prove that the resistivity of the conductor will not change if we doubled the length of the wire keeping the area of cross section same ?
Answers
Explanation:
The electrical resistance of a wire would be expected to be greater for a longer wire, less for a wire of larger cross sectional area, and would be expected to depend upon the material out of which the wire is made.The resistance of a wire can be expressed as R=ρ
A
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 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.
That is, if L becomes 2 L, R becomes 2 R. R
′
=ρ
A
2L
. So, R = 2R'.
Hence, If the length of a wire is doubled, then its resistance becomes 2 times.