Question

Five rods of same dimensions are arranged as shown in 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 temperature, no heat would flow through central rod, if

• A. $K_{1}K_{4}=K_{2} \, K_{3} \, $
• B. $K_{1}=K_{4} \, and \, \, K_{2}=K_{3}$
• C. $\frac{K_{1}}{K_{4}}=\frac{K_{2}}{K_{3}} \, $
• D. $K_{1}K_{2}=K_{3}K_{4}.$

Answer 1

Answer: (A)

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 $\frac{P}{Q}=\frac{R}{S}$ (in terms of resistances)
$\frac{K_{2}}{K_{1}}=\frac{K_{4}}{K_{3}}$
Or $K_{1}K_{4}=K_{2}K_{3}$