Shown a conductor of length `l` having a circular cross section. The radius of cross section varies linearly form `a to b`. The resistivity of the material is`(rho)`.Assuming that `b-altltl`,find the resistance of the conductor.

Explanation

`tanphi=(b-a)/(l)=(y-a)/(x)`
`yl-al=bx-ax`
`l((dy)/(dx))=(b-a)impliesdx=((l)/(b-a))dyto(1)`
Resistance across the elemetal disc under consideration `dR=rho(dx)/(A)to(2)`
From (1) and (2) `dR=rho((l)/(b-a))(dy)/(piy^(2))`
`implies` Resistance across the given conductor,
`R=int_(y=a)^(b)dRimpliesR=rho(l)/(pi(b-a))int_(y=a)^(y=b)(dy)/(y^(2)),becauseR=rho(l)/(piab)`