# Five rods of the same dimension are arranged as shown . AB are maintained at different temperatures . No Heat flows through the central rod ; then

$(a)\;K_{1}K_{4}=K_{2}K_{3}\qquad(b)\;K_{1}K_{2}=K_{3}K_{4}\qquad(c)\;K_{1}K_{3}=K_{2}K_{1}\qquad(d)\;None$

Answer : $\;K_{1}K_{2}=K_{3}K_{4}$
Explanation :
Since no heat flows through the central rod , temperatures at C and D are the same .
The above is like a wheatstone Network .
$\large\frac{L_{1}}{K_{1}A_{1}} \;. \large\frac{L_{2}}{K_{2}A_{2}} = \large\frac{L_{3}}{K_{3}A_{3}} \; . \large\frac{L_{4}}{K_{4}A_{4}}$
$L_{1}=L_{2}=L_{3}=L_{4}$
$A_{1}=A_{2}=A_{3}=A_{4}$
$K_{1}K_{2}=K_{3}K_{4}$