Resistance and Resistivity:
What is Resistance?
Resistance of the conductor is defined as the obstruction posed by the conductor to the flow of electric current.
|From Ohm’s Law, R = V / I|
Hence Resistance of the conductor may also be defined as the ratio of potential difference (V) between ends of the conductor to the current (I) flowing through it.
Cause of Resistance:
Resistance of the conductor is due to the collisions of free electrons with the atoms/ions of the conductor while drifting towards the positive end of a conductor. We know-
| R = V/I = ml / nAe2τ|
R = m/ne2τ X l/A
Put m / ne2τ = ρ = Specific resistance or resistivity of the material of the conductor.
|R = ρ X l/A|
Hence the resistance of the conductor depends upon the dimensions of the conductor and also on the nature of the material of the conductor.
Units of Resistance:
(1) The S.I. unit of resistance is Ohm.
|We know, R = V / I |
1 Ohm = 1 Volt / 1 Ampere
Hence the resistance of the conductor is said to be one ohm if a current of one ampere flows through the conductor against a potential difference of 1 volt applied across its ends.
(2) The C.G.S. or electrostatic unit of resistance is stat-ohm.
| We know, R = V / I |
1 Stat-ohm = 1 Stat-volt / 1 Stat-ampere
Hence the resistance of a conductor is said to be 1 stat-ohm if a current of 1 stat-ampere flows through the conductor when a potential difference of 1 stat-volt is applied across its ends.
(3) International Ohm.
It is defined as the resistance of a 106.3 cm long mercury column of 1 cm2 cross-sectional area and mass 14.45 gram at 0°C.
What is Resistivity?
We know, the resistance of the conductor is directly proportional to the length of the conductor i.e.
|R ∝ l …………(1)|
Also, the resistance of the conductor is inversely proportional to the area of cross-section of the conductor i.e.
|R ∝ 1 / A …………(2)|
Combining (1) and (2)-
| R ∝ l / A|
R = ρ X l/A …………(3)
Where ρ is the constant of proportionality and is called resistivity or specific resistance of the material of the conductor. Its value depends upon the nature of the material of the conductor.
If l = 1 and A = 1, then from (3)
|R = ρ|
Hence specific resistance or resistivity of the material of the conductor is defined as the resistance of the conductor having unit dimensions. The S.I. unit of resistivity if ohm-metre.
Note: The resistivity of silver is 1.47 X 10-8 ohm-metre, the resistivity of copper is 1.72 X 10-8 ohm-metre, the resistivity of germanium (semi-conductor) is 0.60 ohm-metre and the resistivity of glass (insulator) is 1010 – 1014 ohm-metre.