The resistance of a conducting wire is R. What will be the resistance of another similar wire if the length is doubled and the diameter is doubled?

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The resistance of a cylindrical wire is given by the formula

`R = rho*l/A` , where `rho` is the resistivity of the conducting material, which depends only on the properties of the material and, possibly, the temperature. l is the length of the wire and A is the cross-sectional area...

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The resistance of a cylindrical wire is given by the formula

`R = rho*l/A` , where `rho` is the resistivity of the conducting material, which depends only on the properties of the material and, possibly, the temperature. l is the length of the wire and A is the cross-sectional area of the wire.

If the length of the wire is doubled, the new length will be l' = 2l. The cross-sectional area is proportional to the square of the diameter (`A = pid^2/4)`  , so if the diameter of the wire is doubled, the cross-sectional area will be increased four times:

A' = 4A.

The resistivity of the wire does change, so the new resistance will be

`R' = rhol'/(A') = rho (2l)/(4A) = rhol/(2A) = R/2` .

So the resistance of the new wire will be half the resistance of the original wire.

 

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