Equivalent thermal conductivity of figure given below will be given that length of eachh cylinder is l and area of cylinder having thermal conductivity `K_(1)` & `K_(3)` is A while middle cylinder is having `K_(2)`.

Options

A. `(5)/(2[(1)/(K_(1))+(1)/(2K_(2))+(1)/(K_(3))])`
B. `(1)/(((1)/(K_(1))+(1)/(2K_(2))+(1)/(K_(3))))`
C. `(2)/(5[(1)/(K_(1))(1)/(2K_(2))+(1)/(K_(3))])`
D. none of these

Answer

A

Explanation

`(l)/(K_(1)A)+(l)/(2K_(2)A)+(l)/(K_(3)A)=(l)/(KA)+(l)/(2K_(A))+(l)/(KA)`
`(5)/(2K)=((1)/(K_(1))+(1)/(2K_(2))+(1)/(K_(3)))`
`K_(eq)=(5)/(2((1)/(K_(1))+(1)/(2K_(2))+(1)/(K_(3))))`