CHAPTER 1 Variables Circuit Elements School of Computer

CHAPTER 1 Variables & Circuit Elements School of Computer and Communication Engineering, Uni. MAP Prepared By: MUHAMAD SANI MUSTAFA 1

Lecturer : Muhamad Sani Mustafa sani@unimap. edu. my Office: KKF 6 C Textbook: (1) Fundamentals of Electric Circuits – Alexander sadiku (4 th edition) Reference book: (2) Electric Circuits Fundamentals – FLOYD (7 Th edition) (3) Basic Engineering Circuit Analysis – J. David Irwin & R. Mark Nelms( 9 th edition) 2

Syllabus - EKT 101 Chap 1 : Circuit Elements and Variables Overview 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 Circuit Series / 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 Capacitance Inductor, relationship between voltage, current, power and energy, capacitor, relationship between voltage, current, power and energy, seriesparallel combinations for inductance and capacitance. 3

Syllabus - EKT 101 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 Analysis The 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 Calculation Instantaneous power, average (active) and reactive power, the rms value power calculation, complex and power triangle , the maximum power transfer Chap 8 : Three Phase System Circuit Single and Three Phase System (Y and Δ circuit), balanced three phase voltage sources, Y – Y circuit analysis, Y - Δ circuit analysis, power 4 calculation in three phase balanced circuit, average power measurement in three phase circuit.

Basic Electric Circuit Concepts p Review SI p Know the definition of basic electrical quantities : voltage, current, and power p Know the symbols for and definition of independent and dependent sources p Be able to calculate the power absorbed by a circuit element using the passive sign convention 5

Circuit Elements & Variables p Overview of circuit analysis p SI unit p Voltage, currents, power, energy, p elements on the circuit (passive and active) voltage and current source p Ohm’s Law and Kirchhoff’s Law p circuit model p circuit with dependent source. 6

SI Unit SI: 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 Luminous intensity candela cd 7

p Standardized prefixes to signify powers of 10 Power Prefix Symbol 1012 Tera T 109 Giga G 106 Mega M 103 Kilo k 10 -3 Mili m 10 -6 Micro µ 10 -9 Nano n 10 -12 Pico p 10 -15 Femto f 10 -18 Atto a 100 8

Circuit Elements & Variables o Overview of circuit analysis o SI unit o Voltage, currents, power, energy, o elements on the circuit (passive and active) voltage and current source o Ohm’s Law and Kirchhoff’s Law o circuit model o circuit with dependent source. 9

Electric Units p p p Charge Current Voltage Resistance Power » » » Coulomb (C) » » » Ampere (A) » » » Volt (V) » » » Ohm ( ) » » » Watt (W) 10

Electric charge is a property possessed by both electrons and protons. Quantity is CHARGE (Q) Base Unit is COULOMB (C) Examples of correct usage: Charge = 15 Coulombs Q = 15 C 11

Current is the movement of charge in a specified direction. 12

Electric Current Terminology Quantity is CURRENT (I) Base Unit is AMPERE (A) An ampere equals a coulomb per second. Examples of correct usage: Current = 12 Amperes I = 12 A 13

Electric Current Relationships Charge Current = Time Q I= t Examples: Q 14 C = 1. 4 A I = t = 10 s Q 14 C = 10 s t = I = 1. 4 A 14

Types of Current: ex: Used to run ve, refrigerator, sto e, washing machin an d so o n … AC Alternating current (arus ulangalik) Damped alternating current (arus ulangalik teredam) DC ex batteries – used in automobiles or flashlight Direct current (arus terus) Exponential current 15

Voltage Definition of Voltage p. Voltage is the electric pressure or force that causes current. p. It is a potential energy difference between two points. p. It is also known as an electromotive force (emf) or potential. 16

Voltage Terminology Quantity is VOLTAGE (V) Base Unit is VOLT (V) A volt equals a joule per coulomb. Examples of correct usage: Voltage = 32 Volts V = 32 V 17

Voltage Relationships Energy Voltage = Charge Examples: W V= Q = W V= Q 56 J = 28 V 2 C 84 J = 4 C W Q = V = 21 V 18

Resistance Definition of Resistance is the opposition a material offers to current. Resistance is determined by: p Type of material (resistivity) p Temperature of material p Cross-sectional area p Length of material 19

Some Factors That Determine Resistance For a specific material and temperature, this block has given amount of resistance. Doubling the length of the block, doubles the resistance. 20 Doubling the cross-sectional area, halves the resistance.

Resistance Terminology Quantity is RESISTANCE (R) Base Unit is OHM ( ) An ohm equals a volt per ampere. Examples of correct usage: Resistance = 47 ohms R = 47 21

Resistance Relationships Resistivity x length KL Resistance = R= A area Example: 1. 4 x 10 -6 · cm x 2 x 104 cm KL = R= A 0. 28 cm 2 = 0. 1 22

ENERGY 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. 23

POWER Definition of Power is the rate of using energy or doing work. “Using energy” means that energy is being converted to a different form. 24

Power Terminology Quantity is POWER (P) Base Unit is WATT (W) A watt equals a joule per second. Examples of correct usage: Power = 120 Watts P = 120 W 25

Power Relationships Energy Power = Time W P= t Examples: 158 J = 7. 9 W W P = t = 20 s W = Pt = 75 W x 25 s = 1875 J 26

Circuit Elements & Variables p Overview of circuit analysis p SI unit p voltage and currents, power, energy, p elements on the circuit (passive and active) voltage and current source p Ohm’s Law and Kirchhoff’s Law p circuit model p circuit with dependent source. 27

Active and Passive Elements 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 28

Independent Source Current Voltage 29

Dependent Source Voltage Current 30

Ideal Voltage Source Connected in Series 31

Ideal Current Source Connected in Parallel 32

Symbol of Circuit Elements o Resistor R UNIT: Ohm (Ω) 33

Resistor Color Code 34

Resistor Color Code Yellow Violet Red Silver 4700 ± 10 % 35

Resistor Color Code Green = 5 white= 9 Orange = 3 Gold = ± 5 % 59 x 103 ± 5 % = 59, 000 ± 5 % = 59 K ± 5 % 36

Resistor Color Code 4 6 4 0 0 0 ± 2% = 464 k ± 2% 37

Conductance p Conductance is a measure of the ability of an element to conduct electric current p Inverse of resistance p The units is Siemens (S) or mhos 38

p Capacitor C UNIT: Farad (F) L UNIT: Henry (H) p Inductor 39

Circuit Elements & Variables p Overview of circuit analysis p SI unit p voltage and currents, power, energy, p elements on the circuit (passive and active) voltage and current source p Ohm’s Law and Kirchhoff’s Law p circuit model p circuit with dependent source. 40

Short Circuit p R = 0 no voltage difference exists p all points on the wire at the same potential. p Current can flow, as determined by the circuit 41

Open circuit p R = no current flows p Voltage difference can exist, as determined by the circuit 42

Circuit Nodes and Loops p A node is a point where two or more circuit elements are connected. p 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 43

Example: Find the Nodes Vs + - node 44

Example: Find the loops loop 45

Ohm’s Law p George Simon Ohm (1787 -1854) formulated the relationships among voltage, current, and resistance as follows: p The current in a circuit is directly proportional to the applied voltage and inversely proportional to the resistance of the circuit. 46

Kirchhoff Law p Gustav Robert Kirchhoff (1824– 1887) p Models relationship between: p circuit element currents (KCL) p circuit element voltages (KVL) p Introduce two laws: p Kirchhoff Current Law (KCL) p Kirchhoff Voltage Law (KVL) 47

Kirchhoff’s Current Law (KCL) p Current entering node = current exiting (What goes in, must come out) p Convention: +i is exiting, -i is entering p For any circuit node: 48

Kirchhoff’s Current Law (KCL) p No matter how many paths into and out of a single point all the current leaving that point must equal the current arriving at that point. 49

Kirchhoff’s Voltage Law (KVL) p voltage increases = voltage decreases (What goes up, must come down) p Convention: hit minus (-) side first, write negative p For any circuit loop: 50

Kirchhoff’s Voltage Law (KVL) p The voltage drops around any closed loop must equal the applied voltages 51

Circuit Elements & Variables p Overview of circuit analysis p SI unit p voltage and currents, power, energy, p elements on the circuit (passive and active) voltage and current source p Ohm’s Law and Kirchhoff’s Law p circuit model p circuit with dependent source. 52

Circuit Model SERIES PARALLEL-SERIES 53

This complete circuit uses the following: • An energy or power source • A control device • A load • Conductors • Insulation (not shown) 54

Calculating Current S 1 SPST B 1 36 V R 1. 8 k V 36 V = 0. 02 A = 20 m. A I= = R 1800 55

Calculating Resistance A B 1 24 V 0. 03 A R V 24 V R= I = = 800 = 0. 8 k 0. 03 A 56

Calculating Voltage A B 1 0. 15 A R 270 V = IR = 0. 15 A * 270 = 40. 5 V 57

Calculating Power A V 0. 2 A 54 V 270 P = IV = 0. 2 A * 54 V = 10. 8 W P = I 2 R = 0. 2 A * 270 = 10. 8 W P = V 2/R = (54 V * 54 V) / 270 = 10. 8 W 58

Circuit Elements & Variables p Overview of circuit analysis p SI unit p voltage and currents, power, energy, p elements on the circuit (passive and active) voltage and current source p Ohm’s Law and Kirchhoff’s Law p circuit model p circuit with dependent source. 59

Circuit With Dependent Source 60

p Using KVL on the first loop, p Using KCL on the second loop, p Solve the equations, 61

o Using Ohm law for the resistor, 62