Resistance, Specific Resistance and Conductance and Conductivity

 1). Resistance-

-The opposition offered by a substance to the flow of electric current is called its resistance.

-Since current is the flow of free electrons, resistance is the opposition offered by the substance to the flow of free electrons. This opposition occurs because atoms and molecules of the substance obstruct the flow of these electrons.

-Certain substances(e.g. metals such as silver, copper, aluminum etc.) offer very little opposition to the flow of electric current and are called conductors.

-On the other hand, those substances which offer high opposition to the flow of electric current (i.e. flow of free electrons) are called insulators e.g. glass, rubber, mica, dry wood etc.

Unit of resistance-

-The practical unit of resistance is ohm.

-It is represented by the symbol 

Symbol of ohm

-  ONE ohm can be defined as : 

-A wire is said to have a resistance of 1 ohm if a potential difference of 1 volt across its ends causes 1 ampere to flow through it. see fig. below.

Factors Effecting the Resistance-

The resistance R of a conductor then-

-(i) is directly proportional to its length i.e. 

 R ∝ l 

-(ii) is inversely proportional to its area of X-section i.e.

 R ∝ 1/ a 

-(iii) depends upon the nature of material.

-(iv) depends upon temperature. 

 From the first three points (leaving temperature for the time being), 

we have,

where ρ (Greek letter ‘Rho’) is a constant and is known as resistivity or specific resistance of the material. Its value depends upon the nature of the material.

2). Specific Resistance or Resistivity-

-We have seen above that 

 If l = 1 meter, a = 1 meter square  , then, R = ρ 

-Hence specific resistance of a material is the resistance offered by 1 m length of wire of material having an area of cross-section of 1 meter square. [See Fig. below i and  ii].

-Specific resistance can also be defined in another way. 

-Take a cube of the material having each side 1 m. Considering any two opposite faces, the area of cross-section is 1 m2 and length is 1 m [ Fig. (ii)] i.e. l = 1 meter, a = 1 meter square.

-Hence specific resistance of a material may be defined as the resistance between the opposite faces of a meter cube of the material. 

Unit of resistivity- 

-We know that-

-Hence the unit of resistivity will depend upon the units of area of cross-section (a) and length (l). (i) If the length is measured in meters and area of cross-section in m2 , then unit of resistivity will be ohm-meter (Ω m).

3). 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 

                 Whereas resistance of a conductor is the opposition to current flow, the conductance of a conductor is the inducement to current flow.

- 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. 

4). Conductivity- 

-The reciprocal of resistivity of a conductor is called its conductivity. 

-It is denoted by the symbol σ. 

-If a conductor has resistivity ρ, then its conductivity is given by ;

 

 Conductivity,       

  We know that 

Clearly, the SI unit of conductivity is Siemen metre−1 (S m−1).