Two heaters $A$ and $B$ have power ratings of $2 \mathrm{~kW}$ and $3 \mathrm{~kW}$, respectively. T

Question

Two heaters $A$ and $B$ have power ratings of $2 \mathrm{~kW}$ and $3 \mathrm{~kW}$, respectively. They are first connected in series and then in parallel to a fixed power source. The ratio of the total power outputs in these two cases (series to parallel) is

Professor PC Thomas Classes · Answer

(a) : For heaters connected to the same voltage source, resistance $R \propto 1/P$. In a series combination, the equivalent power $P_s$ is given by\ $\frac{1}{P_s} = \frac{1}{P_A} + \frac{1}{P_B}$,\ so $P_s = \frac{2 	imes 3}{2 + 3} = 1.2 \mathrm{~kW}$.\ In a parallel combination, $P_p = P_A + P_B = 2 + 3 = 5 \mathrm{~kW}$.\ The ratio of power output in series to parallel is\ $\frac{1.2}{5} = \frac{12}{50} = \frac{6}{25}$, or $6:25$.