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Question
Two bulbs are rated: bulb A 100W, 120 V bulb B 10 W, 120 V. If both are connected across a 120V supply, which bulb will consume more energy, When in parallel? Also calculate the current through each bulb in the above cases.
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Solution
In the case of bulb A, Power: P = `"V"^2/"R"_"A"`
RA = `"V"^2/"P" = (120 xx 120)/100` = 144 Ω
i.e., Resistance (RA ) of bulb, A = 144 Ω
Similarly resistance RB of bulb, B = `"V"^2/"P"`
`= (120 xx 120)/10 = 1440` Ω
When the bulb are connected in Parallel:
Voltage is the same (120 V) across each bulb.
∴ The current in bulb A or IA = `"V"/"R"_"A" = 120/144 = 0.83` A
∴ The current in bulb B or IB `= 120/1440` = 0.083 A
Hence, power consumed in bulb A = PA = `"V"^2/"R"_"A" = (120 xx 120)/144`
= 100 W
and power consumed in bulb B = PB = `"V"^2/"R"_"B"`
`= (120 xx 120)/1440 = 10 "W"`
Hence, bulb A (100W, 120 V) consumes more energy then bulb B, when both are connected in parallel.
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