Question

The length of a certain wire is kept same while its radius is doubled. what is the change in the resistance of this wire?

Answer 1

The resistance of a wire is given by

`R= (\rho L)/(A)`
where
`\rho` is the resistivity of the material, L the length of the wire and A its cross-sectional area.

In the problem,
`\rho` and L remain the same, while A changes because the radius changes. The area is given by:

`A=\pi r^2`
This means that if we double the radius (2r), the area becomes

`A_(new)= \pi (2r)^2 = 4 \pi r^2 =4A`
And therefore, the new value of the resistance is

`R_(new) = (\rho L)/(4 A)= (1)/(4)R`

So, when the radius is doubled, the resistance becomes
`(1)/(4)` of its original value.