Define resistivity. Write an expression for the resistivity of a substance. Give the meaning of each symbol. b) State the SI unit of resistivity. c) Distinguish between resistance and resistivity. d) Name two factors on which the resistivity of a substance depends and two factors on which it does not depend. e) The resistance of a metal wire of length 1m is 26Ω at 20⸰C. if the diameter of the wire is 0.3mn, what will be the resistivity of the metal at that temperature? Answer:
Resistivity is defined as:
ρ = R×A/l where,
R is the resistance of the conductor
A is the cross-sectional area of the conductor l is the length of the conductor
- The SI unit of resistivity is Ohm-meter
- Following are the differences between resistance and resistivity:
|
Resistance |
Resistivity |
|
Resistance is the property of the conductor |
Resistivity is the property of the material used in the conductor |
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In a conductor, resistance is defined as the opposing force to the flow of electric current |
Resistivity is the opposing force of the flow of electric current in a rod such that the length of the rod is 1m and the cross-sectional area of the rod is 1m2 |
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Parameters such as length, nature of the material used in a conductor, and thickness of the conductor determine the resistance |
Parameters such as length and thickness do not determine the resistivity of the conductor |
- Nature of the material and the temperature of the material determine the resistivity of a Resistivity is independent of the length and the thickness of the conductor.
- Given, l = 1m
R = 26Ω
r = d/2
= 0.3/2
= 0.15mm
= 0.15×10-3m
We know that, ρ = R×A/l
= 1.83×10-6Ωm