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Physics / Electricity / Resistivity
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Resistivity

Resistivity of a conductor is defined as the resistance of a conductor of unit length and unit area of cross-section. Its SI unit is ohm-metre (Q-m). The resistivity of a material does not depend on its length or thickness but depends on the nature of the substance and temperature. It is a characteristic property of the material of the conductor and varies only, if its temperature changes

  large dpi{100} large rho =frac{RA}{L}    

  large therefore  The SI unit of  resistivity

large rho =frac{ohmtimes m^{2}}{m}=ohmtimes meter(Omega m)

Resistance Depends on Temperature:

Thus, the resistance of a pure metallic wire is directly proportional to its absolute temperature. The resistivity of alloys also increases with rise in temperature, but this increase in much smaller compared to pure metals. On decreasing temperature of some metals, the resistance becomes zero at a certain temperature.

For example : Resistance of mercury becomes zero at 4.2 K temperature.

There are certain alloys such as manganin, constantan, nichrome, etc.., whose resistivity is little affected by temperature, that is, their temperature coefficient of resistance is negligible. On account of their high resistivity and negligible temperature coefficient of resistance, these alloys are used to make wires for standard resistance, resistance boxes, etc.

Illustration: A wire of given material having length l and area of cross-section A has a resistance of 10;Omega. What would be the resistance of another wire of the same material having length l/4 and area of cross-section 2.5 A?

Solution:  For first wire, length = l, area of cross-section = A

 and resistance,     R_{1}=10;Omega ,

i.e.,                       large R_{1}=frac{rho l}{A}=10;Omega  

                          large rho =frac{10A}{l} ....(i)

For second wire, length = large l/4, area of cross-section = 2.5 A

and resistance

,large R_2=rho frac{l/4}{2.5A}

Putting the value from Equation I

large R_2=frac{10A}{l};X;frac{l}{4times2.5A}= 1;Omega

So, the resistance of that wire is large 1Omega.


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