200W vs. 50W bulb

[admin]

Two engineering students, Alan and Bob, living in neighbouring college rooms, decided to economise by connecting their ceiling lights in series to a DC supply. They agreed that each would pay equal shares of the electricity bill. However, both decided to try to get better lighting at the others expense. Alan installed a 200W bulb, while Bob installed a 50W bulb. Who got the best deal?

[Heinz R.]

The total dissipation for the two loads in series will be 40W. The 50W bulb will dissipate 32W and the 200W bulb will dissipate 8W. The 200 bulb will certainly not give off any light and the 50W bulb will at best be very dim, if at all. Neither benefits, they both pay.
Silly problem.

[Heinz R.]

BTW, it would have been worse if they both would have been honest or dishonest about it. If they both had selected 50W bulbs, each would only have dissipated 25W and neither one would have gotten any light. Ditto with each one selecting a 200W bulb - each would have dissipated 100W.

[admin]

Heinz R.
You must be an electrical engineer.
Ken.

[Heinz R.]

Ken:
I've been one for 50 years. How can you tell?

[Heinz R.]

On rethinking my BTW reply above I must note that the analysis is wrong but the conclusion remains the same. If both use 50W bulbs then he total dissipation in the series circuit will be 25W and each bulb will dissipate 12.5W. If both use 200W bulbs, the total dissipation will be 100W and each bulb will dissipate 50W. Once again neither bulb dissipates sufficient power to illuminate.
This analysis assumes no changes in resistance in a tungsten filament incandescent bulb, Obviously an oversimplification but I think that was intended in the problem. Of course, bulbs using other technologies (fluorescent, LED, etc.) need to be analyzed entirely differently, but in my opinion will yield the same results of not providing any light.
Lastly, my original answer to the original problem is correct.





 

[admin]

Just a smart guess.
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