Chapter 1

Introduction to Electricity

for CST 162 LAB

Slide content from “Circuit Analysis: Theory and Practice” 4th Ed., by Robbins and Miller, 2007

System International (SI) System of Units

• Electric Current– Ampere (A)

• Electric Voltage– Volt (V)

• Electrical Resistance– Ohm (Ω)

Prefixes

• Metric Prefixes are used for convenience

Significant Digits and Numerical Accuracy

• Significant digits– Digits that carry information – It is a common error to show more digits of

accuracy than are warranted.

Circuit Diagrams

• Electric circuits– Use batteries and resistors as components– Circuit diagrams are used on paper

• Three types of circuit diagrams are used– Pictorial, block, and schematic

Pictorial Diagrams

• Help visualize circuits by showing components as they actually appear

Block Diagrams

• Blocks represent portions of a system

Schematic Diagrams

Chapter 2

Voltage and Current

Atomic Theory

• Atom – Contains a nucleus of protons and neutrons– Nucleus is surrounded by a group of orbiting

electrons

• Electrons are negative, protons are positive

Atomic Theory

• Electrically neutral atom– Equal number of electrons and protons

• Ion– An atom with an excess or deficit of

electrons

Conductors

• Materials with a large numbers of free electrons – Metals are good conductors because they

have few loosely bound valence electrons

Conductors

• Excellent conductors – Silver– Gold– Copper– Aluminum

Electrical Charge

• Unit of charge is the coulomb (C)

• One coulomb = 6.24 × 1018 electrons (or protons)

• The charge on one electron (or proton) =1/ 6.24 × 1018 or 1.6 × 10-19 C

Voltage

• When two objects have a difference in charges– They have a “potential difference” or “voltage” between them

• Unit of voltage is the volt• Thunderclouds

– Millions of volts between them

Voltage

• Difference in potential energy

• Voltage between two points =One volt, “if it requires one joule of energy to

move one coulomb of charge from one point to another”

Voltage

• V = Work/Charge

• Voltage is always measured between two points

coulomb

joulevolt

11

1

Current

• Movement of charge is electric current

• More electrons per second passing through a circuit, the greater the current

• Current is rate of flow of charge

Current

• Unit of current is ampere (A)

• One ampere =Current in a circuit when one coulomb of charge

passes a given point in one second

• Current = Charge/time

• I = Q/t

Current

• Electron current flow– Electrons flow from the negative terminal of a

battery to the positive terminal

• Conventional current flow– We may also assume currents flow from

positive to negative

Current

• Conventional current flow is used in this course, and in our field of study

How to Measure Voltage

• Place voltmeter leads across components

• Red lead is positive

• Black lead is negative

• If leads are reversed, you will read the opposite polarity

How to Measure Current

• Measurable current must pass through meter

• Open the circuit (i.e. disconnect wires) and insert the ammeter, so that the current now flows through the meter

• Connect with correct polarity

Chapter 3

Resistance

Resistance of Conductors

• Resistance of material is dependent on several factors:– Type of Material– Length of the Conductor– Cross-sectional area– Temperature

Type of Material

• Atomic differences of materials cause variations in how electron collisions affect resistance

• Differences produce resistivity

Length

• Resistance of a conductor– Directly proportional to its length– If you double the length of the wire, the

resistance will double

• = length– In meters or feet

Area

• Resistance of a conductor– Inversely proportional to cross-sectional

area of the conductor

• If cross-sectional area is doubled– Resistance will be one half as much

Fixed Resistors

• Resistance of a fixed resistor is constant over a wide temperature range

• Rated by amount of resistance– Measured in ohms (Ω)

• Also rated by power– Measured in watts (W)

Fixed Resistors

• Different resistors for different applications– Molded carbon composition– Carbon film– Metal film– Metal Oxide– Wire-Wound– Integrated circuit packages

Variable Resistors

• Resistance may be changed (varied)– Adjust volume, set level of lighting, adjust

temperature

• Have three terminals– Center terminal connected to wiper arm

• Potentiometers (normally abbreviated to just “Pot”)

• Rheostats

Color Code

• Colored bands on a resistor provide a code for determining– Value– Tolerance– Reliability

Reading color codes

Measuring Resistance

• Use an Ohmmeter

• Remove all power sources to circuit

• Isolate component to be measured

• Connect probes across component

• No need to worry about polarity

• Ohmmeter determines shorts and opens in individual components

Chapter 4

Ohm’s Law

and Energy

Ohm’s Law

• Current in a resistive circuit– Directly proportional to its applied voltage – Inversely proportional to its resistance

R

EI

Ohm’s Law

• For a fixed resistance– Doubling voltage doubles the current

• For a fixed voltage– Doubling resistance halves the current

Ohm’s Law

• Also expressed as E = IR and R = E/I

• Express all quantities in base units of volts, ohms, and amps or utilize the relationship between prefixes

Ohm’s Law in Graphical Form• Linear relationship between current and

voltage• y = mx

– y is the current– x is the voltage– m is the slope

Ohm’s Law in Graphical Form• Slope (m) determined by resistor

conductance

Ohm’s Law in Graphical Form

Open Circuits• Current can only exist where there is a

conductive path

• An “Open circuit” is defined when there is no conductive path

Open Circuits

• If I = 0– Ohm’s Law gives R = E/I = E/0 infinity

• An open circuit has infinite resistance

Voltage Symbols

• Voltage sources– Uppercase E

• Voltage drops– Uppercase V

• V = I*R– “IR” drops

Voltage Polarities

• Polarity of voltage drops across resistors is important in circuit analysis

• Drop is + to – in the direction of conventional current

• To show this, place plus sign at the tail of current arrow

Voltage Polarities

Current Direction

• Current usually proceeds out of the positive terminal of a voltage source

• If the current is actually in this direction, it will be supplying power to the circuit

Current Direction

• If the current is in the opposite direction (going into the positive terminal), it will be absorbing power (like a resistor)

Current Direction

• See two representations of the same current on next slide

• Notice that a negative current actually proceeds in a direction opposite to the current arrow

Current Direction

Power Rating of Resistors

• Resistors must be able to safely dissipate their heat without damage

• Common power ratings of resistors are 1/8, 1/4, 1/2, 1, or 2 watts

Law of Conservation of Energy

• Energy can neither be created nor destroyed– Converted from one form to another

• Examples: – Electric energy into heat– Mechanical energy into electric energy

Law of Conservation of Energy

• Energy conversions– Some energy may be dissipated as heat,

giving lower efficiency

Chapter 5

Series Circuits

Series Circuits

• Two elements in a series– Connected at a single point– No other current-carrying connections at this

point

• A series circuit is constructed by connecting various elements in series

Series Circuits

• Normally– Current will leave the positive terminal of a

voltage source– Move through the resistor(s)– Return to negative terminal of the source

Series Circuits

• Current is similar to water flowing through a pipe– Current leaving the element must be the

same as the current entering the element

• Same current passes through every element of a series circuit

Series Circuits

• The laws, theorems, and rules that you apply to DC circuits– Also apply to AC circuits

Kirchhoff’s Voltage Law (KVL)

• The algebraic sum of the voltage that rises and drops around a closed loop is equal to zero

• ET - V1 - V2 - V3 - ∙∙∙ - Vn = 0

Kirchhoff’s Voltage Law (KVL)

• Another way of stating KVL is: – Summation of voltage rises is equal to the

summation of voltage drops around a closed loop

V1 + V2 + V3 + ∙∙∙ + Vn = ET

Resistors in Series

• Most complicated circuits can be simplified

• For a series circuit– V1 + V2 + V3 = E

– IR1 + IR2 + IR3 = E

– I(R1 + R2 + R3 )= E

– I(R1 + R2 + R3 )= IRtotal (Note: I’s cancel)

Resistors in Series

• Total resistance in a series circuit is the sum of all the resistor values

Interchanging Series Components

• Order of series components– May be changed without affecting operation of

circuit

• Sources may be interchanged, but their polarities can not be reversed

• After circuits have been redrawn, it may become easier to visualize circuit operation

Circuit Ground

• Ground – Point of reference or a common point in a

circuit for making measurements

• One type of grounding is chassis ground

• In this type of grounding– Common point of circuit is often the metal

chassis of the piece of equipment

Circuit Ground

• Chassis ground – Often connected to Earth Ground

• Earth ground– Physically connected to the earth by a metal

pipe or rod

Circuit Ground

• If a fault occurs within a circuit, the current is redirected to the earth

• Voltages are often measured with respect to ground

Ammeter Loading Effects

• An ammeter is placed in a circuit to make a current measurement– Resistance in the meter will affect the circuit

• Amount of loading is dependent upon the instrument and the circuit

Ammeter Loading Effects

• If resistance of the meter is small compared to the resistance of the circuit, the loading effect will be small

Chapter 6

Parallel Circuits

Parallel Circuits

• House circuits contain parallel circuits• The parallel circuit will continue to operate even

though one component may be “open”• Only the “open” or “defective” component will no

longer continue to operate• A light bulb with a broken filament = “open”

Parallel Circuits

Parallel Circuits

• Elements in parallel– When they have exactly two nodes in common

• Elements between nodes – Any device like resistors, light bulbs, etc.

• Elements connected in parallel– Same voltage across them

Parallel Circuits

Series - Parallel Circuits

• Circuits may contain a combination of series and parallel components

• Being able to recognize the various connections in a network is an important step in analyzing these circuits

Series - Parallel Circuits

Parallel Circuits

• To analyze a particular circuit– First identify the node– Next, label the nodes with a letter or number– Then, identify types of connections

Parallel Circuits

Kirchhoff’s Current Law (KCL)

• The algebraic sum of the currents entering and leaving a node is equal to zero

0I

Kirchhoff’s Current Law (KCL)

• Currents entering the node are taken to be positive, leaving are taken to be negative

• Sum of currents entering a node is equal to the sum of currents leaving the node

outin II

Kirchhoff’s Current Law (KCL)

• An analogy: – When water flows in a pipe, the amount of

water entering a point is equal to the amount leaving that point

Resistors in Parallel

• Voltage across all parallel elements in a circuit will be the same

Resistors in Parallel

• For a circuit with 3 resistors: IT = I1 + I2 + I3

321T

321T

1111

RRRR

R

E

R

E

R

E

R

E

Resistors in Parallel

• Total resistance of resistors in parallel will always be less than resistance of smallest resistor

Equal Resistors in Parallel

• Total resistance of equal resistors in parallel is equal to the resistor value divided by the number of resistors

Two Resistors in Parallel

• For only two resistors connected in parallel, the equivalent resistance may be found by the product of the two values divided by the sum

• Often referred to as “product over the sum” formula

21

21

RR

RRR

T

Three Resistors in Parallel• For three resistors in parallel:

• Rather than memorize this long expression– Use basic equation for resistors in parallel

323121

321

RRRRRR

RRRR

T

Voltmeter Loading Effects

• A voltmeter– Meter movement in series with a current-

limiting resistance

• If resistance is large compared with the resistance across which the voltage is to be measured, the voltmeter will have a very small loading effect

Voltmeter Loading Effects

• If this resistance is more than 10 times the resistance across which the voltage is being measured, the loading effect can generally be ignored.

• However, it is usually much higher.