Resistivity of the material of a conductor of uniform cross-section varies along its length as `rho=rho_(0)(1+alpha x)`. Find its resistance if its length is L and area of cross-section is A.

Explanation

Resistance of the material of a conductor of length dx at distance x from one end is
`dR= rho dx/A=rho_(0)(1+alpha x) dx/A`
[Given, `rho=rho_(0)(1+alpha x)`]
The resistance of the material of conductor of length L is
`R=int_(0)^(L) rho_(0) (1+alpha x) dx/A`
`rho_(0)/A[L+1/2 alpha L_(2)]`