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  4. Three rods of same dimensions are arranged as shown in figure they have thermal conductivities K 1, K 2 and K 3. The points P and Q are maintained at different temeratures for the heat to flow at the same rate along P R Q and P Q then which of the following option is correct?

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Q. Three rods of same dimensions are arranged as shown in figure they have thermal conductivities $K _1, K _2$ and $K _3$. The points $P$ and $Q$ are maintained at different temeratures for the heat to flow at the same rate along $P R Q$ and $P Q$ then which of the following option is correct?Physics Question Image

Thermal Properties of Matter

Solution:

The given arrangement of rods can be redrawn as follows
image
It is given that $H _1= H _2$
$\Rightarrow \frac{K A\left(\theta_1-\theta_2\right)}{2 l}=\frac{K_3 A\left(\theta_1-\theta_2\right)}{l}$
$ \Rightarrow K_3=\frac{K}{2}=\frac{K_1 K_2}{K_1+K_2}$