Chapter 7

Electricity

2

Electric charge

Electric charge is an inherent physical property of certain subatomic particles that is responsible for electrical and magnetic phenomena. Charge is represented by the symbol q. The SI units of charge is the coulomb (C).

Like mass, electric charge is a fundamental property of matter. Unlike mass, there are two types of charge:

Positive and Negative.

3

Electric charge, cont’d

Recall that every atom is composed of electrons surrounding a nucleus. The nucleus contains:

protons — positive charge. neutrons — no charge.

Electrons — negative charge. An atom’s atomic

number is the number of protons in the nucleus.

4

Electric charge, cont’d

An atom’s charge is neutral if it has the same number of protons and electrons.

An atom is said to be ionized if the number of electrons and protons is different.

5

Electric charge, cont’d

If the protons outnumber the electrons, there is more positive charge. We call such an atom a positive ion.

If the electrons outnumber the protons, there is more negative charge. We call such an atom a negative ion.

6

Electric force and Coulomb’s law When we bring electric charges together, they

exert a force on each other. Positive charges attract negative charges. Positive charges repel positive charges. Negative charges attract positive charges. Negative charges repel negative charges.

We paraphrase this as:

Like charges repel, unlike charges attract.

7

Electric force and Coulomb’s law, cont’d

The law that describes the forces between electric charges is called Coulomb’s law.

Coulomb’s Law states that the force acting on each of two charged objects is directly proportional to the net charges on the object and inversely proportional to the square of the distance between them:

1 22

q qF

d

8

Electric force and Coulomb’s law, cont’d

The force on q1 is equal and opposite to the force on q2. If the charges increase, the force increases. If the distance increases, the force decreases.

9

Electric force and Coulomb’s law, cont’d

The proportionality constant has a value of 9×109 N-m2/C2.

Coulomb’s law is then:

F is in newtons, q1 & q2 are in coulmbs, and d is in meters.

29 1 2

2 2

N m9 10

C

q qF

d

10

Electric field

The electrostatic force is similar to gravity. The force can act through a distance without

the two charges having to touch. Just as we talk about the gravitational field,

we can also define an electric field.

The electric field lines indicate the direction that a positive charge would move.

force on a charged objectelectric field strength

charge on the object

11

Electric field, cont’d

Here are some illustrations of electric field lines surrounding a positive and a negative charge. The field lines point

away from the positive charge.

The field lines point toward the negative charge.

12

Electric field, cont’d

If the field points to the right: A positive charge would also travel to the right.

The positive charge “thinks” there is a negative charge at the end of the line.

A negative charge would travel to the left. The negative charge

“thinks” there is a positive charge at the start of the line.

13

Electric field, cont’d

An electrostatic precipitator is an example of using electrostatics. Negatively charged wire charge the soot

passing between the plates.

The now negative soot particles are attracted to the positively charged plates.

14

Electric currents

An electric current is a flow of charged particles. It is the rate of flow of electric charge. The amount of charge that flows by per

second:

The SI unit is the ampere (A or amp): 1 amp is 1 coulomb per second.

chargecurrent

time

qI

t

15

Electric currents

Here are some examples of electric current.

Positive current is in the direction of positive charge flow.

16

Resistance

Resistance is a measure of the opposite to current flow. Resistance is represented by R. The SI units of resistance is the ohm (). A conductor is any substance that readily

allows charge to flow through it. An insulator is any substance through which

charge does not readily flow. A semiconductor are substances that fall

between the two extremes.

17

Resistance, cont’d

Resistance of a wire depends on: Composition. The particular substance from

which the object is made. Length. The longer the wire, the higher the

resistance. Diameter. The thinner the wire, the higher the

resistance. Temperature. The higher the temperature, the

higher the resistance.

18

Resistance, cont’d

Resistance is similar to friction. Resistance inhibits the flow of electric charge. Electrons typically produce the current in

metals. The electrons collide with the atoms of the

metal. This slows them down. They also lose some energy to the atoms.

The metal gets hotter.

19

Resistance, cont’d

Superconductivity is a phenomenon in which a substance provides zero resistance to the flow of electric charge. It typically only occurs at rather low

temperatures. The temperature below which

a substance superconducts is called is critical temperature.

The latest superconductors require temperatures around 140 K (-207ºF).

20

Electric current and Ohm’s law

An electric current will flow through a wire only if an electric field is present to exert a force on the charges. We typically use a “power supply” to provide

the electric field and therefore the force. The power supply forces

charges out one terminal, through the wire, and back into the second terminal.

21

Electric current and Ohm’s law, cont’d

Voltage is the work that a charged particle can do divided by the size of the charge. It is the energy per unit charge given to

charged particles by a power supply.

The SI unit is the volt (V). One volt equals one joule per coulomb.

work EV V

q q

22

Electric current and Ohm’s law, cont’d

The flow of charge in an electric circuit is similar to the flow of water through a closed path. The power supply acts like the water pump.

It adds energy to make the current flow. The resistance corresponds to the narrow

section of pipe. The current is like

the flow of water.

23

Electric current and Ohm’s law, cont’d

Ohm’s law specifies that the current in a conductor is equal to the voltage applied to it divided by the resistance:

V is the voltage through the conductor, I is the current passing through the conductor,

and R is the conductor’s resistance.

orV

I V IRR

24

ExampleExample 7.1

A light bulb used in a 3-volt flashlight has a resistance equal to 6 ohms. What is the current in the bulb when it is switched on?

25

ANSWER:

The problem gives us:

The current through the bulb is

ExampleExample 7.1

3 V

6

V

R

3 V0.5 A.

6

VI

R

26

ExampleExample 7.2

A small electric heater has a resistance of 15 ohms when the current in it is 2 amperes. What voltage is required to produce this current?

27

ANSWER:

The problem gives us:

The necessary voltage is

ExampleExample 7.2

15

2 A

R

I

2 A 15

30 V.

V IR

28

Electric current and Ohm’s law, cont’d

A series circuit has only one path for the current to flow. The voltage across the first bulb, plus the

voltage across the second, etc., must equal the battery’s voltage.

The current through each bulb is the same as the current passing through the battery.

29

Electric current and Ohm’s law, cont’d

If the circuit is interrupted, then current no longer flows through the circuit. If one bulb goes bad, then all the bulbs go

dim.

30

Electric current and Ohm’s law, cont’d

A parallel circuit has multiple paths for the current to flow. The current through the first bulb, plus the

current through the second, etc., must equal the current through the battery.

The battery voltage is the same voltage on each bulb.

31

Electric current and Ohm’s law, cont’d

If one bulb goes out, the other bulbs remain lit. There is still a closed path for the electricity to

flow through the circuit.

32

ExampleExample 7.3

Three light bulbs are connected in a parallel circuit with a 12-volt battery. The resistance of each bulb is 24 ohms. What is the current produce by the battery?

33

ANSWER:

The problem gives us:

Since the bulbs are connected in parallel, they each have the same voltage.

So the current through each bulb is:

ExampleExample 7.3

12 V

24

V

R

12 V0.5 A.

24

VI

R

34

ANSWER:

The total current necessary is the sum of the currents through each bulb.

There are three bulbs, so:

ExampleExample 7.3

battery bulb bulb bulb bulb0.5 A 3I I I I I 1

bulb 3 (0.5 A) 0.17 AI

35

Power and energy in electric circuits The power output of a circuit is the rate at

which energy is delivered to the circuit. The power equals:

the energy given to each coulomb of charge, multiplied by the number of coulombs that pass per second.

The energy given to each coulomb of charge is the voltage.

The number of coulombs that pass per second is the current.

36

Power and energy in electric circuits, cont’d

This means the power through a circuit can be written as

The electrical resistance of many substances causes them to get hot.

This type of heating is called ohmic heating.

power voltage current

P VI

37

ExampleExample 7.4

In Example 7.1, we computed the current that flows in a flashlight bulb. What is the power output of the batteries?

38

ANSWER:

The problem gives us:

So the power consumed is

ExampleExample 7.4

3 V

6

0.5 A

V

R

I

0.5 A 3 V

1.5 W

P IV

39

DISCUSSION:

This means the batteries supply 1.5 joules of energy each second.

ExampleExample 7.4

40

Power and energy in electric circuits, cont’d

The current through the filament causes it to get very hot. The filament is a very

thin wire. It is a coil wrapped into

a coil.

The thicker supporting wires do not get as hot.

41

Power and energy in electric circuits, cont’d

A fuse uses ohmic heating to monitor the current through the circuit. If too much current

flows, the fuse gets too hot.

It essentially melts and breaks the circuit.

42

ExampleExample 7.5

An electric hair dryer is rated at 1,875 watts when operating on 120 volts. What is the current flowing through it?

43

ANSWER:

The problem gives us:

The power is given by

Since we want the current, we divide by V:

ExampleExample 7.5

120 V

1,875 W

V

P

.P IV

1,875 W15.6 A.

120 V

PIV

44

DISCUSSION:

The wiring in the house and the hair dryer’s cord must be large enough to handle 15.6 A without overheating.

ExampleExample 7.5

45

Power and energy in electric circuits, cont’d

It is more efficient for the power company to use very high voltage and low current to transmit power. Cross-country power lines use several

hundred-thousand volts. This allows smaller currents to be used. With smaller current, smaller wires can be

used without fear of excessive ohmic heating. This saves money of cable, the supporting

structures, etc.

46

Power and energy in electric circuits, cont’d

Recall our definition of power: The change in energy per unit time.

This means we can write energy as the power multiplied with the elapsed time. The energy change equals the rate at which

energy is transferred time how long it is transferred.

This is similar to the change in distance equaling the rate at which position changes multiplied with the time over which the position changes.

47

Power and energy in electric circuits, cont’d

So we can write the energy in terms of the power:

So if we know the power a circuit uses and how long the circuit operates, we can determine the energy used by the circuit.

EP E Pt

t

48

Power and energy in electric circuits, cont’d

Power companies do not actually charge you for power.

They charge you for energy.

So a kilowatt-hour is really energy.

1 kWh 1 kW 1 h

1,000 W 3600 s

3,600,000 J

49

ExampleExample 7.6

If the hair dryer discussed in Example 7.5 is used for 3 minutes, how much energy does it use?

50

ANSWER:

The problem gives us:

The energy is given in terms of power as:

ExampleExample 7.6

180 s

1,875 W

t

P

1,875 W 180 s

337,500 J.

E Pt

51

DISCUSSION:

This is about the energy: required to melt 2 lb of ice, or of a small car traveling at 60 mph, or of a 150 lb person falling 170 floors.

ExampleExample 7.6

52

AC and DC

There are two types of current flow: direct current (DC) represents current flow

that is always in the same direction. Batteries provide DC.

alternating current (AC) represents current flow that alters direction periodically.

Wall outlets provide AC.

A power adapter converts the AC from the outlet to DC to charge a battery or power some device.

53

AC and DC, cont’d

Here is an example of DC provided by a battery to a light bulb. The current always passes from the positive

battery terminal, through the bulb, and then to the negative terminal.

The current is constant in time.

54

AC and DC, cont’d

Here is an example of AC provided by a wall outlet to a light bulb. The current always passes from the positive

terminal, through the bulb, and then to the negative terminal.

But the terminals swap position over time.

55

AC and DC, cont’d

So the current passing through the bulb changes direction. Our wall outlets operate at 60 Hz. So the current changes direction 120 times

each second.

56

AC and DC, cont’d

Here is one advantage of AC over DC. A transformer is a device that can increase or

decrease AC voltage. If the transformer increases the voltage, it is

called a “step up” transformer. If the transformer decreases the voltage, it is

called a “step down” transformer.

But there is an important consideration.

57

AC and DC, cont’d

The power into the transformer must (ideally) equal the power out.

Recall that electrical power is P = IV. If the voltage is increased (stepped-up), the

current must be decreased by the same factor. If the voltage is decreased (stepped-down),

the current must be increased by the same factor.

Basically, energy must be conserved.