Question

Question #56177

Answer 1

See proof below

Explanation:

The resistance of the first wire is `R=rhol/a`
where `rho=` resistivity for this material
`l=`length
`a=`area `=pir^2` where r is the radius

New length `=l/2`

New radius `=r/2`

The second wire `R_1=rho*(l/2)/(pir^2/4)`

`=(4rhol)/(2pir^2)=(2rhol)/(a)=2R`

So the new resistance is twice the other resistance