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Portion covered : V-I characteristics (linear and non-linear), electrical energy and power, electrical resistivity and conductivity. Carbon resistors, colour code for carbon resistors; series and parallel combinations of resistors; temperature dependence of resistance and resistivity.

A plot of V versus I is called a V-I characteristic

The V-I characteristic of a conductor that obeys Ohm’s Law is a straight line.

RESISTORS Page of 2 6 V-I characteristic of an Ohmic conductor ( eg. metals) Note that the slope and therefore resistance is constant.

Limitation of Ohm’s Law Not all conductors obey Ohm’s Law. Even the ones that do , do so only when physical conditions remain unchanged. By physical condition we mean variables like temperatures, pressure etc. In such cases V and I are not proportional. When V is not proportional to I , Ohm’s law is not valid. Below are some characteristics of some non-ohmic conductors. These are called non ohmic or non-linear conductors. These materials have wide ranging applications.

Resistivity (ρ)

Depending on their resistivity values materials are classified as conductors, insulators and semi conductors. ρconductor > ρ semiconductor >ρinsulator

Conductors The resistivity of metallic conductors are very low and they increase with temperature. That is they have a positive temperature coefficient of resistivity (α).

Note: Certain alloys such as manganin, constantan, nichrome very low temperature coefficient of resistance. This means their resistances do not vary with temperature. Coiled wires of such allows are used in the construction of resistance boxes in the laboratory.

Material ρ (Ωm) at 0oC α (oC)-1

Silver 1.6 x 10-8 0.0041

Copper 1.7 x 10-8 0.0068

Mercury 98 x 10-8 0.0009

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Semiconductors Semiconductors have very high resistivity. They have negative temperature coefficient of resistance. This means their resistance increase with increase in temperature.

Carbon Resistor Carbon ( graphite) has a very low temperature coefficient of resistance. It also has a much higher resistivity than alloys such as constantan. Carbon is therefore increasingly used to make resistors in electronic circuits.

Note that carbon is strictly a semiconductor because of its negative temperature coefficient of resistance.

Advantages of carbon resistor over alloys

1. Alloys have low resistivity. Therefore they need to be coiled to make resistors ( longed the length higher the resistance). This makes them very bulky. Carbon resistors are more compact and can be printed directly onto circuit boards.

2. Carbon resistors are much cheaper to produce.

Insulators

Insulators have very high resistivity and their resistivity does not change with temperature.

Material ρ (Ωm) at 0oC α (oC)-1

Alloys ( maganin etc) 48 x 10-8 0.002 x 10-3

Material ρ (Ωm) at 0oC α (oC)-1

Germanium 0.46 -0.05

Silicon 2300 -0.07

Material ρ (Ωm) at 0oC α (oC)-1

Carbon 3.5 x 10-5 -0.0005

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Colour Code of Carbon Resistors

A carbon resistors looks like this. Note the band of colours.

RESISTORS Page of 5 6The colour code enables us to read the resistance values according to the following schematic.

Mnemonic to remember the colour code

Bright Boys Rave Over Young Girls But Veto Getting Wed.

Black, Brown, Red, Orange , Yellow, Blue Violet, White

Colour Number Multiplier Tolerance (%)

BLACK 0 1

BROWN 1 101

RED 2 102

ORANGE 3 103

YELLOW 4 104

GREEN 5 105

BLUE 6 106

VIOLET 7 107

GRAY 8 108

WHITE 9 109

GOLD 5

SILVER 10

NO COLOR 15

RESISTORS Page of 6 6How to use the colour code?

Start from the left - Digit, Digit, Multiplier = Colour, Colour x 10 colour  in Ohm’s (Ω)

If the first three bands are yellow , red and violet ( see diagram below )Yellow Violet Red = 4 7 2 = 4 7 x 102 = 4700Ω or 4k7 Ohm.

The fourth and fifth bands are used to determine the percentage tolerance of the resistor. Resistor tolerance is a measure of the resistors variation from the specified resistive value.

For the given resistor the colour code used to denote the tolerance rating of a resistor is given as:The colour code used to denote the tolerance rating of a resistor is given as:

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

Look at this example from a text book to understand further .

Also note :

Where resistivity unit conductivity ( unit where S = Siemens

The SI unit of conductance is Siemens (S). Another unit is mho ( ohm - written backwards ),

ρ =1σ

ρ = ( Ωm)σ = S /m)

Conductance =1R