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A conductor of length l has a non-unifor...

A conductor of length `l` has a non-uniform cross-section. The radius of cross-section varies linearly from `a` to `b`. The resistivity of the material is `rho`. Find the resistance of the conductc across its ends.

Text Solution

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In this problem cross-section area is variable so we can't apply formula `(R=(rhol)/A)` directly.

So we assume elementary strip 'PQ' of thickness dx and radius r resistance of this strip is :
`dR=(rhodx)/(pir^(2))`
`"Bt grometry "(r-a)/x=(b-a)/trArrr=(b-a)/lx+a`
`"Resistance of conductor is R"=underset(0)overset(t)int(pdx)/(pi{(b-a)/lx+a})rArrR=(rhol)/(piab)`
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