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Question
Two 120V Light bulbs, one of 25W and other of 200W are connected on series across a 240V line. One bulb burnt instantly. Which one was burnt and why? Explain
Two 120V Light bulbs, one of 25W and other of 200W are connected on series across a 240V line. One bulb burnt instantly. Which one was burnt and why? Explain
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Solution
25W = P1 and 200 W = P2 are the ratings on the bulbs. That means those bulbs are supposed to work at that power ratings. Voltage ratings of hte bulbs are: 120Volts. R1 and R2 are their resistances.
P = V² / R
=> R1 = V² / P1 = 120² / 25 = 576 Ohms ; I1 = V/R1 = 120/576 = 0.2083 Amp
So maximum current this bulb (25 watt) can take is 0.2083 Amp
Similarly R2 = V² / P2 = 120² / 200 = 72 Ohms; I2 = V/R2 = 1.667 Amp
current rating = 1.667 Amp
When both bulbs are connected in series with 240 Volts line,
total resistance in the resistance = R1 + R2 = 648 Ohms
The current in the circuit = I = 240/648 = 0.370 Amperes
Since, 0.370 is more than 0.2083 Amp. the bulb with smaller power Watts rating is burnt.
so 25 watt bulb gets burnt
P = V² / R
=> R1 = V² / P1 = 120² / 25 = 576 Ohms ; I1 = V/R1 = 120/576 = 0.2083 Amp
So maximum current this bulb (25 watt) can take is 0.2083 Amp
Similarly R2 = V² / P2 = 120² / 200 = 72 Ohms; I2 = V/R2 = 1.667 Amp
current rating = 1.667 Amp
When both bulbs are connected in series with 240 Volts line,
total resistance in the resistance = R1 + R2 = 648 Ohms
The current in the circuit = I = 240/648 = 0.370 Amperes
Since, 0.370 is more than 0.2083 Amp. the bulb with smaller power Watts rating is burnt.
so 25 watt bulb gets burnt
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