Two 120v light bulbs ,one of 25w and other of 200w were connected in series across a 240v line.One bulb burnt almost instantaneously .Which one was burnt and why?
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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
maximum current this bulb can take is 0.2083 Amp
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.
P = V² / R
=> R1 = V² / P1 = 120² / 25 = 576 Ohms ; I1 = V/R1 = 120/576 = 0.2083 Amp
maximum current this bulb can take is 0.2083 Amp
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.
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