Five rods of same dimensions are arranged 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 temperatures, no heat flows through the central rod if

Options

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

Answer

A

Explanation

if no heat flow through D then it is like balanced stone bridge `k_(1)k_(4)=k_(2)k_(3)`