A conductor of length l and uniform area of cross-section A has resistance R. What is the resistance of another conductor of length l /2 ,of the same material and double the area of cross-section?What happens to its resistivity when its length and area of cross-section change?Justify your answer
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The resistance of a wire can be expressed as
R=ρ
A
L
A=ρ
R
L
where,
ρ - Resistivity - the factor in the resistance which takes into account the nature of the material is the resistivity
L - Length of the conductor
A - Area of a cross-section of the conductor.
From this relation, we observe that the length is directly proportional to the resistance and the area of cross-section is inversely proportional to the resistance.
In this case, the length of the conductor is doubled (2L) and so the resistance will be 2R. For the resistance to remain the same as R, the area of cross-section is also doubled as 2A.
Hence, the area of cross-section is 2A.
R=ρ
A
L
A=ρ
R
L
where,
ρ - Resistivity - the factor in the resistance which takes into account the nature of the material is the resistivity
L - Length of the conductor
A - Area of a cross-section of the conductor.
From this relation, we observe that the length is directly proportional to the resistance and the area of cross-section is inversely proportional to the resistance.
In this case, the length of the conductor is doubled (2L) and so the resistance will be 2R. For the resistance to remain the same as R, the area of cross-section is also doubled as 2A.
Hence, the area of cross-section is 2A.
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