Resistance, Resistivity and Conductivity
Resistance R in an electric conductor is defined as the quotient of the potential difference V, across the conductor and the current I, flowing through it. Mathematically we have:
R = V/I
The SI unit of resistance is ohm (W), and it is defined as the resistance of a conductor that has current of one Ampere flowing through it and a potential difference of one Volt across it. 1 W = 1V/A. The resistance of a conductor is directly proportional to its length (L) and inversely proportional to its cross-sectional area (A). The proportionality constant is defined as the resistivity (r) of the material of the conductor. The reciprocal of the resistivity gives the conductivity (s) of the material. Mathematically the concepts can be represented by the following equations:
R = rL/A
r = 1/ s
From the field concept point of view, resistivity is also the proportionality constant between the electric field and the current density. Both the quantities are vectors and as mentioned above, the direction of the current density is the same as the electric field producing it. The ratio of the magnitudes of the electric field and the current density is defined as the resistivity. So:
r = E/J
E = rJ
The change in resistivity of a material is also directly proportional to a change in ambient temperature. It is represented by the equation:
(r - r0) = r0 a (T – T0)
Where a, is the mean temperature coefficient of resistivity of the conductor material.
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Quiz
If the radius of a circular conductor is doubled, how will the resistance be affected?
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