A wall consists of alternating blocks withlength 'd' and coefficient of thermal conductivity `k_(1)` and `k_(2)`. The cross sectional area of the blocks are the same. The equivalent coefficient of thermal conductivity of the wall between left and right is:-

Options

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

Answer

B

Explanation

It’s a parallel Combination

`R_(1)=d/(K_(1)A)` `R_(2)=d/(K_(2)A)`
`1/(R_("eq"))=1/(R_(1))+1/(R_(2))+...."upto " n^(th)`
`1/(R_("eq"))=n/(2R_(1))+n/(2R_(2))=n/(2)((R_(1)+R_(2))/(R_(1)R_(2)))`
`R_("eq")=(2(R_(1)R_(2)))/(n(R_(1)+R_(2)))rArr((d//n))/(K_("eq")(A))=(2(d/(K_(1)A))xxd/(K_(2)A))/(nd/(A)(1/(K_(1))+1/(K_(2))))`
`1/(K_("eq"))=2/(K_(1)+K_(2))rArr K_("eq")=(K_(1)+K_(2))/(2)`