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26/07/2021 2:48 pm
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Two exactly similar electric lamps are arranged (i) in parallel, and (ii) in series. If the parallel and series combination of lamps are connected to 220 V supply line one by one, what will be the ratio of electric power consumed by them?
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26/07/2021 2:55 pm
Let resistance of each lamp = R ohms.
Case 1: Parallel connection
Resultant resistance = \(\frac{1}{\frac{1}{R}+ \frac{1}{R}}\)
= \(\frac{R}{2}\)
Electric power consumed P1 = \(\frac{V^2}{R}\)
= \(\frac{220^2}{\frac{R}{2}}\) = \(\frac{96800}{R}\)
Case 2: Series connection
Resultant resistance = R + R = 2R
Electric power consumed P2 = \(\frac{V^2}{2R}\) = \(\frac{24200}{R}\)
\(\frac{P_1}{P_2}\) = \(\frac{\frac{96800}{R}}{\frac{24200}{R}}\)
= \(\frac{4}{1}\)