Three conductors of same length having thermal conductivity $\mathrm{k}_1, \mathrm{k}_2$ and $\mathrm{k}_3$ are connected as shown in figure. Area of cross sections of $1^{ ext {st }}$ and $2^{ ext {nd }}$ conductor are same and for $3^{ ext {rd }}$ conductor it is double of the $1^{ ext {st…

Question

Three conductors of same length having thermal conductivity $\mathrm{k}_1, \mathrm{k}_2$ and $\mathrm{k}_3$ are connected as shown in figure.

Area of cross sections of $1^{\text {st }}$ and $2^{\text {nd }}$ conductor are same and for $3^{\text {rd }}$ conductor it is double of the $1^{\text {st }}$ conductor. The temperatures are given in the figure. In steady state condition, the value of $\theta$ is
_______ ${ }^{\circ} \mathrm{C}$.
(Given : $\mathrm{k}_1=60 \mathrm{Js}^{-1} \mathrm{~m}^{-1} \mathrm{~K}^{-1}, \mathrm{k}_2=120 \mathrm{Js}^{-1} \mathrm{~m}^{-1} \mathrm{~K}^{-1},$ $\mathrm{k}_3=135 \mathrm{Js}^{-1} \mathrm{~m}^{-1} \mathrm{~K}^{-1}$)

Aicharya · Accepted Answer

$\begin{aligned} & \mathrm{R}_1=\frac{2 \mathrm{~L}}{\mathrm{~K}_1 \mathrm{~A}} \\ & \mathrm{R}_2=\frac{2 \mathrm{~L}}{\mathrm{~K}_2 \mathrm{~A}} \\ & \mathrm{R}_3=\frac{\mathrm{L}}{\mathrm{K}_3 \mathrm{~A}} \\ & \frac{\theta-100}{\frac{\mathrm{R}_1 \mathrm{R}_2}{\mathrm{R}_1+\mathrm{R}_2}}+\frac{\theta-0}{\mathrm{R}_3}=0 \\ & \theta=40\end{aligned}$

Three conductors of same length having thermal conductivity $\mathrm{k}_1, \mathrm{k}_2$ and $\mathrm{k}_3$…

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