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Figure shows a conductor of length l having a circular cross - section. The radius of cross - section varies linearly from a to b. The resistivity of the materia is rho. Assuming that b-a lt lt l, find the resistance of the conductor. |
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Answer» Solution :`TAN phi=(b-a)/(1)=(y-a)/(x)` `yl-al=bx-ax`  `1((dy)/(DX))=(b-a)rArrdx=((1)/(b-a))dy rarr(1)` Resistance across the elemental disc under consideration `dR=rho(dx)/(A)rarr(2)` from (1) and (2) `dR=rho((1)/(b-a))(dy)/(piy^(2))` `rArr"Resistance across the given conductor,"` `R=int_(y=a)^(b)dR rArr R=rho(1)/(pi(b-a)).int_(y=a)^(y=b)(dy)/(y^(2)) THEREFORE R=rho(1)/(piab)` |
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