Three identical metal rods `A`, `B` and `C` are placed end to end and a temperature difference is maintained between the free ends of `A` and `C`. If the thermal conductivity of `B(K_(B))` is twice that of `C(K_(C ))` and half that of `A(K_(A))`, `(K_(A)=49w//mK)` calculate the effective thermal conductivity of the system ?

Options

A. `1/3 K_(A)`
B. `3K_(A)`
C. `2K_(A)`
D. `2/3 K_(A)`

Answer

A

Explanation

Given, `K_(B) = K_(A)//2` and `K_(B) = 3K_(C)`
`K_(C) = K_(A)//6`
Rods are in series from so
`L/K= I_(1)/K_(A) + I_(2)/K_(B) + I_(3)/K_(C)` (`therefore` `l = l_(1)=l_(2)=l_(3)`
`(3l)/K = l/(K_(A) + l/(K_(A)//2) + l/K_(A)//6`
or `(3l)/K = 9l/K_(A)` or `K= (K_(A))/3`