Two heaters A and B have power rating of 1 kW and 2 kW , respectively. Those two are first connected in…
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:
2:9
1:2
2:3
1:1
Solution
$\begin{aligned}
& \therefore \text { Power Consumed }=P=\frac{V^2}{R} \\
& \frac{P_A}{P_B}=\frac{R_B}{R_A} \\
& R_A=2 R_B
\end{aligned}$
For Series Combination
$P_S=\frac{V^2}{3 R_B}$
For Parallel Combination
$\begin{aligned}
& P_P=\frac{3 V^2}{2 R_B} \\
& \frac{P_S}{P_P}=\frac{2}{9}
\end{aligned}$