Resistivity
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
The SI unit of resistivity
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 . What would be the resistance of another wire of the same material having length
and area of cross-section 2.5 A?
Solution: For first wire, length = l, area of cross-section = A
and resistance,
i.e.,
....(i)
For second wire, length = , area of cross-section = 2.5 A
and resistance
,
Putting the value from Equation I
So, the resistance of that wire is .
Calculate the resistance of a copper wire of length 1 m and area of cross section | |||
| Right Option : A | |||
| View Explanation | |||
Reciprocal of resistivity( | |||
| Right Option : D | |||
| View Explanation | |||
A wire of length 3 m and area of cross section a. What is the formula for resistivity of the wire and what is the unit of it . b. Calculate the resistivity of wire.
| |||
| Right Option : C | |||
| View Explanation | |||
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