3. Resistor

Resistors (R), are the most commonly used of all electronic components, to the point where they are almost taken for granted. There are many different resistor types available with their principal job being to "resist" the flow of current through an electrical circuit, or to act as voltage droppers or voltage dividers. They are "Passive Devices", that is they contain no source of power or amplification but only attenuate or reduce the voltage signal passing through them. When used in DC circuits the voltage drop produced is measured across their terminals as the circuit current flows through them while in AC circuits the voltage and current are both in-phase producing 0^o phase shift.

Resistors produce a voltage drop across themselves when an electrical current flows through them because they obey Ohm's Law, and different values of resistance produces different values of current or voltage. In all Electrical and Electronic circuit diagrams and schematics, the most commonly used resistor symbol is that of a "zigzag" type line with the value of its resistance given in Ohms, Ω.

a. Resistor Symbol

The symbol used in schematic and electrical drawings for a Resistor can either be a "zigzag" type line or a rectangular box.

All modern resistors can be classified into four broad groups;

1. Carbon Composition Resistor - Made of carbon dust or graphite paste, low wattage values
2. Film or Cermet Resistor - Made from conductive metal oxide paste, very low wattage values
3. Wire-Wound Resistors. - Metallic bodies for heatsink mounting, very high wattage ratings
4. Semiconductor Resistors - High frequency/precision surface mount thin film technology

b. The Standard Resistor Colour Code Chart.

c. The Resistor Colour Code Table.

Colour		Digit	Multiplier	Tolerance
	Black	0	1
	Brown	1	10	± 1%
	Red	2	100	± 2%
	Orange	3	1K
	Yellow	4	10K
	Green	5	100K	± 0.5%
	Blue	6	1M	± 0.25%
	Violet	7	10M	± 0.1%
	Grey	8
	White	9
	Gold		0.1	± 5%
	Silver		0.01	± 10%
	None			± 20%

d. Calculating Resistor Values

The Resistor Colour Code system is all well and good but we need to understand how to apply it in order to get the correct value of the resistor. The "left-hand" or the most significant coloured band is the band which is nearest to a connecting lead with the colour coded bands being read from left-to-right as follows:

Digit, Digit, Multiplier = Colour, Colour x 10 ^colour  in Ohm's (Ω's)

For example, a Resistor has the following coloured markings;

Yellow Violet  Red =  4  7  2 =  4  7 x 10 ² = 4700Ω or 4k7.

The fourth band is used to determines the percentage tolerance of the resistor and is given as;

Brown = 1%, Red = 2%, Gold = 5%, Silver = 10 %

If resistor has no fourth tolerance band then the default tolerance would be at 20%.

e. Connecting Resistors in Series

Resistors can be connected together in either a series connection, or a parallel connection or combinations of both series and parallel together, to produce more complex networks whose overall resistance is a combination of the individual resistors. Whatever the combination, all resistors obey Ohm's Law and Kirchoff's Circuit Laws.

f. Resistors in Series.

Resistors are said to be connected in "Series", when they are daisy chained together in a single line. Since all the current flowing through the first resistor has no other way to go it must also pass through the second resistor and the third and so on. Then, resistors in series have a Common Current flowing through them, for example:

I_R1 = I_R2 = I_R3 = I_AB = 1mA

In the following example the resistors R₁, R₂ and R₃ are all connected together in series between points A and B.

g. Series Resistor Circuit

As the resistors are connected together in series the same current passes through each resistor in the chain and the total resistance, R_T of the circuit must be equal to the sum of all the individual resistors added together. That is

R_T = R₁ + R₂ + R₃

By taking the individual values of the resistors in our simple example above, the total resistance is given as:

R_T = R₁ + R₂ + R₃ = 1kΩ + 2kΩ + 6kΩ = 9kΩ

h. The Potential Divider.

Connecting resistors in series like this across a single DC supply voltage has one major advantage; different voltages appear across each resistor producing a circuit called a Potential or Voltage Divider Network. The circuit shown above is a simple potential divider where three voltages 1V, 2V and 6V are produced from a single 9V supply. Kirchoff's voltage laws states that "the supply voltage in a closed circuit is equal to the sum of all the voltage drops (IR) around the circuit" and this can be used to good effect.

The basic circuit for a potential divider network (also known as a voltage divider) for resistors in series is shown below.

i. Potential Divider Network

j. Resistors in Parallel

Resistors are said to be connected together in "Parallel" when both of their terminals are respectively connected to each terminal of the other resistor or resistors. The voltage drop across all of the resistors in parallel is the same. Then, Resistors in Parallel have a Common Voltage across them and in our example below the voltage across the resistors is given as:

V_R1 = V_R2 = V_R3 = V_AB = 12V

In the following circuit the resistors R₁, R₂ and R₃ are all connected together in parallel between the two points A and B.

k. Parallel Resistor Circuit

In the previous series resistor circuit we saw that the total resistance, R_T of the circuit was equal to the sum of all the individual resistors added together. For resistors in parallel the equivalent circuit resistance R_T is calculated differently.

l. Parallel Resistor Equation

Here, the reciprocal (1/Rn) values of the individual resistances are all added together instead of the resistances themselves. This gives us a value known as Conductance, symbol G with the units of conductance being the Siemens, symbol S. Conductance is therefore the reciprocal or the inverse of resistance, (G = 1/R). To convert this conductance sum back into a resistance value we need to take the reciprocal of the conductance giving us then the total resistance, R_T of the resistors in parallel.

Example No1

For example, find the total resistance of the following parallel network

Then the total resistance R_T across the two terminals A and B is calculated as:

This method of calculation can be used for calculating any number of individual resistances connected together within a single parallel network. If however, there are only two individual resistors in parallel then a much simpler and quicker formula can be used to find the total resistance value, and this is given as:

Next Topic will be on Inductor