72. Two bulbs of wattage 40 W and 100 W rated at 220 V are
connected in series across a 440 V. What will happen?
(a) 40 W bulb will fuse
(b) 100 W bulb will fuse
(c) Both bulbs will fuse
(d) Nothing will happen
Answers
Answer:
If two bulbs of 25W25W and 100W100W rated at 200V200V are connected in 440V440V supply, then
(A) 100100 watt bulb will fuse
(B) 2525 watt bulb will fuse
(C) none of the bulb will fuse
(D) both the bulbs will fuse
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Hint: The resistance of each bulb will be different hence they have different powers. The voltage across each bulb has to be found using the resistance. Then the result will be compared to the voltage rating of the bulbs. By using the formula of the power, then the solution will be determined.
Complete step by step solution:
Given two bulbs having power, P1=25WP1=25W and P2=100WP2=100Wboth are rated at voltage, V=200voltsV=200volts and connected in series with 440440 volts supply.
The expression for power is given as,
P=V2RP=V2R
Where, VV is the voltage and RR is the resistance.
From the above expression,
R=V2PR=V2P
Hence, we can find the resistance of each bulb using this equation for the given power and voltage rating.
⇒R1=V2P1⇒(200V)225W⇒1600Ω⇒R1=V2P1⇒(200V)225W⇒1600Ω
The resistance of 25W25W bulb is 1600Ω1600Ω.
And,
⇒R2=V2P2⇒(200V)2100W⇒400Ω⇒R2=V2P2⇒(200V)2100W⇒400Ω
The resistance of 100W100W is 400Ω400Ω.
Since the two bulbs are connected in series, the total resistance will be R1+R2R1+R2.
The voltage across each bulb will be different. They are connected to 440440 volts supply also.
Hence, the voltage across the 25W25W bulb is given as,
⇒V1=440V×R1R1+R2⇒V1=440V×R1R1+R2
Substituting the values in the above expression,
⇒V1=440V×1600Ω1600Ω+400Ω⇒352V⇒V1=440V×1600Ω1600Ω+400Ω⇒352V
The voltage across 25W25W is 352V352V. This is higher than the rated voltage 200volts200volts. Therefore, the bulb will fuse.
The voltage across 100W100W bulb is given as,
⇒V2=440V×R2R1+R2⇒V2=440V×R2R1+R2
Substituting the values in the above expression,
⇒V2=440V×400Ω1600Ω+400Ω⇒88V⇒V2=440V×400Ω1600Ω+400Ω⇒88V
The voltage across 100W100W is 88V88V. This is lower than the rated voltage 200volts200volts. Therefore, the bulb will not fuse.
Therefore, only the 25W25W bulb will fuse.
The answer is option B
Explanation:
Note: If two bulbs have the same voltage rating but the power is different, then a bulb having high power will have low resistance. And the low power bulb will fuse than the high power bulb. The power is directly proportional to the square of the voltage and inversely proportional to the resistance.