Consider two insulating sheets with thermal resistances $R_1$ and $R_2$ as shown in the figure. The temperature $\theta$ at the junction is:

Two slabs $A$ and $B$ of equal surface area are placed one over the other such that their surfaces are completely in contact. The thickness of slab $A$ is twice that of $B$. The coefficient of thermal conductivity of slab $A$ is twice that of $B$. The first surface of slab $A$ is maintained at $100^{\circ} C$, while the second surface of slab $B$ is maintained at $25^{\circ} C$. The temperature at the contact of their surfaces is (in $^{\circ} C$)

For the figure shown,when arcs $ACD$ and $ADB$ are made of the same material,the total heat current carried between $A$ and $B$ is $H$. If $ADB$ is replaced with another material,the total heat current becomes $2H$. If the temperatures at $A$ and $B$ are fixed at $T_1$ and $T_2$,what is the ratio of the new thermal conductivity to the old thermal conductivity of the arc $ADB$?

Six identical rods are arranged as shown in the figure. The temperature of the junction $B$ will be......... $^oC$

Three rods $AB$, $BC$, and $BD$ made of the same material and having the same cross-section have been joined as shown in the figure. The ends $A$, $C$, and $D$ are held at temperatures of $20^{\circ} C$, $80^{\circ} C$, and $80^{\circ} C$ respectively. If each rod is of the same length, then the temperature at the junction $B$ of the three rods is: (in $^{\circ} C$)

The temperature $\theta$ at the junction of two insulating sheets,having thermal resistances $R_{1}$ and $R_{2}$ as well as top and bottom temperatures $\theta_{1}$ and $\theta_{2}$ (as shown in figure) is given by