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 $^{\circ} C$)

Two metal slabs of same cross-sectional area have thicknesses $d_1$ and $d_2$,and thermal conductivities $K_1$ and $K_2$ respectively,are connected in series. The free ends of the two slabs are kept at temperatures $T_1$ and $T_2$ $(T_1 > T_2)$. The temperature $T$ of their common 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 $^{\circ} C$)

Three rods of the same material,same length,and same cross-sectional area are connected as shown in the figure. Find the temperature of their junction in $^oC$.

$A$,$B$ and $C$ are three identical conductors but made from different materials. They are kept in contact as shown. Their thermal conductivities are $K$,$2K$ and $K/2$. The free end of $A$ is at $100^{\circ} C$ and the free end of $C$ is at $0^{\circ} C$. During steady state,the temperature of the junction of $A$ and $B$ is nearly (in $^{\circ} C$)

Find the effective thermal resistance between $A$ and $B$ of a cube made up of $12$ rods of the same dimensions,with the given thermal conductivities as shown in the figure. [ $l =$ length of rod,$a =$ cross-sectional area of rod ]