Answer
(a) $2R$
(b) $\frac{R}{2}$
Work Step by Step
(a) We know that if the resistors are connected in series then the same amount of current flows across the resistors and for such a combination $P=I^2R$. This equation shows that the power dissipation is directly proportional to the resistance; thus, the resistor having the greatest resistance, that is $2R$, has the greatest rate of energy dissipation.
(b) For the parallel combination, we have $P=\frac{V^2}{R}$. This equation shows that the power is inversely proportional to the resistance at constant voltage. Thus, $\frac{R}{2}$ has the greatest rate of energy dissipation.
