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Question
Two lamps, one rated 220 V, 50 W and the other rated 220 V, 100 W, are connected in series with mains of 220 V. Explain why does the 50 W lamp consume more power.
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Solution
Resistance of 220 V , 50 W lamp is
`"R"_1 = "V"^2/"P"_1 = 220^2/50 = 968 Omega`
Resistance of 220 V , 100 W lamp is
`"R"_2 = "V"^2/"P"_2 = 220^2/100 = 484 Omega`
since the two lamps are connected in series
so same current I passes through each lamp.
Power consumed in 220 V , 50 W lamp is P1 = I2R1
Power consumed in 220 V , 100 W lamp is P2 = I2R2
Since `"R"_1 > "R"_2 , "P"_1 > "P"_2`.
i.e. 50 W lamp consumes more power.
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