Answer
We can rank the power dissipated in order from largest to smallest:
$P_c \gt P_d \gt P_a \gt P_b$
Work Step by Step
We can find an expression for the power dissipated in each case:
(a) $P_a = \frac{(\Delta V)^2}{R}$
(b) $P_b = \frac{(\frac{1}{2}~\Delta V)^2}{2R} = \frac{1}{8} \times \frac{(\Delta V)^2}{R}$
(c) $P_c = \frac{(2~\Delta V)^2}{\frac{1}{2}R} = 8 \times \frac{(\Delta V)^2}{R}$
(d) $P_d = \frac{(2~\Delta V)^2}{2R} = 2 \times \frac{(\Delta V)^2}{R}$
We can rank the power dissipated in order from largest to smallest:
$P_c \gt P_d \gt P_a \gt P_b$
