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

`tan phi =(b-a)/l =(y-a)/x`

`yl -al =bx -ax`
`l(dy)/(dx) =(b-a) rArr dx = (l/(b-a)) dy to (1)`
Resistance across the elemental disc under consideration `dR =rho (ddx)/A`………….(2)
from (1) and (2) `dR = rho(l/(b-a)) (dy)/(piy^(2))`
`rArr` Resistance across the given conductor.
`R= int_(y=a)^(b) dR rArr R= rho l/(pi(b-a)). int_(y=a)^(y=b) (dy)/y^(2), therefore R=rho l/(pi ab)`