The resistivity ρ of the material is related the length L, diameter d and resistance R of the wire. Derive an expression for the resistivity using the method of dimension.
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The resistivity of a material is the resistance of a wire of that material of unit length and unit cross-sectional area. The unit for resistivity is the ohm-metre. The resistivity of a material depends on its nature and the temperature of the conductor, but not on its shape and size. A good conductor has less resistivity, whereas a bad conductor or insulator has high resistivity. The resistivity of semi-conductors lies between that of conductors and insulators. The resistivity of a metallic conductor increases with an increase in its temperature, whereas the resistivity of a semi-conductor decreases with an increase in its temperature.
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