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· Electric charge

Circuits

· Conductors

· Resistivity and Resistance

· Circuit Diagrams

Electric Current & DC Circuits

· Measurement

Electric Circuits

1. Electric Charge

It has been known since ancient times that when certainmaterials are rubbed together, they develop an attraction foreach other. (This can be seen today when you take clothesout of a dryer)In ancient Greece - people noticed that when thread wasspun over a spindle of amber, the thread was attracted to thespindle.The Greek word for amber was "elektron," hence this forcewas called electric.

Electric ChargeIn the 18th century, American Ben Franklin noticed when a rubber rod is rubbed by animal fur, the rod acquires a negative charge, and the animal fur acquires a positive charge.

When a glass rod is rubbed by silk, the rod acquires a positivecharge and the silk obtains a negative charge. Thus, tworubber rods after being charged would repel each other, whilea rubber rod would be attracted to a glass rod.

No new charge is created - instead, it is just separated - thepositive charge acquired by one object is exactly equal inmagnitude and opposite in sign to the charge lost by the otherobject.

When you take two non metallic objects and rub themtogether, you get an interesting effect.Before the contact, there is no interaction between them.Afterwards, the two materials are attracted to each other.

withoutRubbing ...rub after rubbing

The Nature of Charge

Like energy and momentum, charge is neither created nordestroyed, it is conserved.

Opposite charges attract and like charges repel.A s a resultnegatively charged electrons are attracted to the positivenucleus.

Despite the great mass difference, the charge on an electronis exactly equal in magnitude to the charge on a proton, andits magnitude is denoted by "e.“

An electron is said to have a charge of -e anda proton a charge of +e.

Measurement of ChargeThe electron was discovered by J.J. Thomson in 1897, and in aseries of experiments between 1909 and 1913, Robert Millikanand his graduate student, Harvey Fletcher, established the valueof the charge, "e," on an electron.

1. An atom in its normal (non-ionic) state has nocharge. This is due to the fact that atoms:

A have only neutrons.B have no protons or electrons.C have equal numbers of protons and electrons.D have an equal number of protons and neutrons.

2. What object moves freely within the entire atom?A Electron.B Neutron.C Proton.D Nucleus.

3. An atom is composed of:A a central nucleus that is surrounded by neutrons.B an even distribution of electrons and protons in a spherical shape.C a central nucleus surrounded by electrons.D a central nucleus containing protons and electrons.

In conductors, electrons move freely inside the solid. Like chargesrepel, therefore the electrons tend to spread as far apart as possible- which means that they will move to thes urface of the conductor.

Conductors

Insulators

Insulators are materials that have strongly bound electrons that can move only short distances within the solid. Thus, it will be harder for charges to move any significant distance within an insulator.Different insulators have varying levels of insulation capabilities.

Compared to insulators, metals are better conductors ofelectricity because metals contain more free _____.

A positive ions.B negative ions.C protons.D electrons.

Electrons can also flow from Earth, which is an excellentconductor, to the objects, and from the objects to Earth.Earth serves as the ultimate source and destination forelectrons because of its huge size.

Grounding

When a wire is attached between the earth and anotherconductor, excess electrons will flow to the earth leavingthe conductor neutral. This is "grounding." Also, a positivelycharged object will cause electrons to flow to it from the ground.

When you touch an object with a net negative charge, you may get a shock. This is because the conductor wants to get rid of its excess electrons. To do this, electrons flow through you to the ground. If the conductor had an excess positive charge, the electrons would flow from the earth to you. In either case – there is a spark!

Note: grounding is also called "earthing," because of therelationship to Earth.

Electrical circuits and devices are usually grounded to protect from accumulating a net charge that Could shock you.

To ground an electrical device aconductor must run from thedevice into the ground.

Plugs for many electrical devices have a third grounding pin that connects to a wire in the outlet which goes to the ground.

Grounding

1. Electromotive Force – from Electric battery

The symbol for a battery in a circuit diagram. It originated as a schematic drawing of the earliest type of battery, a voltaic pile.

Various cells and batteries (top-left to bottom-right): two AA, one D, one handheld ham radiobattery, two 9-volt (PP3), two AAA, one C, onecamcorder battery, one cordless phone battery.

Line art drawing of a dry cell:1. brass cap, 2. plastic seal, 3. expansion space, 4. porous cardboard, 5. zinc can, 6. carbon rod, 7. chemical mixture.

Within the electrochemical cells of the battery, there is an electric field established between the two terminals, directed from the positive terminal towards the negative terminal. The negative terminal is described as the low potential terminal.

The SI unit on electric potential difference is the volt,  V (in honor of Alessandro Volta). 

How battery works:In a battery-powered electric circuit, the chemical energy is used to do work on a positive test charge to move it from the low potential terminal to the high potential terminal. Chemical energy is transformed into electric potential energy within the internal circuit (i.e., the battery).

Once at the high potential terminal, a positive test charge will then move through the external circuit and do work upon the light bulb or the motor or the heater coils, transforming its electric potential energy into useful forms for which the circuit was designed. The positive test charge returns to the negative terminal at a low energy and low potential, ready to repeat the cycle (or should we say circuit) all over again.

2. CircuitsAn electric circuit is an external path that charges can follow between two terminals using a conducting material.

Requirements •the path must be complete and unbroken--There must be a closed conducting loop in the external circuit that stretches from the high potential, positive terminal to the low potential, negative terminal.

•The Requirement of an Energy Supply--There must be an energy supply capable doing work on charge to move it from a low energy location to a high energy location and thus establish an electric potential difference across the two ends of the external circuit.

Electromotive Force and Current

In an electric circuit, an energy source and an energy consuming deviceare connected by conducting wires through which electric charges move.

Symbols for circuit elements

A Ideal conductor - generally assume that that R=0 Ideal EMF NOTE – device is asymmetric Ideal Resistor EMF with internal resistance Ideal Voltmeter - generally assume that that R=∞ - No current flows through an ideal voltmeter – Ideal Ammeter - generally assume that that R=0 Electrically, an ideal ammeter is a perfect conductor

Electromotive Force and Current

Within a battery, a chemical reaction occurs that transfers electrons fromone terminal to another terminal.

The maximum potential difference across the terminals is called the electromotive force (emf).

emf give circuit voltage supply which is represented by V

Batteries and CurrentThe battery pushes current through the circuit. A battery acts like a pump, pushing charge through the circuit. It is the circuit's energy source.

Charges do not experience an electrical force unless there is adifference in electrical potential (voltage).Therefore, batteries have a potential difference between their terminals.

The positive terminal is at a higher voltage than the negative terminal.

Electromotive Force and Current

The electric current is the amount of charge per unit time that passesthrough a surface that is perpendicular to the motion of the charges.

t

qI

One coulomb per second equals one ampere (A).

Current, resistance and electromotive force

Current is a concept with wide spread applications describing the rate of flow of some quantity that can be:

-Throughput of cars per time interval:

-water volume coming out of a hose per time interval:

20.1 Electromotive Force and Current

If the charges move around the circuit in the same direction at all times,the current is said to be direct current (dc).

If the charges move first one way and then the opposite way, the current is said to be alternating current (ac).

20.1 Electromotive Force and Current

Example 1 A Pocket Calculator

The current in a 3.0 V battery of a pocket calculator is 0.17 mA. In one hourof operation, (a) how much charge flows in the circuit and (b) how much energydoes the battery deliver to the calculator circuit?

(a)

(b)

C 61.0s 3600A1017.0 3 tIq

J 8.1V 0.3C 61.0Charge

Energy Charge Energy

20.1 Electromotive Force and Current

Conventional current is the hypothetical flow of positive charges that wouldhave the same effect in the circuit as the movement of negative charges thatactually does occur.

Electron's journey through a circuit

In the wires of electric circuits, an electron is the actual charge carrier.

zigzag path that results from countless collisions with the atoms of the conducting wire

Demohttp://phet.colorado.edu/en/simulations/category/physics/electricity-magnets-and-circuits

Battery - resistor circuit

Circuit Construction Kit (DC Only)

Eg1. 12 C of charge passes a location in a circuit in 10seconds. What is the current flowing past the point?

Eg2.A circuit has 10 A of current.H ow long does it take 20C of charge to travel through the circuit?

Eg3. 20 C of charge passes a location in a circuit in 30seconds. What is the current flowing past the point?

eg4. A circuit has 10 A of current. How much charge travels through the circuit after 20s?

Eg5.A circuit has 3 A of current. How long does it take 45 C of charge to travel through the circuit?

eg6 A circuit has 2.5 A of current. How much charge travels through the circuit after 4s?

Basic Circuits•The circuit cannot have gaps.•The bulb had to be between the wire and the terminal.•A voltage difference is needed to make the bulb light.•The bulb still lights regardless of which side of the•battery you place it on.

3. Conductor’s Resistance

Some conductors "conduct" better or worse than others. Reminder:conducting means a material allows for the free flow of electrons.

The flow of electrons is just another name for current.

Another way to look at it is that some conductors resist current to a greater or lesser extent.

We call this resistance, R. Resistance is measured in ohms which is noted by the Greek symbol omega (Ω)

4. Ohm’s Law

The resistance (R) is defined as the ratio of the voltage V applied across a piece of material to the current I throughthe material.

4. Ohm’s Law

OHM’S LAW

The ratio V/I is a constant, where V is thevoltage applied across a piece of materialand I is the current through the material:

SI Unit of Resistance: volt/ampere (V/A) = ohm (Ω)

IRVRI

V or constant

4 Ohm’s Law

To the extent that a wire or an electrical device offers resistance to electrical flow,it is called a resistor.

4 Ohm’s Law

Example 1 A Flashlight

The filament in a light bulb is a resistor in the formof a thin piece of wire. The wire becomes hot enoughto emit light because of the current in it. The flashlightuses two 1.5-V batteries to provide a current of0.40 A in the filament. Determine the resistance ofthe glowing filament.

5.7A 0.40

V 0.3

I

VR

2.A flashlight has a resistance of 30 Ω and is connected by a wire to a 90 V source of voltage. What is the current in the flashlight?

3.What is the current in a wire whose resistance is3 Ω if 1.5 V is applied to it?

5. How much voltage is needed in order to producea 0.70 A current through a 490 Ω resistor?

6. How much voltage is needed in order to producea 0.5 A current through a 150 Ω resistor?

7. What is the resistance of a rheostat coil, if 0.05 A ofcurrent flows through it when 6 V is applied across it?

8. What is the resistance of a rheostat coil, if 20 A of current flows through it when 1000 V is applied across it?

5 Resistance and Resistivity

For a wide range of materials, the resistance of a piece of material of length L and cross-sectional area A is

A

LR

resistivity in units of ohm·meter

the measure of a conductor's resistance to conduct is called its resistivity. Each material has a different resistivity.Resistivity is abbreviated using the Greek letter rho (ρ).Combining what we know about A, L, and ρ, we can find aconductor's total resistance.

Resistance, R, is measured in Ohms (Ω). Ω is the Greek letter Omega.

Cross-sectional area, A, is measured in m2

Length, L, is measured in m

Resistivity, ρ, is measured in Ωm

5 Resistance and Resistivity

A

LR

What is the resistance of agood conductor?Low; low resistance meansthat electric charges are free to move in a conductor.

Check:Rank the following materials in order of bestconductor to worst conductor.

A Iron, Copper, PlatinumB Platinum, Iron, CopperC Copper, Iron, Platinum

5 Resistance and Resistivity

Example 3 Longer Extension Cords

The instructions for an electric lawn mower suggest that a 20-gauge extensioncord can be used for distances up to 35 m, but a thicker 16-gauge cord shouldbe used for longer distances. The cross sectional area of a 20-gauge wire is5.2x10-7Ω·m, while that of a 16-gauge wire is 13x10-7Ω·m. Determine the resistance of (a) 35 m of 20-gauge copper wire and (b) 75 m of 16-gauge copper wire.

2.1m105.2

m 35m1072.127-

8

A

LR (a)

(b)

99.0m1013

m 75m1072.127-

8

A

LR

3.What is the resistance of a 2 m long copper wirewhose cross-sectional area of 0.2 mm2?

4. An aluminum wire with a length of 900 m and cross sectionalarea of 10 mm2 has a resistance of 2.5 Ω.What is the resistivity of the wire?

6. What is the cross-sectional area of a 10Ω copper wireof length is 10000 meters ?

7. What is the length of a 10 Ω copper wire whosediameter is 3.2 mm?

20.3 Resistance and Resistivity

Impedance Plethysmography.

calf

2

calf V

L

LV

L

A

LR

6. Electric Power

IVP

ELECTRIC POWER

When there is current in a circuit as a result of a voltage, the electricpower delivered to the circuit is:

SI Unit of Power: watt (W)

Many electrical devices are essentially resistors:

RIIRIP 2

R

VV

R

VP

2

Electrical PowerLet's think about this anotherway...The water at the top has GPE & KE.As the water falls, it loses GPE and the wheel gets turned, doing work. When the water falls to the bottom it is now slower, having done work.Electric circuits are similar.A charge falls from high voltage to low voltage.In the process of falling energy may be used (light bulb, run a motor, etc).

Electric Power

Example 5 The Power and Energy Used in aFlashlight

In the flashlight, the current is 0.40A and the voltageis 3.0 V. Find (a) the power delivered to the bulb and(b) the energy dissipated in the bulb in 5.5 minutesof operation.

20.4 Electric Power

(a)

(b)

W2.1V 0.3A 40.0 IVP

J100.4s 330 W2.1 2PtE

2.A toy car's electric motor has a resistance of 17 Ω; findthe power delivered to it by a 6-V battery.

3. A toy car's electric motor has a resistance of 6 Ω; findthe power delivered to it by a 7-V battery.

4.What is the power consumption of a flash light bulbthat draws a current of 0.28 A when connected to a 6V battery?

5. What is the power consumption of a flash light bulbthat draws a current of 0.33 A when connected to a100 V battery?

6. A 30Ω toaster consumes 560 W of power: howmuch current is flowing through the toaster?

7. A 50Ω toaster consumes 200 W of power: howmuch current is flowing through the toaster?

8. When 30 V is applied across a resistor it generates 600W of heat: what is the magnitude of its resistance?

9. When 100 V is applied across a resistor it generates200 W of heat: what is the magnitude of its resistance?

Circuit Diagrams

*Note: Circuit diagrams do not show where each part is physically located.

7. Series WiringThere are many circuits in which more than one device is connected toa voltage source.

Series wiring means that the devices are connected in such a waythat there is the same electric current through each device.

Series Wiring

SIRRRIIRIRVVV 212121

321 RRRRSSeries resistors

Series Wiring

Example 8 Resistors in a Series Circuit

A 6.00 Ω resistor and a 3.00 Ω resistor are connected in series witha 12.0 V battery. Assuming the battery contributes no resistance to the circuit, find (a) the current, (b) the power dissipated in each resistor,and (c) the total power delivered to the resistors by the battery.

Series Wiring

(a)

(b)

(c)

00.9 00.3 00.6SR A 33.1 00.9

V 0.12

SR

VI

W6.10 00.6A 33.1 22 RIP

W31.5 00.3A 33.1 22 RIP

W9.15 W31.5 W6.10 P

Series Wiring

Personal electronic assistants.

8. Parallel Wiring

Parallel wiring means that the devices areconnected in such a way that the same voltage is applied across each device.

When two resistors are connected in parallel, each receives current from the battery as if the other was not present.

Therefore the two resistors connected inparallel draw more current than does eitherresistor alone.

Parallel Wiring

Parallel Wiring

The two parallel pipe sections are equivalent to a single pipe of thesame length and same total cross sectional area.

Parallel Wiring

PRV

RRV

R

V

R

VIII

111

212121

parallel resistors

321

1111

RRRRP

Parallel Wiring

Example 10 Main and Remote Stereo Speakers

Most receivers allow the user to connect to “remote” speakers in additionto the main speakers. At the instant represented in the picture, the voltageacross the speakers is 6.00 V. Determine (a) the equivalent resistanceof the two speakers, (b) the total current supplied by the receiver, (c) thecurrent in each speaker, and (d) the power dissipated in each speaker.

Parallel Wiring

(a)

00.8

3

00.4

1

00.8

11

PR 67.2PR

(b) A 25.2 67.2

V 00.6rmsrms

PR

VI

Parallel Wiring

A 750.0 00.8

V 00.6rmsrms

R

VI(c) A 50.1

00.4

V 00.6rmsrms

R

VI

(d) W50.4V 00.6A 750.0rmsrms VIP

W00.9V 00.6A 50.1rmsrms VIP

Parallel Wiring

Conceptual Example 11 A Three-Way Light Bulband Parallel Wiring

Within the bulb there are two separate filaments.When one burns out, the bulb can produce onlyone level of illumination, but not the highest.

Are the filaments connected in series orparallel?

How can two filaments be used to produce threedifferent illumination levels?

9. Circuits Wired Partially in Series and Partially in Parallel

20.9 Internal Resistance

Batteries and generators add some resistance to a circuit. This resistanceis called internal resistance.

The actual voltage between the terminals of a batter is known as theterminal voltage.

20.9 Internal Resistance

Example 12 The Terminal Voltage of a Battery

The car battery has an emf of 12.0 V and an internalresistance of 0.0100 Ω. What is the terminal voltagewhen the current drawn from the battery is (a) 10.0 Aand (b) 100.0 A?

(a) V 10.0 010.0A 0.10 IrV

11.9VV 10.0V 0.12

(b) V 0.1 010.0A 0.100 IrV

11.0VV 0.1V 0.12

20.10 Kirchhoff’s Rules

The junction rule states that the total current directed into a junction mustequal the total current directed out of the junction.

20.10 Kirchhoff’s Rules

The loop rule expresses conservation of energy in terms of the electric potential and states that for a closed circuit loop, the total of all potentialrises is the same as the total of all potential drops.

20.10 Kirchhoff’s Rules

KIRCHHOFF’S RULES

Junction rule. The sum of the magnitudes of the currents directedinto a junction equals the sum of the magnitudes of the currents directedout of a junction.

Loop rule. Around any closed circuit loop, the sum of the potential dropsequals the sum of the potential rises.

20.10 Kirchhoff’s Rules

Example 14 Using Kirchhoff’s Loop Rule

Determine the current in the circuit.

20.10 Kirchhoff’s Rules

rises potentialdrops potential

V 24 0.8V 0.6 12 II

A 90.0I

20.10 Kirchhoff’s Rules

20.10 Kirchhoff’s Rules

Reasoning Strategy

Applying Kirchhoff’s Rules

1. Draw the current in each branch of the circuit. Choose any direction. If your choice is incorrect, the value obtained for the current will turn outto be a negative number.

2. Mark each resistor with a + at one end and a – at the other end in a waythat is consistent with your choice for current direction in step 1. Outside abattery, conventional current is always directed from a higher potential (theend marked +) to a lower potential (the end marked -).

3. Apply the junction rule and the loop rule to the circuit, obtaining in the processas many independent equations as there are unknown variables.

4. Solve these equations simultaneously for the unknown variables.

20.11 The Measurement of Current and Voltage

A dc galvanometer. The coil ofwire and pointer rotate when thereis a current in the wire.

20.11 The Measurement of Current and Voltage

An ammeter must be inserted intoa circuit so that the current passesdirectly through it.

20.11 The Measurement of Current and Voltage

If a galvanometer with a full-scalelimit of 0.100 mA is to be used to measure the current of 60.0 mA, a shunt resistance must be used so thatthe excess current of 59.9 mA can detour around the galvanometer coil.

20.11 The Measurement of Current and Voltage

To measure the voltage between two pointsin a circuit, a voltmeter is connected betweenthe points.

20.12 Capacitors in Series and Parallel

Parallel capacitors 321 CCCCP

VCCVCVCqqq 212121

20.12 Capacitors in Series and Parallel

212121

11

CCq

C

q

C

qVVV

Series capacitors 321

1111

CCCCS

20.13 RC Circuits

Capacitor charging

RCto eqq 1

RCtime constant

20.13 RC Circuits

Capacitor discharging

RCtoeqq

RCtime constant

20.13 RC Circuits

20.14 Safety and the Physiological Effects of Current

To reduce the danger inherent in using circuits, proper electrical grounding is necessary.