Two metal rods are arranged as shown in the figure. Their thermal conductivities are $K_1$ and $K_2$. What is their equivalent thermal conductivity?

$A$ temperature difference of $120\,^oC$ is maintained between the two ends of a uniform rod $AB$ of length $2L$. Another bent rod $PQ$,of the same cross-section as $AB$ and length $\frac{3L}{2}$,is connected across $AB$ as shown in the figure. In the steady state,the temperature difference between $P$ and $Q$ will be close to .......... $^oC$.

Three rods of the same material and same cross-sectional area,but different lengths $10 \, cm$,$20 \, cm$,and $30 \, cm$,are connected at a junction $O$ as shown in the figure. What is the temperature of the junction $O$ in $^{\circ} C$?

$A$ slab consists of two parallel layers of two different materials of same thickness having thermal conductivities $K_1$ and $K_2$. The equivalent conductivity of the combination is

In the following figure,two insulating sheets with thermal resistances $R$ and $3R$ are shown. The temperature $\theta$ at the interface is ...... $^oC$.

Consider a compound slab consisting of two different materials having equal thickness and thermal conductivities $K$ and $2K$ respectively. The equivalent thermal conductivity of the slab is