The question is:
Mr.X decorated his house with fairy lights on a celebration.He bought 40 bulbs and operated at 220V. He found all the bulbs are glowing with different brightness. He called his friend Mr.Y. He rearranged and made the bulbs glow equally.
a)What was the problem with Mr.X's set up?Give reason.
b)How did Mr.Y arrange the bulbs.
The following is my understanding (The time is same in all cases and subcases):
Firstly, the brightness of a bulb depends upon the energy consumed by it.
There are two cases:When the resistance is same in all the bulbs and when the resistance is different for different bulbs.
Case 1:Resistance is same in all bulbs.
Subcase 1:The bulbs are connected in parallel.
$H=\frac{v^2}{R}*t$.
Since the resistance and the voltage both remain same, energy consumed by every bulb is same and hence they all glow with equal brightness.
Subcase 2:The bulbs are connected in series.
$H=I^2Rt$.
Since the resistance and the current through it remain same, in this case also, the energy consumed must be the same.
Hence the situation given in the problem will not arise if all the bulbs have the same resistance.
Case 2:When the bulbs have different resistances.
Subcase 1:If the bulbs are connected in parallel.
$V=IR$.
The voltage is same for all the bulbs. The resistances are different. Hence, the current will be divided among the bulbs with respect to their resistance. Since each bulb has different resistance, it glows with different brightness. If current passes through it according to each bulb's requirement,then the bulbs will glow by using their maximum power and will glow with different brightness.
Subcase 2:The bulbs are connected in series.
$H=I^2Rt$
The current through each bulb is the same. The resistances are different. Hence, the energy consumed by each bulb is different.
My understanding makes me conclude that the question is wrong. I am utterly confused about this problem. A book's solution indicates that we should only check for potential difference.Can anyone please tell me the mistakes in my understanding,if any, and provide me with a proper solution to the problem?Any help is appreciated.
Best Answer
The question setter forces you to think for yourself about the possibilities. If MrX had wired some bulbs in series and some in Parallel then there would be a difference in brightness assuming all bulbs were the same wattage. Series connection of all bulbs would not be practical for 40 bulbs. MrY simply arranged all bulbs in parallel. If bulbs were of differing wattage then a combination of parallel and serial connection would be required to get equal glow from all connected bulbs. Assuming MrX bought 20 x 60W and 20 x 20W globes, MrY would have to series 60W and 20W bulbs and then put these in strings in parallel with each other. Don't over think the problem.