A composite rod made of three rods of equal length and cross-section as shown in the fig. The thermal conductivities of the materials of the rods are $K/2, 5K$ and $K$ respectively. The end $A$ and end $B$ are at constant temperatures. All heat entering the face Agoes out of the end $B$ there being no loss of heat from the sides of the bar. The effective thermal conductivity of the bar is
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$\frac{3 l}{K}=\frac{l}{k / 2}+\frac{l}{5 k}+\frac{l}{k}$
$\frac{3 l}{K}=\frac{2 l}{k}+\frac{l}{5 k}+\frac{l}{k}=\frac{10 l+l+5 l}{5 k}=\frac{16 l}{5 k}$
$K=\frac{15 k}{16}$
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