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?

Two plates of the same thickness with coefficients of thermal conductivities $K_1$ and $K_2$ and cross-sectional areas $A_1$ and $A_2$ are connected as shown. Find the effective coefficient of thermal conductivity $K_{eq}$.

$A$ 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

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 identical metal wires of thermal conductivities $K_{1}$ and $K_{2}$ respectively are connected in series. The effective thermal conductivity of the combination is

$A$ composite slab consists of two materials having coefficients of thermal conductivity $K$ and $2K$,and thicknesses $x$ and $4x$ respectively. The temperatures of the two outer surfaces of the composite slab are $T_2$ and $T_1$ $(T_2 > T_1)$. The rate of heat transfer through the slab in a steady state is $\left[\frac{A(T_2 - T_1)K}{x}\right] \cdot f$,where '$f$' is equal to: