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

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:

$\displaystyle{R}=\rho\cdot\frac{{L}}{{A}}$

where

$\displaystyle\rho$ 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:

$\displaystyle{R}=\rho\cdot\frac{{y}}{{x}}$

When the length and cross-sectional area of the conductor is doubled, the new resistance will be:

$\displaystyle{R}_{{{n}{e}{w}}}=\rho\cdot\frac{{{2}{y}}}{{{2}{x}}}$

And it simplifies to

$\displaystyle{R}_{{{n}{e}{w}}}=\rho\cdot\frac{{y}}{{x}}$

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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Wednesday, September 19, 2012