Two heaters A and B have power rating of \( 1\text{ kW} \) and \( 2\text{ kW} \), respectively. Those two are first connected in series and then in parallel to a fixed power source. The ratio of power outputs for these two cases is:

Resistances are \( R_A = \frac{V^2}{1} \) and \( R_B = \frac{V^2}{2} \). In series, total resistance \( R_s = R_A + R_B = \frac{3}{2} R_A \), so \( P_s = \frac{V^2}{R_s} = \frac{2}{3}\text{ kW} \). In parallel, \( P_p = P_A + P_B = 3\text{ kW} \). Thus \( \frac{P_s}{P_p} = \frac{2/3}{3} = \frac{2}{9} \).