c
From the given circuit, net resistances \({{\rm{R}}_I} = 1\,\Omega ,{{\rm{R}}_{{\rm{II}}}} = 1/2\,\Omega ,{{\rm{R}}_{{\rm{III}}}} = 3/2\,\Omega \)

It is clear that \(\mathrm{R}_{3}>\mathrm{R}_{1}>\mathrm{R}_{2}\)

Hence, \({P_3} < {P_1} < {P_2}\)

As Power \((P)\) \(=\frac{\mathrm{V}^{2}}{\mathrm{R}} \Rightarrow \mathrm{P} \propto \frac{1}{\mathrm{R}}\)