Electric Circuits Legacy Problem #11 Guided Solution

Electrical devices consume energy, and the rate at which they consume their energy is given by the power rating of the electrical device. For instance, a 7.5 watt night light bulb consumes energy at the rate of 7.5 joules per second. Now the power is equal to the energy divided by the time, so if I rearrange the equation, I can calculate the amount of energy used by multiplying the power rating by the time the device is used. So here for the night light bulb, I can take 7.5 watts and multiply it by 8 hours, and from that I can determine the amount of energy used in a single evening. Now that would come out to be about 60 watt hours, which is not the most typical unit of energy consumption. The more typical unit used by electrical utility companies is kilowatt hours, so if I move the decimal place three places to the left, I'll end up with .060 kilowatt hours for the amount of energy used during a single evening. Now in Part B of this problem, we want to determine the annual cost of using this 7.5 watt night light bulb. What I've done in Part A is determine the energy used in a single evening. So for a 365 day year, I can just take this .060 kilowatt hours and multiply by 365 days, and that would give me the total energy used in a year. Now the utility company charges Alfredo's home 13 cents per kilowatt hours. So if I multiply this figure by 13 cents, I would get the cost in cents of using this 7.5 watt night light bulb for an entire year. And if I move the decimal place two places to the left, I would have the cost in dollars, and it would be $2.847. Now in Part C of this problem, I'm asked to calculate the annual savings that would result if Alfredo replaced the 7.5 watt low energy incandescent night light bulb with a high efficiency .5 watt LED night light bulb. So what I need to do is repeat the same calculations I did in Part A and Part B, and then subtract the cost of using this .5 watt light bulb from the cost of using the 7.5 watt night light bulb. So as I do my calculations here, I'm going to have to take the .5 watts and multiply by the 8 hours, and then move the decimal place three places to the left. That will give me the energy for a day. And then if I multiply by 365 days, I'll get the energy used for a year. And then if I multiply by 13 cents, I'll get the cost for that year. And if I move the decimal place two places to the left again, I'll get the cost in dollars. When I do the calculations, I get just a little short of $0.190. Now I can subtract this from the $2.847, and I'll find that I save $2.657 over the course of a year, simply by replacing the low efficiency 7.5 watt bulb by the higher efficiency .5 watt bulb. I can round this numerical value to two significant digits, and it becomes a $2.7 savings over the course of a year.