Question

A wire of length l and cross-sectional area a has resistance r. part a what will be the resistance rstretched of the wire if it is stretched to twice its original length? assume that the density and resistivity of the material do not change when the wire is stretched. express your answer in terms of the wire's original resistance r.

Answer 1

The resistance is given by


`R= (\rho L)/(A)`

where ρ is the resistivity, L is the length and A is the cross sectional area.
The volume of the conductor can't change, we don't create or destroy matter. The volume is given by L*A. This product must be kept constant. If we double the length, we must halve the area. Doing this we get:


`R'=(\rho 2L)/( (1)/(2) A)=4R`