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A solid cylindrical wire of length l has...

A solid cylindrical wire of length l has cross-section radius a as shown below. The specific resistance of material is given as `rho=rho_(0)r`, where r is distance from axis of cylinder and `rho_(0)` is a positive constant quantity. The resistance across its ends is :

A

`(rho_(0)l)/(2pia)`

B

`(rho_(0)l)/(pia^(2))`

C

`(rho_(0)l)/(pia)`

D

`(2rho_(0)l)/(pi)`

Text Solution

Verified by Experts

The correct Answer is:
A
dR = Resistance of thin cylindrical shell of radius r and thickness (dr) `therefore dR =(rho l)/(2 pi r dr)`
Infinite number of thin cylinders are connected parallel to each other
`therefore (1)/(R )= int (1)/(dR)`
`rArr (1)/(R ) = int (2 pi r dr)/(rho l) =(2 pi)/(rho_(0)l) overset(a) underset(0) int (rdr)/(r)`
`rArr (1)/(R) =(2 pi a)/(rho 0l) therefore R =(rho 0 l)/(2 pi a)`
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