kΩ

With the resistance spread evenly, the centre splits the 220 kΩ in half: about 110 kΩ to each end. 220 kΩ is the fixed end-to-end value, not the value to the wiper.

1 MΩ

The end-to-end resistance is fixed at the potentiometer's value, 1 MΩ, wherever the wiper is; only the resistance from each end to the wiper depends on the knob.

19 kΩ

The two parts always add up to the whole track: 25 kΩ − 6,2 kΩ = 18,8 kΩ, nearest 19 kΩ. Adding them, 31,2 kΩ, would be more than the 25 kΩ end-to-end value, which never changes.

10 kΩ

The two readings add up to the whole track: 2,2 kΩ + 7,9 kΩ = 10,1 kΩ, so it is a 10 kΩ potentiometer. Their difference, 5,7 kΩ, has no meaning here.

15 kΩ

A third of the track, 22 kΩ ÷ 3 = 7,33 kΩ, lies between the wiper and the near end, so the far end has 22 − 7,33 = 14,67 kΩ, nearest 15 kΩ; 7,3 kΩ is the near end.

Potentiometer

The potentiometer symbol is a rectangle, the resistive track, with an arrowhead against its side for the wiper that moves along it. A relay also has moving contacts, but its symbol shows a coil and switch.

Leave it unconnected or join it to the wiper

Used as a two-terminal variable resistor, a potentiometer needs one end and the wiper; the spare end may be left free or joined to the wiper. Joining both ends would stop it reaching its full value.

Volume control

Potentiometers are widely used as controls, such as the volume control of a receiver or audio amplifier. The potentiometer only sets how much signal goes on; the amplifier does the amplifying.

Its value can be varied

The diagonal arrow means 'variable': through the resistor rectangle it makes the variable-resistor symbol. It is not a connection and does not show the direction of current.

Carbon, or a coil of wire

The track is a strip of carbon or a coil of resistance wire, with a known resistance between its ends. Copper has far too little resistance to make a useful track.

By turning a rotary knob

Most potentiometers are circular, with a knob that turns the wiper round the track. Straight ones with a slider, as on audio mixing desks, exist too, but they are fewer.

No: they are there for the explanation

The manual adds A, B and W only to explain how the resistances change; it says such labels are not usual on circuit diagrams, so a real diagram shows the plain symbol.

Nothing: the connections are the same

Symbols may be drawn upright or on their side; the direction does not change the component or how it is connected. The manual drew the potentiometer upright only for convenience.