d
(d) Equation of thermal conductivity of the given combination \({K_{eq}} = \frac{{{l_1} + {l_2}}}{{\frac{{{l_1}}}{{{K_1}}} + \frac{{{l_2}}}{{{K_2}}}}} = \frac{{x + 4x}}{{\frac{x}{K} + \frac{{4x}}{{2K}}}} = \frac{5}{3}K\).

Hence rate of flow of heat through the given combination is \(\frac{Q}{t} = \frac{{{K_{eq}}.A({T_2} - {T_1})}}{{(x + 4x)}} = \frac{{\frac{5}{3}K\,A\,({T_2} - {T_1})}}{{5x}}\)=\(\frac{{\frac{1}{3}K\,A\,({T_2} - {T_1})}}{x}\) On comparing it with given equation we get \(f = \frac{1}{3}\)