Five rods of same dimensions are arrranged as shown in the figure. They have thermal conductivities `K_(1), K_(2), K_(3), K_(4)` and `K_(5)`. When points `A` and `B` are maintained at different themperature, no heat flows through the central rod if

Options

A. `K_(1) = K_(4)` and `K_(2) = K_(3)`
B. `K_(1) K_(4) = K_(2) K_(3)`
C. `K_(1) K_(2) = K_(3) K_(4)`
D. `(K_(1))/(K_(4)) = (K_(2))/(K_(3))`

Answer

B

Explanation

(2) No heat will flow in in `CD` if
`(R_(AC))/(R_(AD)) = (R_(CB))/(R_(DB)) implies (K_(3))/(K_(1)) = (K_(4))/(k_(2))`
`K_(1) K_(4) = K_(2) K_(3)`