Five rods of same dimensions are arranged as shown in figure. They have thermal conductivities K1, K2, K3, K4 and K5. When points A and B are maintained at different temperature, no heat would flow through central rod, if

Question

Five rods of same dimensions are arranged as shown in figure. They have thermal conductivities K1, K2, K3, K4 and K5. When points A and B are maintained at different temperature, no heat would flow through central rod, if <img class="img-fluid question-image" alt="Question" src="https://cdn.tardigrade.in/q/nta/p-9kqhhirr7bjh.png" /> (A) K1K4=K2 K3  (B) K1=K4 and K2=K3 (C) (K1/K4)=(K2/K3)  (D) K1K2=K3K4.

Tardigrade Admin · Accepted Answer

The equivalent electrical circuit, figure in these cases is of Wheatstone bridge. No current would flow through central rod

C D

when the bridge is balanced. The condition for balanced Wheatstone bridge is

\frac{P}{Q} = \frac{R}{S}

(in terms of resistances)

\frac{K _{2}}{K _{1}} = \frac{K _{4}}{K _{3}}

Or

K_{1} K_{4} = K_{2} K_{3}

Q. Five rods of same dimensions are arranged as shown in figure. They have thermal conductivities $K_{1}, K_{2}, K_{3}, K_{4} an d K_{5} .$ When points $A an d B$ are maintained at different temperature, no heat would flow through central rod, if

$K_{1} K_{4} = K_{2} K_{3}$

$K_{1} = K_{4} an d K_{2} = K_{3}$

$\frac{K _{1}}{K _{4}} = \frac{K _{2}}{K _{3}}$

$K_{1} K_{2} = K_{3} K_{4} .$

Q. Five rods of same dimensions are arranged as shown in figure. They have thermal conductivities K1​,K2​,K3​,K4​andK5​. When points AandB are maintained at different temperature, no heat would flow through central rod, if

K1​K4​=K2​K3​

K1​=K4​andK2​=K3​

K4​K1​​=K3​K2​​

K1​K2​=K3​K4​.

The equivalent electrical circuit, figure in these cases is of Wheatstone bridge. No current would flow through central rod CD when the bridge is balanced. The condition for balanced Wheatstone bridge is QP​=SR​ (in terms of resistances) K1​K2​​=K3​K4​​ Or K1​K4​=K2​K3​

Q. Five rods of same dimensions are arranged as shown in figure. They have thermal conductivities $K_{1}, K_{2}, K_{3}, K_{4} an d K_{5} .$ When points $A an d B$ are maintained at different temperature, no heat would flow through central rod, if

$K_{1} K_{4} = K_{2} K_{3}$

$K_{1} = K_{4} an d K_{2} = K_{3}$

$\frac{K _{1}}{K _{4}} = \frac{K _{2}}{K _{3}}$

$K_{1} K_{2} = K_{3} K_{4} .$