Wednesday, September 19, 2012

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.

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