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Question
Two bulbs are rated: bulb A 100W, 120 V bulb B 10W, 120 V. If both are connected across a 120V supply, which bulb will consume more energy, When in series? Also calculate the current through each bulb in 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 series:
R = RA + RB = 144 + 1440 = 1584 Ω
∴ Current in the circuit `= "V"/"R" = 120/1584 = 0.076` A
Being in series, the same current passes through both the bulbs.
Power consumed in bulbs A = PA = i2 RA = (0.076)2 × 144 = 0.8317 W
Power consumed in bulbs B = PB = i2 RB = (0.076)2 × 144 = 8.317 W
This clearly shows that PA < PB i.e., bulb B (10W, 120 V) consumes more energy when these are connected series.
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