Model a torch battery of length l to be made up of a thin cylindrical bar of radius 'a' and a concentric thin cylindrical shell of radius 'b' filled in between with an electrolyte of resistivity `rho` (see figure). If the battery is connected to a resistance of value R, the maximum Joule heating in R will take place for :

Options

A. Option1 `R=(rho)/(2 pil) (b/a)`
B. Option2 `R=(2 rho )/(pil )I n (b/a)`
C. Option3 `R=(rho )/(pi l)I n (b/a)`
D. Option4 `R=(rho )/(2 pi l ) I n (b/a)`

Answer

D

Explanation

`dR = rho (dr )/(2pi r l)`
`int dR =(rho )/(2 pi l ) int_(a) ^(b) 1/r dr `
` R= rho/(2 pi l) [Ln (r ) ]_(a)^(b)`
` R= (rho )/( 2pi l) Ln (b/a)`
`r=R`
for max heat transfer