Conductance
The reciprocal of resistance of a conductor is called its conductance (G). If a conductor has resistance R, then its conductance G is given by;
G = 1/R
The SI unit of conductance is mho (i.e., ohm spelt backward). These days, it is a usual practice to use siemen as the unit of conductance. It is denoted by the symbol S.
Conductivity: The reciprocal of resistivity of a conductor is called its conductivity. It is denoted by the symbol s . If a conductor has resistivity r , then its conductivity is given by;
We know that 
. Clearly, the SI unit of conductivity is siemen metre_1 (Sm_1).
Classification of Materials on the basis of Electrical Conductivity
On the basis of electrical conductivity, the materials are classified as (i) insulators (ii) con-ductors (iii) semiconductors.
Insulators: Those materials whose electrical conductivity is negligible are called insulators, e.g. mica, glass, wood, rubber etc. When a small potential difference is applied across an insu-lator, practically no current flows through it. There are practically no free electrons in an insulator. For this reason, they are poor conductors of electric current as well as heat.
Conductors: Those materials whose electrical conductivity is very high are called conductors, e.g. copper, silver, aluminium etc. Metals are generally good conductors. When a small potential difference is applied across a conductor, a large current flows through it. There are a large number of free electrons in a conductor. For this reason, they are good conductors of electric current as well as heat.
Semiconductors: Those materials whose electrical conductivity lies inbetween conductors and insulators are called semiconductors, e.g. germanium, silicon etc. When a small potential difference is applied across a semiconductor, a very weak current flows through it.
The conductivity of a semiconductor can by increased by adding controlled amount of suitable impurities. Semiconductors are being widely used in the manufacture of a variety of electronic devices.
Carbon Resistors
A component whose function in a circuit is to provide a specified value of resistance is called a resistor. The most commonly used resistors in electrical and electronic circuits are the carbon resistors. A carbon resistor is made from powdered carbon mixed with a binding material and baked into a small tube with a wire attached to each end. These small-sized resistors are manufactured in values from a fraction of an ohm to several million ohms.
Colour code for carbon resistors: Since a carbon resistor is physically quite small, it is more convenient to use a colour code indicating the resistance value than to imprint the numerical value on the case. In this scheme, there are generally four colour bands A, B, C and D printed on the body of the resistor as shown in
Fig. The first three colour bands (A, B and C) give the value of the resistance while the fourth band (D) tells about the tolerance in percentage. The table below shows the colour code for resistance values and colour code for tolerance. 
| Colour Code for Resistance Values | |||
|---|---|---|---|
| Black | 0 | Green | 5 |
| Brown | 1 | Blue | 6 |
| Red | 2 | Violet | 7 |
| Orange | 3 | Grey | 8 |
| Yellow | 4 | White | 9 |
| Color code for Tolerance Values | |
|---|---|
| Gold | ± 5% |
| Silver | ± 10% |
| No Color | ± 20% |
To read the resistance value, we refer to the first three colour bands (A, B and C). The first two colour bands (A, B) specify the first two digits of the resistance value and the third colour band (C) gives the number of zeros that follow the first two digits. Suppose the first three colour bands (A, B, C) on the resistor are red, brown, orange respectively. Then value of the resistance is 21, 000 W.
Red: 2
Brown: 1
Orange: 000
Hence, value = 21,000
The fourth band D gives the value of tolerance in percentage. If colour of the fourth band is gold, tolerance is ± 5 per cent and if silver, then tolerance is ± 10 per cent. If the fourth band is omitted, the tolerance is assumed to be ± 20 per cent. 
Note: In order to remember the colour code, the above sentence may be helpful.
Temperature Dependence of Resistivity
When temperature of the conductor increases, due to thermal agitation, collision between electrons and atoms increases and hence relaxation time 
between the successive collision decreases thus drift speed decreases. Due to this the conductivity decreases and the resistivity increases as the temperature increases. For small temperature variations,
where 
and 
are resistivities at temperatures T and T0 respectively and a is a constant for the given material. The constant a is called the temperature coefficient of resisitivity.
As temperature changes, the length and the area also change. But these changes are quite small and the factor l/A may be treated as constant. Then 
and hence
[If (
) £ 300°C]Important Points
F If R1 and R2 are the resistances at t1oC and t2oC respectively then 
.
If DT > 300°C then 
where a and b are temperature coefficient of resistance (unit = per°C)
For metals their temperature coefficient of resistance a> 0. So resistance increases with temperature.
For solid non-metal a = 0. So resistance is independence of temperature.
For semi-conductor a < 0 i.e. resistance decreases with temperature rise.
For electrolyte a < 0 i.e. resistance decreases with temperature rise.
At low temperature, the resistance of super conductors becomes exactly zero. (e.g. Hg below 4.2 K or Pb below 7.2 K).