Problem 7 - Applied Physics

Question

Six \(50.0-\mathrm{W}\) bulbs are operated for \(25.0 \mathrm{~h}\) on a \(115-\mathrm{V}\) circuit. If energy costs $$\$ 0.075$$ per $\mathrm{kWh}$$, find the cost of operating them.

Step-by-Step Solution

Answer

The cost of operating them is $0.56.

Step 1: Calculate Total Energy Consumption

First, find out how much energy the bulbs use in total. Each bulb is rated at \(50.0\) watts and runs for \(25.0\) hours, so the energy used by one bulb is \(50.0 \, \text{W} \times 25.0 \, \text{h} = 1250 \, \text{Wh} = 1.25 \, \text{kWh}\). As there are 6 bulbs, the total energy consumed is \(6 \times 1.25 \, \text{kWh} = 7.5 \, \text{kWh}\).

Step 2: Calculate the Total Cost of Energy

Now, calculate the cost for the total energy consumed. The cost per kilowatt-hour is \(\\(0.075\). Therefore, the cost is \(7.5 \, \text{kWh} \times \\)0.075 \, \text{per kWh} = \$0.5625\).

Step 3: Convert Calculation to Cost

To express the cost as money, round \\(0.5625 to two decimal places, which gives a final answer of \\)0.56.

Key Concepts

electricity consumption

Electricity consumption refers to the amount of electric energy used by an appliance over a certain period. Understanding this concept is essential when calculating energy costs.
For our example, each bulb has a power rating of 50 watts, which means they consume energy at a rate of 50 joules per second.
If a bulb operates for 25 hours, the total electricity consumption becomes 1,250 watt-hours (Wh), which we convert to kilowatt-hours (kWh) by dividing by 1,000.
Thus, one bulb uses 1.25 kWh, and for six bulbs the total electricity consumption is 7.5 kWh. This calculation is an essential first step in figuring out energy costs.

power and energy

Power and energy are closely related but distinct concepts in physics.
Power measures the rate at which energy is used or transferred and is measured in watts (W), where 1 watt equals 1 joule per second.
Energy, on the other hand, signifies the total amount of work or heat done and is commonly measured in kilowatt-hours (kWh) for electricity purposes.

• Each 50-W bulb uses power at a constant rate, continuously consuming energy as it burns.
• The energy consumed over time is the total power multiplied by the time in hours.

For this reason, knowing both the power rating in watts and the period of use is vital for accurate energy tracking. In our problem, the power and time equation gives us the bulbs' total energy use.

cost per kilowatt-hour

The cost per kilowatt-hour (kWh) is a crucial figure in energy billing, reflecting the price at which electricity is sold.
To calculate the total cost, simply multiply the total energy consumption by the cost per kWh.

• In our scenario, the energy consumption of 7.5 kWh, multiplied by the given cost of 0.075 per kWh, results in the total expense.
• This calculation indicates how much it costs to use the bulbs over the specified time period.

Understanding how cost per kilowatt-hour affects your bill can lead to more conscious energy use and potential savings.