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.

Options

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

Answer

A

Explanation

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))))`