What is the cost of lighting a 500-watt outdoor light for 8 hours, if electricity costs 7.5 cents per kilowatt-hour?
The Correct Answer and Explanation is:
To calculate the cost of lighting a 500-watt outdoor light for 8 hours, we follow these steps:
Step 1: Convert watts to kilowatts
First, we need to convert the power consumption from watts to kilowatts, because the cost of electricity is typically charged per kilowatt-hour (kWh).
[
1 \text{ kilowatt} = 1000 \text{ watts}
]
So, to convert 500 watts to kilowatts:
[
500 \, \text{watts} = \frac{500}{1000} \, \text{kilowatts} = 0.5 \, \text{kilowatts}
]
Step 2: Calculate the total energy used in kilowatt-hours
Now, we calculate how much energy the light uses in kilowatt-hours over 8 hours of operation.
[
\text{Energy used} = \text{Power in kilowatts} \times \text{Time in hours}
]
[
\text{Energy used} = 0.5 \, \text{kilowatts} \times 8 \, \text{hours} = 4 \, \text{kWh}
]
Step 3: Calculate the cost of electricity
Next, we calculate the cost of using 4 kWh of electricity. We know that the electricity costs 7.5 cents per kWh. To find the total cost, we multiply the energy used (in kWh) by the cost per kWh.
[
\text{Cost} = \text{Energy used} \times \text{Cost per kWh}
]
[
\text{Cost} = 4 \, \text{kWh} \times 7.5 \, \text{cents per kWh} = 30 \, \text{cents}
]
Final Answer:
The cost of lighting a 500-watt outdoor light for 8 hours is 30 cents.
Explanation:
In this problem, we used basic principles of electrical energy consumption. The light consumes 500 watts, but since the electricity cost is based on kilowatt-hours, we converted watts to kilowatts. After calculating the total energy used over 8 hours, we multiplied that energy usage by the cost per kilowatt-hour to find the total cost. Understanding how to convert between units of power and apply energy costs is important for calculating electricity bills in real-world situations.