Question

Two identical metal wires of thermal conductivities $K_1$ and $K_2$ respectively are connected in series. The effective thermal conductivity of the combination is -

• A. $\frac{2K_1{K}_2}{K_1+K_2}$
• B. $\frac{K_1+K_2}{K_1{K}_2}$
• C. $\frac{K_1+K_2}{2K_1{K}_2}$
  
• D. $\frac{K_1{K}_2}{K_1+K_2}$
  

Answer 1

The correct option is A $\frac{2K_1{K}_2}{K_1+K_2}$


The equivalent thermal resistance of the combination is given by,

$R_{\text{eq}}=R_1+R_2$

$\Rightarrow \frac{1}{K_{\text{eq}}}\frac{2l}{A}=\frac{l}{K_{1}A}+\frac{l}{K_{2}A}$

Where, $A$ is the area of the cross-section of the wire and $l$ is the length of the wire.

$\Rightarrow \frac{2}{K_{\text{eq}}}=\frac{1}{K_1}+\frac{1}{K_2}$

$\Rightarrow K_{\text{eq}}=\frac{2K_1{K}_2}{K_1+K_2}$

Therefore, option $\left(A\right)$ is the correct answer.