Know Current Electricity | Part 2 | Definitions, Formula, S.I. units

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Know Current Electricity Part 1

Specific resistance (Resistivity)

At a particular temperature, the electric resistance of a conductor is observed to depend on the following factors -

1.      Length of the conductor
2.      Area of cross section of the conductor
3.      Nature of material of the conductor

    It is found that, the resistance (R) of a conductor is directly proportional to its length (l) and inversely proportional to its area of cross section (A).

Formula

     R ∝ l            and           R ∝ 1 

                                                 A  

                    or     R ∝  l

                                    A

                   or      R = l 

                                   A

Where, ρ is a constant of proportionality and is called a specific resistance 

                       ρ  = RA 

                                l

         Where, R is in 

                      A is in m^2

                      l  is in m

                  ρ =  1Ω  1m^2

                            1m

                  ρ = 1        Ωm

       The resistivity of material is the resistance of the wire of unit length and unit area of cross-section.

Note- Resistance of different materials of same dimensions will be different.

Conductivity

     Reciprocal of the resistivity is called conductivity of the material. 

               σ   = 1              (1/ohm - m)
                        ρ

S.I. unit - Siemens/metre

Resistivity depends upon

Conductors: Those materials whose resistivity is negligibly small are called conductor e.g. silver, copper, aluminum, etc.

Insulator: Those materials whose resistivity is very are called insulator e.g. glass, rubber, etc.

Semiconductor: Those materials whose resistivity lies between that of conductor and insulators are called semiconductor e.g. silicon, germanium, etc.

Temperature dependence of resistance

Resistance of any material depends on its temperature. For metals, its found that, the resistance increases with temperature. The resistance temperature relationship for metallic conductor is quite linear as shown below

                       

   

Temperature coefficient of resistance

Formula

             α = Rt - R0

                     R0t

  Note- The temperature coefficient of resistance is defined as the increase in resistance per unit original resistance at 0°C, per degree rise in temperature.

          The resistivity of metal conductor increases with temperature. Such materials have a positive temperature coefficient (PTC), where Semiconductor have a negative temperature coefficient (NTC).

          The resistance of PTC thermistors increase non-linearly with temperature and resistance of NTC thermistors decreases non-linearly with temperature.

Superconductivity 

We know that resistivity of material depends on temperature. For some metals and alloy, resistivity suddenly become zero at a particular low temperature. The temperature is called critical temperature (Tc). That is such materials lose their resistivity completely and become perfect conductors,
e.g. resistance of mercury falls to 0Ω at 4.2K.