# Electrical Power

by Ron Kurtus (revised 19 June 2016)

The electrical power used in operate an electrical device is defined as the potential energy or voltage times the current passing through the device. This is true for both direct current (DC) and alternating current (AC) devices and could also apply to a whole electrical system, such as the the power used in running your household appliances.

Electrical power can be compared to the mechanical definition of power as the work done over a period of time. The electric company uses the power used over a period of time to calculate the energy used and thus your electric bill.

Questions you may have include:

• How do you determine electrical power?
• How is it compared with mechanical power?
• How is your electric bill calculated?

This lesson will answer those questions. Useful tool: Units Conversion

## Determining electrical power

The electrical power required to operate a device is the input voltage times the current required.

P = VI

where

• P = electrical power
• V = voltage used
• I = current in amperes
• VI is V times I

Electrical power is measured in watts. If the amount of watts is large, kilowatts are used. 1 kilowatt = 1000 watts, just as 1 kilometer = 1000 meters. The abbreviation for kilowatt is usually kW.

### Current

If you look at the top of a light bulb, you will see its power rating. One example is a 100 watt light bulb. Thus P = 100W. You can use the equation P = VI for electrical power to determine the amount of current passing through that light bulb.

If your house voltage is V = 110 volts, then you can see that 100W = 110V * I. Thus I = 100 / 110 = 0.91 amps.

### Resistance

You can also find the resistance of the light bulb, using Ohm's Law: V = IR.

V = 110V

I = 0.91A

V = IR = 110V = 0.91A * R

Thus R = 110 / 0.91 = 120.9 ohms.

## Comparing with mechanical power

The standard or mechanical definition of power is the work per unit time. (See Work for more on that subject.) In other words, power equals work divided by time.

P = W / T

where P = power in watts, W = the work done in joules and T = the time of measurement. Since energy is often defined as the ability to do work, let's substitute energy E for work and rearrange the equation:

E = PT

Thus, the electrical energy used is the electrical power times the time. If we measure the electrical power as kilowatts and the time as hours, we get the energy used by an electrical system in terms of kilowatt-hours. That is the unit of measurement the electric company uses when determining your bill.

## Calculating your electric bill

Knowing about electrical power can help you in understanding how your electric bill is calculated. The electric company sends you a bill determined by the amount of work the electricity has done or amount of energy expended in kilowatt-hours. Most homes have an electric meter outside that measures the amount of electric energy used by the house over a period of time.

Many electric companies charges about \$0.07 per kilowatt-hour. Thus, you multiply the number of kilowatts of electricity you use times the amount of time you use it and multiply that by \$0.07 to get your electric bill.

For example, if you used a 1500-watt hair dryer for 100 hours in a month at a cost of \$0.07 per kilowatt-hour, the electric company would bill you for:

1500 watt * 100 hours = 150,000 watt-hours = 150 kilowatt-hours.

Thus your bill would amount to:

150 kilowatt-hours * \$0.07 / kW-hr = \$10.50.

## Summary

Electrical power is voltage times current. Your electric bill is based on the electrical power times the time used, in kilowatt-hours. Knowing how much power you used and the electric rate charged, you can determine your electric bill.

Power can be electrifying

## Resources and references

Ron Kurtus' Credentials

### Websites

DC and AC Electricity Resources

Physics Resources

### Books

Basic Electricity by Bureau of Naval Personnel; Dover Pubns; (1970) \$14.95 - Provides thorough coverage of the basic theory of electricity and its applications

Teach Yourself Electricity and Electronics by Stan Gibilisco; McGraw-Hill; (2001) \$34.95 - Guide for professionals, hobbyists and technicians desiring to learn AC and DC circuits

## Questions and comments

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