Saturday, June 9, 2018

If the area of a conductor doubled and also the length, what would be the change in the new resistance?

The resistance of a conductor is computed using the formula:
R = rho * L/A
where
rho is the resistivity of the material
L is the length of the conductor, and
A is the cross-sectional area of the conductor.
For this problem, let the length of the conductor be y and its cross-sectional area be x. Applying the formula above, the resistance of the conductor will be:
R =rho * y/x
When the length and cross-sectional area of the conductor is doubled, the new resistance will be:
R_(n ew) = rho*(2y)/(2x)
And it simplifies to
R_(n ew) = rho * y/x
Notice that the R_new is the same with the original R. 
Therefore, when the length and cross-sectional area of the conductor are increased by the same factor, there is no change in resistance.
http://hyperphysics.phy-astr.gsu.edu/hbase/electric/resis.html

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