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CHAPTER CHAPTER 11

EKT 101 [Electric Circuit I]: EKT 101 [Electric Circuit I]: V2010/11V2010/11

School of Computer and School of Computer and Communication Engineering, Communication Engineering,

UniMAPUniMAP Prepared By: Prepared By:

Shahadah binti AhmadShahadah binti Ahmad

Variables & Variables & Circuit Circuit

ElementsElements

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Lecturer : Shahadah AhmadLecturer : Shahadah Ahmad

shahadah@unimap.edu.my

Office: KKF 8B Office: KKF 8B

Textbook: Textbook:

(1) Fundamentals of Electric Circuits – Alexander (1) Fundamentals of Electric Circuits – Alexander sadiku (4sadiku (4thth edition) edition)

Reference book: Reference book:

(2) Electric Circuits Fundamentals – FLOYD (7(2) Electric Circuits Fundamentals – FLOYD (7ThTh edition)edition)

(3) Basic Engineering Circuit Analysis – J.David (3) Basic Engineering Circuit Analysis – J.David Irwin & R.Mark Nelms( 9Irwin & R.Mark Nelms( 9thth edition) edition)

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Chap 1 : Circuit Elements and VariablesOverview of circuit analysis, SI unit, voltage and currents, power, energy, elements on the circuit (passive and active) voltage and current source, Ohm’s Law, Kirchhoff’s Law, circuit model, circuit with dependent source. Chap 2 : Resistive CircuitSeries / Parallel circuit, voltage divider circuit, current divider circuit, voltage and current measurement, Wheatstone Bridge, equivalent circuit for delta-wye (Pi-Tee).

Chap 3 : Circuit Analysis Methods Introduction to the Node-Voltage Method, the Node-Voltage Method with dependent sources and special cases, introduction to Mesh-Current Method, Mesh-Current Method with dependent sources and special cases, source transformations, Thevenin and Norton equivalent circuit, maximum power transfer and superposition. Chap 4 : Inductance and CapacitanceInductor, relationship between voltage, current, power and energy, capacitor, relationship between voltage, current, power and energy, series-parallel combinations for inductance and capacitance.

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Chap 5 : First-Order and Second-Order Response of RL and RC Circuit Natural response of RL and RC Circuit, Step Response of RL and RC Circuit, general solutions for natural and step response, sequential switching, introduction to the natural and step response of RLC circuit, natural response of series and parallel RLC circuit, Step response of series and parallel RLC circuit. Chap 6: Sinusoidal Steady-State AnalysisThe sinusoidal source, the sinusoidal response, the phasor and phasor diagram, the passive circuit elements in the frequency domain, impedances and reactance, Kirchhoff’s Laws in frequency domain, techniques of circuit analysis in frequency domain Chap 7 : Sinusoidal Steady-State Power CalculationInstantaneous power, average (active) and reactive power, the rms value power calculation, complex and power triangle , the maximum power transfer Chap 8 : Three Phase System CircuitSingle and Three Phase System (Y and Δ circuit), balanced three phase voltage sources, Y – Y circuit analysis, Y - Δ circuit analysis, power calculation in three phase balanced circuit, average power measurement in three phase circuit.

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Basic Electric Circuit Basic Electric Circuit ConceptsConcepts Review SI Know the definition of basic electrical

quantities : voltage, current, and power Know the symbols for and definition of

independent and dependent sources Be able to calculate the power absorbed by

a circuit element using the passive sign convention

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Circuit Elements & Circuit Elements & VariablesVariables

Overview of circuit analysisOverview of circuit analysis SI unitSI unit Voltage, currents, power, energy, Voltage, currents, power, energy, elements on the circuit (passive elements on the circuit (passive

and active) voltage and current and active) voltage and current sourcesource

Ohm’s Law and Kirchhoff’s LawOhm’s Law and Kirchhoff’s Law circuit modelcircuit model circuit with dependent source.circuit with dependent source.

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SI UnitSI: International System of Unit is used by all the

major engineering societies and most engineers throughout the world.

Quantity Base unit Symbol

Length Meter m

Mass Kilogram kg

Time second s

Electric current Ampere A

Thermodynamic temperature

Kelvin K

Luminousintensity

candela cd

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Standardized prefixes to signify powers of 10

Power Prefix Symbol

1012 Tera T

109 Giga G

106 Mega M

103 Kilo k

100

10-3 Mili m

10-6 Micro µ

10-9 Nano n

10-12 Pico p

10-15 Femto f

10-18 Atto a

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Overview of circuit analysisOverview of circuit analysis SI unitSI unit Voltage, currents, power, Voltage, currents, power,

energy, energy, elements on the circuit (passive elements on the circuit (passive

and active) voltage and current and active) voltage and current sourcesource

Ohm’s Law and Kirchhoff’s LawOhm’s Law and Kirchhoff’s Law circuit modelcircuit model circuit with dependent source.circuit with dependent source.

Circuit Elements & Circuit Elements & VariablesVariables

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Electric UnitsElectric Units

Charge »»» Coulomb (C) Current »»» Ampere (A) Voltage »»» Volt (V) Resistance »»» Ohm () Power »»» Watt (W)

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Electric charge is a property possessed by both electrons and protons.

Quantity is

CHARGE (Q)

COULOMB (C)Base Unit is

Examples of correct usage:

Charge = 15 Coulombs

Q = 15 C

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Current is the movement of charge in a specified direction.

CurrentCurrent

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Electric Current Terminology

Quantity is CURRENT (I)

AMPERE (A)Base Unit is

Examples of correct usage:Current = 12 Amperes

I = 12 A

An ampere equals a coulomb per second.

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Electric Current Relationships

Current = I =

Examples:

Charge Time

Qt

I = Qt =

14 C 10 s

= 1.4 A

t = QI =

14 C 1.4 A

= 10 s

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Types of Current:Types of Current:i

t

i

t

Direct current (arus terus)Alternating current

(arus ulangalik)

Damped alternating current(arus ulangalik teredam) Exponential current

ACDC

ex: Used to run

refrigerator,

stove, washing

machine, and so

on…

ex batteries – used in

automobiles or flashlight

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Voltage is the electric pressure or force that causes current.

It is a potential energy difference between two points.

It is also known as an electromotive force (emf) or potential.

Definition of Voltage

VoltageVoltage

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Voltage Terminology

Quantity is VOLTAGE (V)

VOLT (V)Base Unit is

Examples of correct usage:Voltage = 32 Volts

V = 32 V

A volt equals a joule per coulomb.

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Voltage Relationships

Voltage = V =

Examples:

EnergyCharge

WQ

V = WQ =

56 J 2 C

= 28 V

Q = WV =

84 J 21 V

= 4 C

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Resistance is the oppositiona material offers to current.

Resistance is determined by:

Type of material (resistivity)

Temperature of material Cross-sectional area

Length of material

Definition of Resistance

ResistanceResistance

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Some Factors That Determine Resistance

For a specific material and temperature, this block has given amount of resistance.

Doubling the length of the block, Doubling the cross-sectional area,

doubles the resistance.halves the resistance.

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Resistance Terminology

Quantity is RESISTANCE (R)

OHM ()Base Unit is

Examples of correct usage:

Resistance = 47 ohmsR = 47

An ohm equals a volt per ampere.

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Resistance Relationships

Resistance = R =

Example:

Resistivity x length area

KLA

R = KLA

=

= 0.1

1.4 x10-6 cm x 2 x104 cm 0.28 cm2

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Work (W)consists of a force moving through a distance.

Energy (W)is the capacity to do work.

The joule (J)is the base unit for both energy and work.

The amount of work done equals the amount of

energy used (converted).

Fifty joules of energy are

required to do fifty joules of

work.

ENERGYENERGY

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Power is the rate of using energy or doing work.

“Using energy” means that energy is being converted to a different form.

Definition of Power

POWER

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Power Terminology

Quantity is POWER (P)

WATT (W)Base Unit is

Examples of correct usage:

Power = 120 Watts

P = 120 W

A watt equals a joule per second.

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Power Relationships

Power = P =

Examples:

Energy Time

W t

P = W t =

158 J 20 s

= 7.9 W

W = Pt = 75 W x 25 s = 1875 J

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Circuit Elements & Circuit Elements & VariablesVariables

Overview of circuit analysisOverview of circuit analysis SI unitSI unit voltage and currents, power, voltage and currents, power,

energy, energy, elements on the circuit (passive elements on the circuit (passive

and active) voltage and current and active) voltage and current sourcesource

Ohm’s Law and Kirchhoff’s LawOhm’s Law and Kirchhoff’s Law circuit modelcircuit model circuit with dependent source.circuit with dependent source.

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Active and Passive Active and Passive ElementsElements

Circuit Elements

Active elements•capable of generating electric energy•Example : voltage and current sources

Passive elements•incapable of generating electric energy•Example : resistor, inductor, capacitor, diode and etc

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Independent SourceIndependent Source

Voltage

Current

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xs iV xs Vi

Voltage Current

Dependent SourceDependent Source

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Ideal Voltage Source Ideal Voltage Source Connected in SeriesConnected in Series

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Ideal Current Source Ideal Current Source Connected in ParallelConnected in Parallel

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Symbol of Circuit Symbol of Circuit ElementsElements

Resistor

R

UNIT: Ohm (Ω)

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Resistor Color CodeResistor Color Code

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Yellow

4 10 %

Silver

7

Violet

00

Red

Resistor Color CodeResistor Color Code

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Green = 5 white= 9 Orange = 3 Gold = 5 %

59 x 103 5 % =59,000 5 % =59 K 5 %

Resistor Color CodeResistor Color Code

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4 0 0 06 4 2% = 464 k 2%

Resistor Color CodeResistor Color Code

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ConductanceConductance

Conductance is a measure of the ability of an element to conduct electric current

Inverse of resistance The units is Siemens (S) or mhos

v

i

R

1G

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Capacitor

Inductor

C UNIT: Farad (F)

L UNIT: Henry (H)

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Circuit Elements & Circuit Elements & VariablesVariables

Overview of circuit analysisOverview of circuit analysis SI unitSI unit voltage and currents, power, voltage and currents, power,

energy, energy, elements on the circuit (passive elements on the circuit (passive

and active) voltage and current and active) voltage and current sourcesource

Ohm’s Law and Kirchhoff’s LawOhm’s Law and Kirchhoff’s Law circuit modelcircuit model circuit with dependent source.circuit with dependent source.

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Short CircuitShort Circuit

R = 0 no voltage difference exists all points on the wire are at the same

potential. Current can flow, as determined by the

circuit

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Open circuitOpen circuit

R = no current flows Voltage difference can exist, as

determined by the circuit

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Circuit Nodes and LoopsCircuit Nodes and Loops

A node is a point where two or more circuit elements are connected.

A loop is formed by tracing a closed path in a circuit through selected basic circuit elements without passing through any intermediate node more than once

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Example: Find the Example: Find the NodesNodes

+

-Vs

node

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Example: Find the loopsExample: Find the loops

loop

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Ohm’s Law George Simon Ohm (1787-1854)

formulated the relationships among voltage, current, and resistance as follows:

The current in a circuit is directly proportional to the applied voltage and inversely proportional to the resistance of the circuit.

IRV

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Kirchhoff LawKirchhoff Law Gustav Robert Kirchhoff (1824–1887) Models relationship between:

circuit element currents (KCL) circuit element voltages (KVL)

Introduce two laws: Kirchhoff Current Law (KCL) Kirchhoff Voltage Law (KVL)

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Current entering node = current exiting(What goes in, must come out)

Convention: +i is exiting, -i is entering For any circuit node:

0i

Kirchhoff’s Current Law Kirchhoff’s Current Law (KCL)(KCL)

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No matter how many paths into No matter how many paths into and out of a single point all the and out of a single point all the current leaving that point must current leaving that point must equal the current arriving at that equal the current arriving at that point. point.

Kirchhoff’s Current Law Kirchhoff’s Current Law (KCL)(KCL)

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voltage increases = voltage decreases(What goes up, must come down)

Convention: hit minus (-) side first, write negative

For any circuit loop:

0v

Kirchhoff’s Voltage Law Kirchhoff’s Voltage Law (KVL)(KVL)

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The voltage drops around any The voltage drops around any closed loop must equal the applied closed loop must equal the applied voltages voltages

Kirchhoff’s Voltage Law Kirchhoff’s Voltage Law (KVL)(KVL)

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Circuit Elements & Circuit Elements & VariablesVariables

Overview of circuit analysisOverview of circuit analysis SI unitSI unit voltage and currents, power, voltage and currents, power,

energy, energy, elements on the circuit (passive elements on the circuit (passive

and active) voltage and current and active) voltage and current sourcesource

Ohm’s Law and Kirchhoff’s LawOhm’s Law and Kirchhoff’s Law circuit modelcircuit model circuit with dependent source.circuit with dependent source.

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PARALLEL-SERIES

Circuit Model

SERIES

PARALLEL

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This complete circuit uses the following:

• An energy or power source

• A control device• A load• Conductors • Insulation (not shown)

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Calculating CurrentCalculating Current

I =VR

= 36 V1800

= 0.02 A = 20 mA

S1

SPST

R

1.8 k

B1

36 V

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Calculating ResistanceCalculating Resistance

R = V I =

24 V 0.03 A

= 800 = 0.8 k

R

B1

24 V

A0.03 A

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Calculating VoltageCalculating Voltage

V = IR = 0.15 A * 270 = 40.5 V

R

B1

A0.15 A

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Calculating PowerCalculating Power

P =

0.2 A

IV = 0.2 A * 54 V= 10.8 W

V54 V

P = I2R = 0.2 A * 0.2 A * 270 = 10.8 W

P = V2/R = (54 V * 54 V) / 270 = 10.8 W

A

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Circuit Elements & Circuit Elements & VariablesVariables

Overview of circuit analysisOverview of circuit analysis SI unitSI unit voltage and currents, power, voltage and currents, power,

energy, energy, elements on the circuit (passive elements on the circuit (passive

and active) voltage and current and active) voltage and current sourcesource

Ohm’s Law and Kirchhoff’s LawOhm’s Law and Kirchhoff’s Law circuit modelcircuit model circuit with dependent source.circuit with dependent source.

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Circuit With Dependent Circuit With Dependent SourceSource

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Using KVL on the first loop,

0205500 ii

Using KCL on the second loop,

Solve the equations,

ii

iii

6

5

0

0

Ai

Ai

24

4

0

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Using Ohm law for the resistor,

V480

)20(iv o0