Consider four circuits shown in the figure below. In which circuit power dissipated is greatest (Neglect the internal resistance of the power supply)

For the same ideal source, total power is $P=\frac{E^2}{R_{\text{eq}}}$. So the circuit with the smallest equivalent resistance dissipates the greatest power. For option $A$, two resistors $R$ are in parallel. $$R_{\text{eq}}=\frac{R}{2}$$ For option $B$, two resistors $R$ are in series. $$R_{\text{eq}}=2R$$ For option $C$, two resistors $R$ are in parallel first, then in series with one more $R$. $$R_{\text{eq}}=\frac{R}{2}+R=\frac{3R}{2}$$ For option $D$, one branch has two resistors in series and this branch is in parallel with one resistor $R$. $$R_{\text{eq}}=\frac{(2R)(R)}{2R+R}=\frac{2R}{3}$$ Comparing $\frac{R}{2}, 2R, \frac{3R}{2}, \frac{2R}{3}$, the smallest is $\frac{R}{2}$. Hence the greatest power is in option $A$.