Two different materials $M_1, M_2$ of equal dimensions (length $L$ and uniform cross-sectional area $A$ ) having thermal conductivities $k_1$ and $k_2$ respectively are connected together through a bolt $M_3$. The bolt (length $=2 L$, area $=A / n$ ) is of another material with thermal conductivity $k_3$ such that $n \gg 1$. The left sides of the material $M_1$ and $M_3$ are kept at the temperature $T_1$ whereas the right sides of the material $M_2$ and $M_3$ are kept at the temperature $T_2$ as shown in the figure below such that $T_1 \gt T_2$. Assume that the bolt $\left(M_3\right)$ is thermally insulated from materials $M_1$ and $M_2$. The equivalent thermal resistance of this system is

• A

  $\frac{L\left(k_1+k_2\right)}{A k_1 k_2}$
• B

  $\frac{L}{\left(k_1+k_2\right) A}$
• C

  $\frac{L\left(k_3+2 n\left(k_1+k_2\right)\right)}{A\left(k_1+k_2\right) n k_3}$
• Correct answer
  D

  $\frac{2 n L\left(k_1+k_2\right)}{A\left(2 n k_1 k_2+k_2 k_3+k_3 k_1\right)}$

Hence, the correct answer is option: 'D'.