Suppose that you and your roommate are sharing the electric bill in your apartme

Question

Suppose that you and your roommate are sharing the electric bill in your apartment and that it comes to $60/month, at the average rate of $0.1975 per kilowatt-hour. Your roommate never turns the lights off, which you estimate results in the lights being switched on for an average of 19 hours per day – 6 hours more than needed. The room is lit with seven, 60 W incandescent bulbs, which you can assume are powered by a 115 V constant voltage source.
(a) How much does lighting cost you and your roommate per month?

Explanation / Answer

60W at 115V ==> it takes 60W power when operated at 115V

the 60W incandescent bulbs have a resistance of R= V2/W = 220.5 ohm

so the energy used by each bulb is W*time(h) = 60*19*30 = 34.2 KWH

at average rate of $0.1975 per kilowatt-hour

total cost = 6.755 $/month

this is total cost of lighting of one bulb

due to 7bulbs it is 47.28 $/month

since 6 hrs is actually not usable Hence the unusable cost = 47.28*(19-6)/19 = 39.82$/month

so my cost is 39.82 / 2 = 19.9$/month

for my friend cost is 39.82/2 + (47.28 - 39.82) = 27.37 $/month

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