if the diameter of a conductor is decreased by 4 times and the length is increased by 2times find the new resistance.If original resistance is 25 ohms.
Answers
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.