Question

A typical cost for electrical power is $0.120 per kilowatthour. (a) Some people leave their porch light on all the time. What is the yearly cost to keep a 75-W bulb burning day and night? (b) Suppose your refrigerator uses 400 W of power when it's running, and it runs 8 hours a day. What is the yearly cost of operating your refrigerator?

Short answer

Porch light costs $78.84/year; refrigerator costs $140.16/year.

Step-by-step solution

Convert Watts to Kilowatts for the Porch Light

First, convert the power consumption of the porch light from watts to kilowatts. Since 1 kilowatt is 1000 watts, a 75-W bulb is 0.075 kW.

Calculate the Total Kilowatt-hours for the Porch Light

The bulb runs continuously, so it operates 24 hours a day for 365 days a year. Multiply the power consumption in kilowatts by the number of hours in a year: \[ 0.075 ext{ kW} imes 24 ext{ hours/day} imes 365 ext{ days/year} = 657 ext{ kWh/year} \]

Calculate the Cost for the Porch Light

Multiply the total kilowatt-hours by the cost per kilowatt-hour: \[ 657 ext{ kWh/year} imes 0.120 ext{ dollars/kWh} = 78.84 ext{ dollars/year} \]This is the yearly cost to keep the porch light on.

Convert Watts to Kilowatts for the Refrigerator

Convert the power usage of the refrigerator from watts to kilowatts. A 400-W appliance is 0.400 kW.

Calculate the Daily Kilowatt-hours for the Refrigerator

Multiply the power consumption by the number of hours the refrigerator runs daily: \[ 0.400 ext{ kW} imes 8 ext{ hours/day} = 3.2 ext{ kWh/day} \]

Calculate the Yearly Kilowatt-hours for the Refrigerator

Multiply the daily kilowatt-hours by the number of days in a year to get the yearly consumption: \[ 3.2 ext{ kWh/day} imes 365 ext{ days/year} = 1168 ext{ kWh/year} \]

Calculate the Cost for the Refrigerator

Multiply the yearly kilowatt-hours by the cost per kilowatt-hour: \[ 1168 ext{ kWh/year} imes 0.120 ext{ dollars/kWh} = 140.16 ext{ dollars/year} \]This is the yearly cost of operating the refrigerator.

Key concepts

Kilowatt-Hour

The kilowatt-hour (kWh) is a unit of energy that measures electricity consumption. It's an essential concept for calculating the energy use of household electrical appliances. When you use electricity, you're billed by how much energy you consume, and the kilowatt-hour is the standard unit for measuring this energy.

Suppose you have an appliance that's rated at 1000 watts (or 1 kW) and you run it for an hour. The energy used during that time is 1 kWh. That's because a kilowatt-hour is the energy you would use if you kept a 1000-watt appliance running for one hour.

Understanding kilowatt-hours helps you manage your electricity usage and control costs. By knowing how many kilowatt-hours your devices consume, you can compare them and make smarter decisions about their use.

Power Consumption

Power consumption is all about the rate at which an appliance uses energy. It's typically measured in watts (W), which tells us how much energy an appliance uses at any moment. When more energy-consuming appliances are used, more electricity is consumed, leading to higher costs.

To convert power consumption from watts to kilowatts, remember this: 1 kilowatt is equal to 1000 watts. For example, if you have a 75-W light bulb and want to calculate its power consumption in kilowatts, divide by 1000, getting 0.075 kW. This conversion allows you to calculate how much energy an appliance uses in kilowatt-hours over time.

Keeping track of power consumption helps you control your electricity bill by knowing which appliances use the most power.

Cost per Kilowatt-Hour

The cost per kilowatt-hour is the price electric companies charge for one kilowatt-hour of energy. This cost can vary based on where you live, the time of year, or even the time of day. Understanding this cost is crucial for estimating your electricity expenses.

In the example exercise, the cost is $0.120 per kWh. To find out how much money it costs to use an appliance, simply multiply the total kWh used by the cost per kWh.

Calculating costs using the cost per kilowatt-hour allows you to forecast your electricity expenses and budget accordingly. Being aware of this cost helps you use electricity more efficiently and reduces waste.

Electrical Power Usage

Understanding your electrical power usage involves knowing how much energy your household appliances consume over time and the pattern of your electricity consumption.

For instance, if you run a 400-W refrigerator for 8 hours a day, you consume 3.2 kWh daily. By multiplying this daily usage by 365 days, you discover how much energy the appliance uses yearly, which you can then convert to costs using the cost per kilowatt-hour.

By understanding electrical power usage patterns, you can identify areas where you might save energy, whether by using appliances more efficiently or considering more energy-efficient models.

Mathematical Calculations

Mathematical calculations are the backbone of understanding energy costs. These calculations transform abstract concepts into practical information you can use to manage your electricity consumption.

Here’s the basic formula:

• Convert power ratings from watts to kilowatts.
• Calculate total energy consumption in kilowatt-hours.
• Multiply by cost per kilowatt-hour to get the cost.

For example, for a 0.4 kW refrigerator used for 8 hours daily, the steps are:

• Calculate daily kWh: 0.4 kW * 8 hours = 3.2 kWh.
• Calculate yearly kWh: 3.2 kWh/day * 365 days = 1168 kWh/year.
• Calculate cost: 1168 kWh * $0.120/kWh = $140.16/year.

Understanding these calculations empowers individuals to make informed decisions about their energy use and costs.