## What is Resistance

*Resistance*

Being familiar with Voltage and Resistance is the key to understanding electronic circuitry. Resistance is a measure of how difficult it is for current to flow through something. Some materials such as glass, ceramics, wood and most plastics do not easily carry a current and so are considered to be ‘insulators’. That is why you will see power lines hung from their pylons by a series of ceramic discs. Current flows easily through metals, especially along the surface of the metal, so cables are made from metal wires surrounded by a layer of plastic insulation. The higher grade cables have wire cores made up of many small-diameter strands as this increases the surface area of the metal for any given cross-sectional area of the metal core (it also makes the cable more flexible, and generally, more expensive).

There is a very important, third group of materials, silicon and germanium in particular, which fall between conductors and insulators. Not surprisingly, these are called ‘semi-conductors’ and the amount of current they can carry depends on the electrical conditions in which they are placed. Much, much more about this later on.

While a metal wire carries current very well, it is not perfect at the job and so has some ‘resistance’ to current flowing through it. The thicker the wire, the lower the resistance. The shorter the wire, the lower the resistance. The first researchers used this characteristic to control the way circuits operated. Sometimes, as higher resistances were needed, the researcher used to need long lengths of wire which would get tangled up. To control the wire, a board with nails along each side was used and the wire wound backwards and forwards across the board like this:

When drawing a circuit diagram, the researcher would sketch the wire on the board giving a zig-zag line which is still used today to represent a ‘resistor’ although different methods of construction are now used. An alternative symbol for a resistor is a plain rectangle as shown above.

If a resistor is connected across a battery, a circuit is formed and a current flows around the circuit. The current cannot be seen but that does not mean that it is not there. Current is measured in ‘Amps’ and the instrument used to display it is an ‘ammeter’. If we place an ammeter in the circuit, it will show the current flowing around the circuit. In passing, the ammeter itself, has a small resistance and so putting it in the circuit does reduce the current flow around the circuit very slightly. Also shown is a bulb. If the current flowing around the circuit is sufficiently high and the bulb chosen correctly, then the bulb will light up, showing that current is flowing, while the ammeter will indicate exactly how much current is flowing:

Shown on the right, is the way that this circuit would be shown by an electronics expert (the ‘Resistor’, ‘Ammeter’ and ‘Lamp’ labels would almost certainly not be shown). There are several different styles of drawing circuit diagrams, but they are the same in the basic essentials. One important common feature is that unless there is some very unusual and powerful reason not to do so, every standard style circuit diagram will have the positive voltage line horizontally at the top of the diagram and the negative as a horizontal line at the bottom. These are often referred to as the positive and negative ‘rails’. Where possible, the circuit is drawn so that its operation takes place from left to right, i.e. the first action taken by the circuit is on the left and the last action is placed on the right.

Resistors are manufactured in several sizes and varieties. They come in ‘fixed’ and ‘variable’ versions. The most commonly used are the ‘fixed’ carbon ‘E12’ range. This is a range of values which has 12 resistor values which repeat: 10, 12, 15, 18, 22, 27, 33, 39, 47, 56, 68, 82 and then: 100, 120, 150, 180, 220, 270, 330, 390, 470, 560, 680, 820 and then: 1000, 1200, 1500, 1800, 2200, 2700, 3300, 3900, 4700, 5600, 6800, 8200, etc. etc. Nowadays, circuits often carry very little power and so the resistors can, and are, made in very small physical sizes. The higher the resistance value of a resistor, the less current will flow through it when a voltage is placed across it. As it can be difficult to see printing on small resistors clustered together on a circuit board and surrounded by other larger components, the resistor values are not written on the resistors, instead, the resistors are colour-coded. The unit of measurement for resistors is the ‘ohm’ which has a very small size. Most resistors which you encounter will be in the range 100 ohms to 1,000,000 ohms. The higher the resistance of any resistor, the smaller the current which will flow through it.

The colour code used on resistors is:

0 Black

1 Brown

2 Red

3 Orange

4 Yellow

5 Green

6 Blue

7 Purple (Violet if your colour vision is very good)

8 Grey

9 White

Each resistor has typically, three colour bands to indicate its value. The first two bands are the numbers and the third band is the number of noughts:

Green: 5

Blue: 6

Red: 2 noughts

Value: 5,600 ohms or 5.6K

Yellow: 4

Purple: 7

Green: 5 noughts

Value: 4,700,000 ohms or 4.7M or 4M7

The colour bands are read from left to right and the first band is close to one end of the body of the resistor. There is often a fourth band which indicates the manufacturing tolerance: you can ignore that band.

Examples:

Red, Red, Red: 2 2 00 ohms or 2K2

Yellow, Purple, Orange: 4 7 000 ohms or 47K

Brown, Black, Brown: 1 0 0 ohms or 100R

Orange, Orange, Orange: 3 3 000 ohms or 33K

Brown, Green, Red: 1 5 00 ohms or 1K5

Brown, Green, Black: 1 5 no noughts, or 15 ohms

Blue, Grey, Orange: 6 8 000 ohms or 68K

Brown, Green, Green: 1 5 00000 ohms or 1,500,000 ohms or 1M5

Yellow, Purple, Brown: 4 7 0 ohms

As there are only 12 standard resistor values per decade, there are only 12 sets of the first two colour bands:

**10**: Brown/Black

**12**: Brown/Red

**15**: Brown/Green

**18**: Brown/Grey

**22**: Red/Red

**27**: Red/Purple

**33**: Orange/Orange

**39**: Orange/White

**47**: Yellow/Purple

**56**: Green/Blue

**68**: Blue/Grey

**82**: Grey/Red

The details above give you all the basic information on resistor colour codes but there are a few additional refinements. There is an extra colour band further down the body of the resistor as shown here:

This extra band is used to indicate the manufacturing tolerance of the construction of the resistor. Resistor values are never exact and this rarely has any significant effect on their use in circuits. If some circuit needs very accurate resistor values in it, then buy several resistors of the same nominal value and use an ohm-meter to measure that actual value of each particular resistor and if none are perfect, then use two or more resistors to give the exact value wanted.

The tolerance band has the following codes:

Silver is ± 10% (i.e. a 10K resistor of this type should be between 9K and 11K)

Gold ± 5% (i.e. a 10K resistor of this type should be between 9.5K and 10.5K)

Red ± 2% (i.e. a 10K resistor of this type should be between 9.8K and 10.2K)

Brown ± 1% (i.e. a 10K resistor of this type should be between 9.9K and 10.1K)

Green ± 0.5% (i.e. a 10K resistor of this type should be between 9.95K and 10.05K)

Blue ± 0.25% (i.e. a 10K resistor of this type should be between 9.975K and 10.025K)

Purple ± 0.1% (i.e. a 10K resistor of this type should be between 9.99K and 10.01K)

This type of resistor in the 10% and 5% ranges are the most common as they are the cheapest to buy and so tend to be the most popular. Recently, however, two additions to the coding have been introduced in order to allow for very high specification resistors which the average constructor may never come across. Each of these additions involves one additional colour band. The first additional colour band allows an extra digit in the resistor value, and looks like this:

As before, the colour coding is exactly the same, with the fourth colour band specifying the number of zeros after the digits indicated by the colour bands in front of it. So, in the example shown above, the first band being Red indicates a “2”. The second colour band being Purple indicates a “7”. The third colour band being Green indicates a “5” and the fourth colour band being Red indicates “2 zeros”, so putting those together it produces the value of 27,500 ohms, which can also be written as 27.5 K or more briefly as 27K5.

Another example of this is:

The fourth colour band coding has also been extended to include two other colours: Gold: meaning “no zeros and divided by 10” and Silver: meaning “no zeros and divided by 100”.

So, for example, if the resistor had a fourth colour band which was silver, then the value would be:

Finally, for very high-quality applications (typically military applications), there can be a sixth colour band positioned outside the tolerance band, and that final colour band states how much the resistance value can be expected to alter with changes in temperature. This is not something which is likely to be of any interest to you, but the codes for that final colour band are:

Brown: 0.01% of the resistor value for each degree Centigrade change in temperature.

Red: 0.005% of the resistor value for each degree Centigrade change in temperature.

Yellow: 0.0025% of the resistor value for each degree Centigrade change in temperature.

Orange: 0.0015% of the resistor value for each degree Centigrade change in temperature.

To put this in context, the worst of these represents a change of 1% in the resistor value when moving from the temperature of ice to the temperature of boiling water. Is this something which you really care about? I don’t.

Leaving the details of identifying individual resistors, we now come to the interesting part: what happens when there are several resistors in a circuit. The important thing is to keep track of the voltages generated within the circuit. These define the currents flowing, the power used and the way in which the circuit will respond to external events. Take this circuit:

What is the voltage at point ‘A’? If you feel like saying “Who cares?” then the answer is “you” if you want to understand how circuits work, because the voltage at point ‘A’ is vital. For the moment, ignore the effect of the voltmeter used to measure the voltage.

If R1 has the same resistance as R2, then the voltage at ‘A’ is half the battery voltage, i.e. 4.5 Volts. Half the battery voltage is dropped across R1 and half across R2. It does not matter what the actual resistance of R1 or R2 is, as long as they have exactly the same resistance. The higher the resistance, the less current flows, the longer the battery lasts and the more difficult it is to measure the voltage accurately.

There is no need to do any calculations to determine the voltage at point “A” as it is the ratio of the resistor values which determines the voltage. If you really want to, you can calculate the voltage although it is not necessary. The method for doing this will be shown you shortly. For example, if R1 and R2 each have a value of 50 ohms, then the current flowing through them will be 9 volts / 100 ohms = 0.09 Amps (or 90 milliamps). The voltage drop across R1 will be 50 ohms = Volts / 0.09 amps or Volts = 4.5 volts. Exactly the same calculation shows that the voltage across R2 is exactly 4.5 volts as well. However, the point to be stressed here is that it is the ratio of R1 to R2 which controls the voltage at point “A”.

If R1 has half as much resistance as R2, then half as much voltage is dropped across it as is dropped across R2, i.e. 3 Volts is dropped across R1, giving point ‘A’ a voltage of 6 Volts and that is what the voltmeter will show. Again, it does not matter what the actual value of R1 is in ohms, so long as R2 has exactly twice the resistance (shown by a higher number on the resistor).

If R1 has twice as much resistance as R2, then twice as much voltage is dropped across it as is dropped across R2, i.e. 6 Volts is dropped across R1, giving point ‘A’ a voltage of 3 Volts. Here are some examples with different resistors:

The same division of the supply voltage can be produced by positioning the slider of a variable resistor at different points by rotating the shaft of the device:

This determination of the voltage levels is the key factor to understanding electronic circuitry. The voltage levels control what currents flow and how every circuit will perform, so it is essential to understand what is happening. Stick with this section until you understand it, and if necessary, ask questions about what you find difficult.

First, please understand that a good battery is an unlimited source of voltage and that voltage does not get “used up” when a resistor or whatever is connected across it:

There can be some difficulty in understanding the “0-volt” connection in a circuit. All this means is that it is the return line for current flowing from the battery. Most conventional circuits are connected to both sides of the battery and that allows a current to flow around a closed “circuit” from one terminal of the battery to the other terminal.

It is normal practice to draw a circuit diagram so that the Plus terminal of the battery is at the top and the minus terminal is at the bottom. Many circuit diagrams show the negative line at the bottom connected to the ground or an “earth” connection, which is literally a metal rod driven into the ground to make a good electrical connection to the ground. This is done because the Earth is literally a vast reservoir of negative electricity. However, in reality, most circuits are not connected directly to the Earth in any way. The standard circuit diagram can be visualised as being like a graph of voltage, the higher up the diagram, the higher the voltage.

Anyway, when there is a circuit connected across the battery, the negative or “0V” line just indicates the return path to the battery for the current flow:

This principle applies immediately to the following circuit:

Here we encounter two new components. The first is ‘VR1’ which is a variable resistor. This device is a resistor which has a slider which can be moved from one end of the resistor to the other. In the circuit above, the variable resistor is connected across the 9 Volt battery so the top of the resistor is at +9 Volts (relative to the battery Minus terminal) and the bottom is at 0 Volts. The voltage on the slider can be adjusted from 0 Volts to 9 Volts by moving it along the resistor by turning the shaft of the component (which normally has a knob attached to it).

The second new device is ‘TR1’ a transistor. This semiconductor has three connections: a **C**ollector, a **B**ase and an **E**mitter. If the base is disconnected, the transistor has a very high resistance between the collector and the emitter, much higher than the resistance of resistor ‘R1’. The voltage dividing mechanism just discussed means that the voltage at the collector will therefore, be very near to 9 Volts – caused by the **ratio** of the transistor’s **C**ollector/**E**mitter resistance compared to the resistor “R2”.

If the voltage on the base of the transistor is raised to 0.7 volts by moving the slider of the variable resistor slowly upwards, then this will feed a small current to the base which then flows out through the emitter, switching the transistor ON causing the resistance between the collector and the emitter to drop instantly to a very low value, much, much lower than the resistance of resistor ‘R2’. This means that the voltage at the collector will be very close to 0 Volts. The transistor can therefore be switched on and off just by rotating the shaft of the variable resistor:

If a bulb is used instead of R2, then it will light when the transistor switches on. If a relay or opto-isolator is used, then a second circuit can be operated:

If a buzzer is substituted for R2, then an audible warning will be sounded when the transistor switches on. If a light-dependent resistor is substituted for VR1, then the transistor will switch on when the light level increases or decreases, depending on how the sensor is connected. If a thermistor is used instead of VR1, then the transistor can be switched on by a rise or fall in temperature. The same goes for sound, windspeed, water speed, vibration level, etc. etc. – more of this later.

We need to examine the resistor circuit in more detail:

We need to be able to calculate what current is flowing around the circuit. This can be done using “Ohms Law” which states that “Resistance equals Voltage divided by Current” or, if you prefer: **“Ohms = Volts / Amps”** which indicates the units of measurement.

In the circuit above, if the voltage is 9 Volts and the resistor is 100 ohms, then by using Ohm’s Law we can calculate the current flowing around the circuit as 100 Ohms = 9 Volts / Amps, or Amps = 9 / 100 which equals 0.09 Amps. To avoid decimal places, the unit of 1 milliamp is used. There are 1000 milliamps in 1 Amp. The current just calculated would commonly be expressed as 90 milliamps which is written as 90 mA.

In the circuit above, if the voltage is 9 Volts and the resistor is 330 ohms, then by using Ohm’s Law we can calculate the current flowing around the circuit as 330 = 9 / Amps. Multiplying both sides of the equation by “Amps” gives: Amps x 330 ohms = 9 volts. Dividing both sides of the equation by 330 gives: Amps = 9 volts / 330 ohms which works out as 0.027 Amps, written as 27 mA.

Using Ohm’s Law we can calculate what resistor to use to give any required current flow. If the voltage is 12 Volts and the required current is 250 mA then as Ohms = Volts / Amps, the resistor needed is given by: Ohms = 12 / 0.25 Amps which equals 48 ohms. The closest standard resistor is 47 ohms (Yellow / Purple / Black).

The final thing to do is to check the wattage of the resistor to make sure that the resistor will not burn out when connected in the proposed circuit. The power calculation is given by: **Watts = Volts x Amps**. In the last example, this gives Watts = 12 x 0.25, which is 3 Watts. This is much larger than most resistors used in circuitry nowadays.

Taking the earlier example, Watts = Volts x Amps, so Watts = 9 x 0.027 which gives 0.234 Watts. Again, to avoid decimals, a unit of 1 milliwatt is used, where 1000 milliwatts = 1 Watt. So instead of writing 0.234 Watts, it is common to write it as 234 mW.

This method of working out voltages, resistances and wattages applies to any circuit, no matter how awkward they may appear. For example, take the following circuit containing five resistors:

As the current flowing through resistor ‘R1’ has then to pass through resistor ‘R2’, they are said to be ‘in series’ and their resistances are added together when calculating current flows. In the example above, both R1 and R2 are 1K resistors, so together they have a resistance to current flow of 2K (that is, 2,000 ohms).

If two, or more, resistors are connected across each other as shown on the right hand side of the diagram above, they are said to be ‘in parallel’ and their resistances combine differently. If you want to work out the equation above, for yourself, then choose a voltage across Rt, use Ohm’s Law to work out the current through Ra and the current through Rb. Add the currents together (as they are both being drawn from the voltage source) and use Ohm’s Law again to work out the value of Rt to confirm that the 1/Rt = 1/Ra + 1/Rb + …. equation is correct. A spreadsheet is included which can do this calculation for you.

In the example above, R4 is 1K5 (1,500 ohms) and R5 is 2K2 (2,200 ohms) so their combined resistance is given by 1/Rt = 1/1500 + 1/2200 or Rt = 892 ohms (using a simple calculator). Apply a common-sense check to this result: If they had been two 1500 ohm resistors then the combined value would have been 750 ohms. If they had been two 2200 ohm resistors then the combined value would have been 1100 ohms. Our answer must therefore lie between 750 and 1100 ohms. If you came up with an answer of, say, 1620 ohms, then you know straight off that it is wrong and the arithmetic needs to be done again.

So, how about the voltages at points ‘A’ and ‘B’ in the circuit? As R1 and R2 are equal in value, they will have equal voltage drops across them for any given current. So the voltage at point ‘A’ will be half the battery voltage, i.e. 6 Volts.

Now, point ‘B’. Resistors R4 and R5 act the same as a single resistor of 892 ohms, so we can just imagine two resistors in series: R3 at 470 ohms and R4+R5 at 892 ohms. Common-sense rough check: as R3 is only about half the resistance of R4+R5, it will have about half as much voltage drop across it as the voltage drop across R4+R5, i.e. about 4 Volts across R3 and about 8 Volts across R4+R5, so the voltage at point ‘B’ should work out at about 8 Volts.

We can use **Ohm’s Law** to calculate the current flowing through point ‘B’:

**Ohms = Volts / Amps**, ( or Amps = Volts / Ohms or Volts = Ohms x Amps)

(470 + 892) = 12 / Amps, so

Amps = 12 / (470 + 892)

Amps = 12 / 1362 or

Amps = 0.00881 Amps (8.81 milliamps).

Now that we know the current passing through (R4+R5) we can calculate the exact voltage across them:

Resistance = Volts / Amps so

892 = Volts / 0.00881 or

Volts = 892 x 0.00881

Volts = 7.859 Volts.

As our common-sense estimate was 8 Volts, we can accept 7.86 Volts as being the accurate voltage at point ‘B’.

**The Potentiometer**. Just before we leave the subject of resistors and move on to more interesting subjects, we come across the term ‘potentiometer’. This term is often shortened to ‘pot’ and many people use it to describe a variable resistor. I only mention this so that you can understand what they are talking about. A variable resistor is not a potentiometer and really should not be called one. You can skip the rest of this part as it is not at all important, but here is what a potentiometer is:

A fancy name for voltage is ‘potential’, so a circuit powered by a 12 Volt battery can be described as having a ‘potential’ of zero volts at the negative side of the battery and a ‘potential’ of plus twelve volts at the positive side of the battery. Ordinary folks like me would just say ‘voltage’ instead of ‘potential’.

When a voltmeter is used to measure the voltage at any point in a circuit, it alters the circuit by drawing a small amount of current from the circuit. The voltmeter usually has a high internal resistance and so the current is very small, **but** even though it is a small current, it **does** alter the circuit. Consequently, the measurement made is not quite correct. Scientists, in years gone by, overcame the problem with a very neat solution – they measured the voltage without taking **any** current from the circuit – neat huh? They also did it with a very simple arrangement:

They used a sensitive meter to measure the current. This meter is built so that the needle is in a central position if no current is flowing. With a positive current flowing, the needle deflects to the right. With a negative current flowing, the needle moves to the left. They then connected a variable resistor ‘VR1’ across the same battery which was powering the circuit. The top end of VR1 is at +12 Volts (they called that ‘a potential of +12 Volts’) and the bottom end of VR1 is at zero volts or ‘a potential of zero volts’.

By moving the slider of VR1, any voltage or ‘potential’ from zero volts to +12 Volts could be selected. To measure the voltage at point ‘A’ without drawing any current from the circuit, they would connect the meter as shown and adjust the variable resistor until the meter reading was exactly zero.

Since the meter reading is zero, the current flowing through it is also zero and the current taken from the circuit is zero. As no current is being taken from the circuit, the measurement is not affecting the circuit in any way – very clever. The voltage on the slider of VR1 exactly matches the voltage at point ‘A’, so with a calibrated scale on the variable resistor, the voltage can be read off.

The slick piece of equipment made up from the battery, the variable resistor and the meter was used to measure the ‘potential’ (voltage) at any point and so was called a ‘potentiometer’. So, please humour me by calling a variable resistor a ‘variable resistor’ and not a ‘potentiometer’. As I said before, this is not at all important, and if you want to, you can call a variable resistor a ‘heffalump’ so long as you know how it works.

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