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A cylindrical conductor of length l and ...


A cylindrical conductor of length l and inner radius `R_(1)` and outer radius `R_(2)` has specific resistance `rho`. A cell of emf `epsilon` is connected across the two lateral faces of the conductor. Find the current drown from the cell.

A

`(2pi l epsilon)/(rho"In"(R_(2))/(R_(1)))`

B

`(2pil epsilon)/(rho(R_(2)^(2)-R_(1)^(2)))`

C

`(2l epsilon)/(rhopi(R_(2)^(2)-R_(1)^(2)))`

D

none of these

Text Solution

Verified by Experts

The correct Answer is:
A
Consider the differential element of the cylinder as shown in the figure.
`thereforeR=underset(R_(1))overset(R_(2))intrho(dx)/(2pixl)" "(becauseR=rho(l)/(a))`
`impliesR=(rho)/(2pil)"In"(R_(2)//R_(1))`
`I=(epsilon)/(R),impliesI=(2pi//epsilon)/(rho"In"((R_(2))/(R_(1))))`
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