Explanation

(c) In series combination, the net resistance
$R_{s} = R + 2R = 3R$
Heat produced in $R_{s},$
$H_{s} = \frac{V^{2}}{R_{s}} = \frac{V^{2}}{3R}\ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ldots(i)$
I parallel combination, the net resistance
$R_{P} = \frac{R \times 2R}{R + 2R} = \frac{2R^{2}}{3R} = \frac{2}{3}\ R$
Heat produced in $R_{P},$
$H_{P} = \frac{V^{2}}{R_{P}} = \frac{V^{2}}{2R/3} = \frac{3V^{2}}{2R}\ \ \ \ \ \ \ \ \ \ldots(ii)$
Dividing Eq. (i) by Eq. (ii), we obtain
$\frac{H_{s}}{H_{p}} = \frac{V^{2}/3R}{3V^{2}/2R} = \frac{2}{9}$