RESISTANCE AND RESISTIVITY

The resistance of a conductor is the obstruction offered by the conductor to the flow of electric current through it.

Resistance (R) of a conductor is defined as the ratio of the potential difference (V) across the ends of the conductor to the current (I) flowing through it i.e.

R=V/l

The S.I unit of resistance is Ohm. Where 1 Ohm= 1volt/1ampere=1V/1A

Thus 1 ohm is the resistance of a conductor through which a current of 1 ampere flows when a potential difference of 1 volt is applied across the ends of the conductor.

cause of the resistance of a wire: Resistance of a given conducting wire is due to the collisions of free electrons with each other, the ions or atoms of the conductor and the walls of the conductor during their drift towards the positive end of the conductor which in turn depends upon the arrangements of atoms in the conducting material as well as on the length and thickness of the conducting wire.

R=V/I=ml/Ane²t (discussed in Ohm’s law and its derivation)

Or                                                           R=m/ne² t (l/A)

Or                 R= ρl/A                                   (1)

Where ρ =m/ne²t is the specific resistance or electrical resistivity of the material of the conductor.

From equation (1), we note that the resistance of a given conductor depends upon the various factors as given below:

(a) Length (l). The resistance (R) of a conductor is directly proportional to the length (l) of the conductor that is resistance of the conductor becomes double if its length is doubled.

Thus        R α l                                                                        (2)

(b) Area of cross-section (A). The resistance of a conductor is inversely proportional to the area of cross –section of the conductor that is resistance of the conductor becomes half when its area of cross-section is doubled.

Thus R α 1/A                                                                          (3)

(c) The resistance of a conductor also depends upon the nature of material and temperature of the conductor.

Thus by adding equations(2) and (3) ,we get

R α l/A

Or                      R=ρ l/A                                                             (4)

Where p is constant and is known as specific resistance or electrical resistivity of the material of the conductor.

If l=1.A=1 then from equation (4), R=ρ

Thus, specific resistance (or electrical resistivity) of the material of a conductor is defined as the resistance of unit length and unit area of cross-section of the conductor thus it is also the resistance of unit cube of a material of a conductor.

From equation (4),                                                   ρ=RA/l

Thus unit of ρ=ohm*m²/m=ohm-m or Ω m

As                                     ρ =m/ne²t

The electrical resistivity or specific resistance (ρ) depends upon n and t i.e on nature of the material of the conductor and not on the dimensions of the conductor. If relaxation time t decreases, then resistivity ρ increases as

ρ  α 1/t