CapacitanceMedium
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:
Options
A.$1:2$
B.$2:3$
C.$1:1$
D.$2:9$
Solution
Sol. [Key Concept: Heater power ratings and heat produced (P = V²/R)]
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
$${P_{P} = \frac{3V^{2}}{2R_{B}} }{\frac{P_{S}}{P_{P}} = \frac{2}{9} }$$
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