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

• A. $\frac{K_1+K_2}{2}$
• B. $K_1+K_2$
• C. $\frac{3(K_1+K_2)}{2}$
• D. $2(K_1+K_2)$

Answer 1

The correct option is A $\frac{K_1+K_2}{2}$

Formula used: $R=\frac{l}{KA}$

The given rods are in parallel combination, so equivalent thermal resistance for the rods,

$\frac{1}{R}=\frac{1}{R_1}+\frac{1}{R_2}$

$\frac{K_{eq}\left(2A\right)}{d}=\frac{K_{1}A}{d}+\frac{K_{2}A}{d}$

$\Rightarrow K_{eq}=\frac{K_1+K_2}{2}$