Electric Power

Georgia Perimeter College

Objectives

Describe the electric power dissipated in a circuit, in terms of electrical heating effect also known as “joule heat”.
Determine the household energy consumption in terms of electric power ratings and cost per kilowatt-hour.

This section addresses, in whole or in part, the following Georgia GPS standard(s):

S8P2. Students will be familiar with the forms and transformations of energy.
c. Compare and contrast the different forms of energy (heat, light, electricity, mechanical motion, sound) and their characteristics.

S8P5. Students will recognize characteristics of gravity, electricity, and magnetism as major kinds of forces acting in nature.
b. Demonstrate the advantages and disadvantages of series and parallel circuits and how they transfer energy.
c. Investigate and explain that electric currents and magnets can exert force on each other.

This section addresses, in whole or in part, the following Benchmarks for Science Literacy:

Magnetic forces are very closely related to electric forces and can be thought of as different aspects of a single electromagnetic force. Moving electric charges produce magnetic forces and moving magnets produce electric forces. The interplay of electric and magnetic forces is the basis for electric motors, generators, and many other modern technologies, including the production of electromagnetic waves.
Electrical energy can be produced from a variety of energy sources and can be transformed into almost any other form of energy. Moreover, electricity is used to distribute energy quickly and conveniently to distant locations.
Energy can change from one form to another, although in the process some energy is always converted to heat. Some systems transform energy with less loss of heat than others.

This section addresses, in whole or in part, the following National Science Education Standards:

Energy is a property of many substances and is associated with heat, light, electricity, mechanical motion, sound, nuclei, and the nature of a chemical. Energy is transferred in many ways.

Electrical circuits provide a means of transferring electrical energy when heat, light, sound, and chemical changes are produced.

In most chemical and nuclear reactions, energy is transferred into or out of a system. Heat, light, mechanical motion, or electricity might all be involved in such transfers.

Electricity in circuits can produce light, heat, sound, and magnetic effects. Electrical circuits require a complete loop through which an electrical current can pass.

Electric Power

Electrical devices such as a filament light bulb, electric motor, or heater convert electric energy into radiant heat (of a light bulb), mechanical energy (to run an electric motor), and other forms of energy. The voltage source supplies energy to a circuit and this energy is converted into other forms as charges flow through the wires and the devices in the circuit. The rate at which energy is converted into other forms is known as electric power. Generally, power = energy ¸ time.

Household electrical devices are usually designed to operate at 120 V or 240 V. Each device draws a certain electric current from the voltage source to perform its function. In fact, some manufacturers actually indicate the required current (amp) and voltage (volt) ratings for operating their devices. From this data, one can determine the power consumption and the cost of operating the device for a specified time.

Measuring electric power

Electric power (P) is calculated using electrical quantities (current I, voltage V, and resistance R) already discussed. The electric power used by an appliance depends on the voltage and the current used. Thus:

Electric power = current x voltage

using the symbols:

P = I x V

Electric power is expressed in units of watts (W), where 1 watt = 1 ampere x 1 volt.

In electric devices where the electrical heating effect (also known as "joule heat") is desired, such as an electric heater, the filament or heating element of the device usually has a relatively low resistance (though higher than the resistance of the connecting wires). Due to this low resistance of the element, a large current passes through the heating element. Also, because of the small resistance of the connecting wires of the portable heater or hair-dyer cord, the wires dissipate a noticeably small amount of joule heat and become warm.

The electric power transferred into joule heat can be calculated in terms of the current through the resistance of the element. From Ohm's law, the voltage, V = I x R. So substituting for the voltage (V) in the equation for power above, then electric power

P = I x V = I x (I x R) = I² x R

i.e. Electric power due to joule heat transfer = (current squared) x resistance.

If only the values of the voltage and the resistance are known, then from Ohm's law, since I = V ¸ R, the electric power

P = V x I = V x (V ¸ R) = V² ¸ R

i.e. Electric power due to joule heat transfer = (voltage squared) ¸ resistance.

Electric Power Ratings

Electrical appliances are often rated in terms of the rate at which such appliances consumes electric energy. Some appliances convert energy at a faster rate than others depending on their electric power rating, measured in watt (W) or thousands of watt (1000 watt = 1 kilowatt, kW).

Since power is generally defined as power = energy ¸ time, then the electrical energy consumed by an appliance is defined as: Energy = Power consumption x Time

So, with the electric power expressed in kilowatt (kW) and time in hours (h), the unit of electric energy is the kilowatt-hour (kWh). Electrical utility companies charge for energy consumption in terms of the cost per kilowatt-hour.

Consider the power ratings for the household appliances: coffee maker (1000 W), hair dryer (1.2 kW), and clothes dryer (5400 W). Given that the cost per kilowatt-hour charged by Georgia Power for electrical energy consumption is 8 cents per kWh, the cost of operating a 1000 W coffee maker for two hours is determined as:

Energy = 1000 W x 2 h = 2000 watt-hour = 2 kWh, and

Total cost = (cost per kWh) x (energy in kWh) = (8 cents /kWh) x (2 kWh) = $0.16.

Measuring Electricity

(From the Energy Information Administration)

Electricity is measured in units of power called watts. It was named to honor James Watt, the inventor of the steam engine. One watt is a very small amount of power. It would require nearly 750 watts to equal one horsepower. A kilowatt represents 1,000 watts. A kilowatthour (kWh) is equal to the energy of 1,000 watts working for one hour. The amount of electricity a power plant generates or a customer uses over a period of time is measured in kilowatthours (kWh). Kilowatthours are determined by multiplying the number of kW's required by the number of hours of use. For example, if you use a 40-watt light bulb 5 hours a day, you have used 200 watts of power, or 0.2 kilowatthours of electrical energy.

See our Energy Calculator section to learn more about converting units.

Review Question

1. What is the direct cost of operating a 100-W light bulb for one month (30 days) at the cost of 10 cents per kWh?

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Content provided by Mr. Martin O. Okafor, Georgia Perimeter College

Some content provided by the Energy Information Administration.

Page created by Pamela J.W. Gore
Georgia Perimeter College,
Clarkston, GA

Page created March 10, 2007
Modified May 18, 2007