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Chapter 5: Problem 33

Houses in the U.S. are equipped with circuit protection rated to 100 or 200 Amps, typically. If a 100 A house is operating at \(80 \%\) of its rated capacity, \(^{52}\) how much power is it consuming (at \(120 \mathrm{~V}\) )? If sustained for a month, how many kWh will show up on the bill? At \(\$ 0.15 / \mathrm{kWh}\), what is the cost?

Short Answer

Expert verified
Answer: The cost of the electricity bill for the house is $1036.8.

Step by step solution

01

Calculate the operational current

First, we need to calculate the operational current of the house. Since, it's operating at \(80\%\) of its rated 100 Amps capacity, the operational current (I) can be calculated as: \(I = 100 \mathrm{A} \times 80\% = 100 \times 0.8 = 80 \mathrm{A}\)
02

Calculate the power consumed

Now that we have the operational current, we can calculate the power consumed using the formula, \(P = VI\). We have given V = 120 Volts and I = 80 A. \(P = 120 \mathrm{V} \times 80 \mathrm{A} = 9600 \mathrm{W} = 9.6 \mathrm{kW}\) So, the house is consuming 9.6 kW of power.
03

Calculate the energy consumed in a month

Next, we will find out the energy consumed in kWh over a month. Let's assume there are 30 days in a month. So the energy (E) consumed can be calculated as: \(E = P \times \mathrm{Time\ (in\ hours)}\) \(E = 9.6 \mathrm{kW} \times 30 \times 24 = 9.6 \times 720 = 6912 \mathrm{kWh}\) Therefore, 6912 kWh of energy will be consumed in a month.
04

Calculate the cost of energy consumption

Lastly, we will calculate the cost of energy consumed at a rate of \(0.15\) per kWh. The cost (C) can be calculated as: \(C = E \times \mathrm{Rate\ per\ kWh}\) \(C = 6912 \mathrm{kWh} \times \$0.15 = \$1036.8\) So, the cost of the electricity bill for the month will be $1036.8.

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Most popular questions from this chapter

If we have \(6 \times 10^{23}\) molecules, \(^{53}\) and each molecule releases \(1 \mathrm{eV}\) in a chemical reaction, how many kJ (per mole, as it turns out) is this reaction?

A refrigerator cycles on and off. Let's say it consumes electrical power at a rate of \(150 \mathrm{~W}\) when it's on, and (essentially) \(0 \mathrm{~W}\) when it's off. If it spends half of its time in the on-state, what is its average power? How much energy does it consume in a 24 -hour day, in kWh? At a typical electricity cost of \(\$ 0.15\) per \(\mathrm{kWh}\), about how much does it cost per year to run the refrigerator?

If a typical metabolic intake is \(2,000 \mathrm{kcal}\) each day, approximately how much energy does this translate to for one day, in units of \(\mathrm{kWh}\) ? Compare this to a typical American household's electricity usage of \(30 \mathrm{kWh}\) in a day.

A generic \(\$ 10\) pizza might contain about \(2,500 \mathrm{kcal}\). What is this in \(\mathrm{kWh}\) ? Electricity typically costs \(\$ 0.15\) per \(\mathrm{kWh},{ }^{44}\) so how much would a pizza's amount of energy cost in electrical terms? Which of the two is a cheaper form of energy?

A car headlight using light emitting diodes (LEDs) operates at about \(15 \mathrm{~W}\). If drawing from the car's \(12 \mathrm{~V}\) battery, how much current, in Amps, flows to the headlight?
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