Two rods $A$ and $B$ of different materials are welded together as shown in figure. Their thermal conductivities are $K_1$ and $K_2$ . The thermal conductivity of the composite rod will be :

Question

Two rods  $A$  and  $B$  of different materials are welded together as shown in figure. Their thermal conductivities are  $K_1$  and  $K_2$ . The thermal conductivity of the composite rod will be :

cdquestions Admin · Accepted Answer

$R _{1}=\frac{ d }{ k _{1} A }$ $R _{2}= d K _{2} A$ $\operatorname{Req}=\frac{ R _{1} R _{2}}{ R _{1}+ R _{2}}$ $\frac{ d }{ keq (2 A )}=\frac{\left(\frac{ d }{ k _{1} A }\right)\left(\frac{ d }{ k _{2} A }\right)}{ A }\left(\frac{1}{ k _{1}}+\frac{1}{ k _{2}}\right)$ $\frac{1}{2 keq }=\frac{\frac{1}{ k _{1} k _{2}}}{\frac{ k _{1}+ k _{2}}{ k _{1} k _{2}}}=\frac{1}{ k _{1}+ k _{2}}$ $keq =\frac{ k _{1}+ k _{2}}{2}$

Answer

$\frac{3(K_1 + K_2)}{2}$

Answer

$K_1 + K_2$

Answer

$2( K_1 + K_2)$

Answer

$\frac{K_1 + K_2}{2} $

Two rods \(A\) and \(B\) of different materials are welded together as shown in figure. Their thermal conductivities are \(K_1\) and \(K_2\). The thermal conductivity of the composite rod will be :

The Correct Option is D

Solution and Explanation

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