Question

Two heaters A and B have power rating of 1 kW and 2 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: 

(1) 1 : 1 

(2) 2 : 9 

(3) 1 : 2 

(4) 2 : 3

Answer 1

Correct option is : (2) 2 : 9 

Power Consumed \(= P = \frac{V^2}{R}\) 

\(\frac{P_A}{p_B}=\frac{R_B}{R_A}\) 

\(R_A = 2R_B\) 

For Series Combination 

\(P_S = \frac{V^2}{3R_B}\) 

For Parallel Combination 

\(P_P = \frac{3V^2}{2R_B}\) 

\(\frac{P_S}{P_P} = \frac{2}{9}\)