20.4 Electric Power and Energy

Understand the physics of resistance in a wire.

The wire's resistance can be changed to see how they affect it.

Many people have electricity.

There are power transmission lines.
We think of lightbulbs in terms of their power ratings.
We will compare a 25-W bulb with a 60-W bulb.
The 60-W bulb needs to draw more current to have a better power rating.
The resistance of the 60-W bulb must be lower than that of the 25-W bulb.
If we increase power, we also increase voltage.
When a 25-W bulb that is designed to operate on 120 V is connected to 120 V, it briefly glows and then burns out.

The potential difference the charge moves through is expressed as, where is the charge moved and is the voltage.

The product of current times voltage is electric power.

The units of watt are familiar to power users.
Power has units of joules per second, or watt, since the SI unit for potential energy is the joule.
You can charge a cell phone or other electronic device from an auxiliary power outlet in a car.
The circuit can deliver a maximum power if these outlets are rated at 20 A.
Electric power may be expressed as kilovolt-amperes in some applications.

To see the relationship of power to resistance, we combine the two laws.

The first equation is always valid and the other two can only be used for resistors.

The power supplied by the voltage source and the power dissipated by the Resistor are the same in a simple circuit.

There are three different expressions for electric power.

The lower the resistance, the greater the power delivered.
The effect of applying a higher voltage is greater than expected.
When the voltage is doubled to a 25-W bulb, its power almost triples to 100 W, burning it out.
The power of the bulb would be exactly 100 W, but it would be higher at higher temperatures.

We can find the power by knowing the voltage and current.

We can find the power with the knowledge of the voltage and resistance.

The 30 W dissipated by the hot light.

When it's cold, the 411 W is higher.
As the bulb's temperature increases, the initial power decreases.

There are several ways to find the current when the bulb is cold.

The cold current is higher than the steady-state value of 2.50 A, but it will quickly decline as the bulb's temperature increases.

As a device comes on, most circuit breakers are designed to tolerate very high currents for a short time.
Special "slow blow" fuses are required in some cases, such as with electric motors.

The higher your electric bill is, the more electric appliances you use.

The fact is based on the relationship between power and energy.
You pay for the use of energy.

The energy used by a device is 20.34.

The longer the lightbulbs are on, the greater their use.

It is easy to estimate the cost of operating electric appliances if you know their power consumption rate in kilowatts, the time they are on in hours, and the cost per kilowatt-hour for your electric utility.

It is possible to convert kilowatt-hours to joules.

Reducing the time of use is one way to reduce the electrical energy used.

This will result in a reduced impact on the environment.

Some of the fastest ways to reduce electrical energy in a home or business are improvements to lighting.

20% of a home's use of energy goes to lighting, while 40% goes to commercial establishments.
The fluorescent lights are four times more efficient than the incandescent lights.
A 15-W bulb has the same brightness and color as a 60-W bulb.
A bent tube inside a globe or a spiral-shaped tube is connected to a standard screw-in base that fits standard incandescent light sockets.
They last up to 10 times longer because of the less heat transfer.
The significance of an investment in such bulbs is addressed in the next example.
The new whiteLED lights are 5 times longer than the old ones and are twice as efficient.
Their cost is still high.

The relationship is useful in many different ways.

The power level and duration of your activity are related to the amount of energy you use in exercise.
Power level and time are related to the amount of heating by a power source.
The power and time of exposure are related to the radiation dose.

The energy used in kilowatt-hours and the cost per kilowatt-hour are used to find the operating cost.

The total cost will be $7.20 for 1000 hours.

The electricity cost will be $7.20/4 since the CFL uses 15 W and not 60 W. The investment cost will be a tenth of the bulb cost for that time period of use, or 0.1 dollars per pound.

For 1000 hours, the total cost will be $1.

Even though the initial investment is higher, it is cheaper to use the CFLs.

The increased cost of labor that a business must include for replacing the incandescent bulbs more often has not been figured in.

Take a look at the total wattage used in the rest rooms.

Most of the examples dealt with so far have constant voltage sources.

The current is a constant once it is established.
It is the state of the circuit.
The majority of well-known applications use a time-varying source.
The circuit is known as an alternating current circuit if the source varies frequently.
Commercial and residential power serves a lot of our needs.
Around the world, the AC voltages and frequencies are different.

A simple resistance circuit uses the voltage and current in phase.

AC sources have different frequencies and peak voltages.

There is a potential difference between the terminals of the AC source.

The expression is given by.

Figure 20.17 shows a schematic of a simple circuit.

The current in the resistor is the same as the driving voltage.

As the current repeatedly goes through zero, the fluorescent light bulb's Resistor will light up and dim 120 times per second.
If you wave your hand back and forth between your face and a fluorescent light, you will see a stroboscopic effect.
The power is variable because the light output fluctuates.
The power is supplied.

Their product is non- negative and fluctuates between zero and, since the voltage and current are in phase here.

The average power is.

The 60-W light bulb in your desk lamp has an average power consumption of 60 W.

The areas above and below the line are equal, but it can also be proven using trigonometric identities.

To get a root mean square, the quantity is squared, its mean is found, and the square root is taken.

The average value for AC is zero.

Most household electricity is 120 V AC, which means it is 120 V. The 1.0-kW microwave oven consumes a lot.

The equivalent DC values for a simple resistive circuit are the rms and average values.

The equations for power are similar to those for DC, but rms and average values are used for AC.

120 V is 60.0 W and we can find the peak power from the average power.

The AC voltage can change from 170 V to and back 60 times a second.

A constant 120 V is the equivalent DC voltage.

Peak power is the amount of power at a time.

The power swings from zero to 120 W one hundred twenty times per second, and the power averages 60 W.

AC is the most common power-distribution system.

In most parts of the world, the 120-V AC is used for homes and on the job, but the power is transmitted at much higher voltages.
It is cheaper to build a few large electric power-generation plants than it is to build many small ones.
It is important that energy losses are minimized when sending power long distances.
High voltages can be transmitted with less power losses than low ones.
The user's voltage is reduced for safety reasons.
AC is used in most large power distribution systems because it is easier to increase and decrease it than DC.

To reduce power loss in the transmission lines, power is distributed over large distances.

The power plant's voltages are stepped up by passive devices called transformers, which can be found in many places around the world.
The transformer reduces the voltage transmitted for safe use.

We can find the current flowing from and then the power dissipated in the lines by taking the ratio to the total power transmitted.

To find the current, we rearrange the relationship.

The power dissipated in the lines is found by knowing the current and resistance.

An acceptable loss is one-fourth of a percent.

If 100 MW of power had been transmitted at 25 kV, a current of 4,000 A would have been required.
This would result in a power loss of 16.0% in the lines.
The lower the voltage, the more current is needed.
Lower-resistance lines can be built, but they require larger and more expensive wires.
There would be no loss in the transmission lines if the lines were economically produced.
There is a limit to current in superconductors.
AC is used in most large-scale power distribution systems because it is easier to raise and lower than high voltages.