EDEXCEL NATIONAL CERTIFICATE/DIPLOMA UNIT 67 - FURTHER ELECTRICAL PRINCIPLES NQF LEVEL 3 OUTCOME 3 TUTORIAL 1 - SINGLE PHASE AC CIRCUITS

Save this PDF as:
 WORD  PNG  TXT  JPG

Size: px
Start display at page:

Download "EDEXCEL NATIONAL CERTIFICATE/DIPLOMA UNIT 67 - FURTHER ELECTRICAL PRINCIPLES NQF LEVEL 3 OUTCOME 3 TUTORIAL 1 - SINGLE PHASE AC CIRCUITS"

Transcription

1 EDEXCE NATIONA CETIFICATE/DIPOMA UNIT 67 - FUTHE EECTICA PINCIPES NQF EVE 3 OUTCOME 3 TUTOIA - SINGE PHASE AC CICUITS Unit content 3. Understand the behaviour of single-phase alternating current (AC) circuits Series, and C alternating current (AC) circuits: current and phase angle in series combinations of C circuits (, C, C); construction of phasor diagrams and relationship with voltage and impedance triangles for each of the three types of, and C combinations; power factor (cos Φ) and power triangle e.g. apparent power (S = VI), true or active power (P = VI cos Φ) and reactive power (Q = VI sin Φ); conditions for series resonance e.g. inductive reactance equals capacitive reactance (X = X C ); Q factor (voltage magnification) e.g V Q,Q V C,and its importance in high and low frequency circuits. Parallel: evaluation of the voltage, current and phase angle in parallel combinations of resistance, inductance and capacitance e.g., C, C and C; construction of phasor diagrams for impedance and phase angle; conditions for parallel resonance in an C circuit e.g. supply current and voltage in phase; Impedance at resonance e.g. dynamic resistance e.g. D IC Q ; filter circuits e.g. high pass, low pass, band pass, band stop. I C ; Q factor (current magnification) It assumed that the student has studied the Electrical and Electronic principles module. D.J.Dunn

2 . POWE FACTO COECTION Industrial users of electric power often place inductive loads on the supply in the form of large motors and transformers. This may be regarded as an inductor in series with a resistor and produces a current that lags the supply voltage. The true power is that developed across the resistive load and is given by P = I and is measured in Watts. Consider a resistor in series with an inductor. The inductive voltage phasor leads the resistive voltage phasor by 90 o. The resultant voltage is the supply voltage. The apparent power is the product of V and I and often stated as S = VI. This is not measured in Watts but in Volt Amps. V/I is the impedance Z and is given by Z X The POWE FACTO is the ratio of the true power to the apparent power and is defined as P I I P.F. cos hence P = VI cos() S VI V Z In order to reduce the power factor a series capacitor is needed to produce capacitive reactance equal and opposite to the inductive reactance. Ideally X C = X This is obtained from the relationship X / = tan X eactive power is defined as Q VI sin Z WOKED EXAMPE No. An ac load takes.5 kw of power from a supply 0V at 60 Hz. The current is 30 A. Determine the power factor and the size of a capacitor needed in series to correct it. SOUTION P.F. = True Power /Apparent Power = 500/(0 x 30) = = cos - (P.F.) = cos = 40.7 o True Power = I = 30 = 500 W = 500/900 =.777 X / = tan = 0.86 X = 0.86 =.39 X C =.39 = /(fc) C = /( x 60 x.39) = 0.00 F D.J.Dunn

3 SEF ASSESSMENT EXECISE No.. A consumer takes 0 kw of power from an ac supply at 40 V and 50 Hz. Due to an inductive power factor, the current is 00 A. Determine the power factor and the size of a capacitor required to correct it. (0.004 F). An electrical load comprises of a resistance of 00 and an inductor of 0.6 H in series. The supply is at 40 V and 50 Hz. Determine the Power factor. (0.47 ) 3. An ac supply to a consumer is at 0V and 50 Hz with a current of 0 A. It is found that there is a lagging phase angle of 0 o. Determine the Power Factor, the true power and the size of a capacitor that would make the power factor. (0.364,.6 kw and 874 μf) D.J.Dunn 3

4 . SEIES CICUITS We know from previous studies that the relationship between current and voltage for any component is related as a ratio X = V/I. For a resistor this ratio is resistance but for an inductor it is called inductive reactance X and for a capacitor capacitive reactance X C. Inductive reactance increases with frequency and is given by X = f Capacitive reactance decreases with frequency and is given by X C π f C When current flows in an C circuit, the relationship between it and the resulting voltage is called the IMPEDANCE Z. V Z I V and I are the resulting r.m.s. volts and current. Since reactance is V/I it follows that it is also a phasor. The phasor diagram for a series C circuit may be drawn as shown with drawn horizontally to make it easier. WOKED EXAMPE No. X XC Z X XC and tan A resistor of value 470 is connected in series with a capacitor of F and an inductor of 50 mh and a voltage is applied across it. A current of 00 ma (rms) is produced. Determine the impedance, the phase angle between the voltage and current and the applied voltage when the frequency is 50 Hz SOUTION X = πf = π x 50 x 50 x 0-3 =5.7 Ω X C = /πfc = /(π x 50 x x 0-6 ) =44.6 Ω Z X X Ω C X XC tan tan V S = I Z = 0. x = 48.7 V rms o D.J.Dunn 4

5 SEF ASSESSMENT EXECISE No.. A resistor of value 4 is connected in series with a capacitor of 47 F and an inductor of 0 μh and a voltage is applied across it. A current of 50 ma (rms) is produced. Determine the impedance, the phase angle between the voltage and current and the applied voltage when the frequency is 00 Hz. (34 Ω, o and.7 V). A resistor of value 0. is connected in series with a capacitor of 4.7 F and an inductor of 5 mh and 0.5 V rms is applied across the ends. Determine the impedance, the phase angle between the voltage and current and the rms current when the frequency is 000 Hz. (.455 Ω, o and 04 ma) 3. PAAE CICUITS. The main point about parallel circuits is that the voltage is common to each and the current is different. It is often easier to use the idea of ADMITTANCE and CONDUCTANCE so this is defined next. ADMITTANCE and CONDUCTANCE These are mainly used in the solution of parallel circuits. Conductance is the inverse of resistance and is denoted G. G It follows that I = V G Admittance is the inverse of impedance and is denoted Y. Y Z It follows that I = V Y Susceptance is the inverse of reactance and is denoted B. B X It follows that I C = V B C for a capacitor and I = V B for an inductor. The units of Y, G and B are Siemens symbol S. S = Ω - PAAE ESISTOS The circuit shows two resistors in parallel. The parallel rule tells us Z Alternatively or Y G G Z D.J.Dunn 5

6 PAAE ESISTO, INDUCTO AND CAPACITO Consider the parallel circuit below. The voltage is common to all components but the current in the inductor is reactive and leads the voltage by 90 o and the current in the capacitor lags by 90 o. Since the current in the resistor is in phase with the voltage, the phasor diagram for the currents is like this. It is convenient to draw the phasors with I horizontal and the resultant current is as shown. The resultant current = I I I C I I XC The phase angle is tan If we substitute I = V G and I = V B and I C = V B C B BC Y B BC G tan G It also follows that we may represent G, B and Y as phasors. You should decide which method you prefer to use. The parallel circuit may be represented with G, B and Y as shown. WOKED EXAMPE No. 3 For the three circuits shown below, determine the supply current and phase angle between the supply voltage and current when 50 V rms is applied. SOUTIONS (a) Y B B G S C I = V S x Y = 50 x = 6.96 A B BC 0 0. tan tan.8 G 0.5 o D.J.Dunn 6

7 (b) Y B B G S C I = V S x Y = 50 x 0.8 = 3.98 A B BC tan tan 6.6 G 0.5 (c) Y B B G S C I = V S x Y = 50 x 0.08 = A B BC tan tan.8 G 0. o o SEF ASSESSMENT EXECISE No. 3. In a parallel C circuit, = 75 k, = 5 μh and C = 0. nf. The voltage supply is 0.5 V at Mz. Calculate the admittance, impedance of the circuit, the current and the phase angle. (0.09 S, 5.9 Ω, 9.4 ma and 45.5 o ). In a parallel C circuit, = k, = 40 mh and C = 0 nf. The voltage supply is V at 00 khz. Calculate the admittance, impedance of the circuit, the current and the phase angle. (0.03 S, 33 Ω, 6 ma and 88.9 o ) D.J.Dunn 7

8 4. ESONANT CICUITS. SEIES A series circuit is resonant when the inductive reactance is equal and opposite of the capacitive reactance. It follows that the phase angle is zero. At this condition the reactance is equal to and is a minimum value. For a given circuit, there will be a frequency f o where this occurs. For resonance, X C = X f o = /f o C where f o is the resonant frequency. earranging we have: (π fo)(π foc) π f0 C fo f o (π ) C π C Q FACTO It is quite possible to obtain voltages across a capacitor or inductor larger the supply voltage. We get a magnification. To define this we use the Q factor defined as follows. Q = V C /V for a capacitor and V /V for an inductor. The Q factor may also be based on the current ratio, especially for parallel circuits. At resonance V = I since the capacitive and inductive components are equal and opposite so V C = I X C = I/πfC QC π f C o V = I X = I πf Q π f o At any other frequency the Q factor is lower and needs to be worked out the hard way. Note that in both cases, the smaller the value of the larger the Q factor. et s take some typical values V S = 0, C = mf and = mh = 0. Ω. The resonant frequency is fo 79.6 Hz Q C = /f o C = 0 Q = f o / = π C π x0 x x 0 If we calculate V and V C over a range of frequencies we get the following result. We see that the voltages peak at resonance is 00 giving Q = 0 as predicted. If is zero, then in theory we get an infinite voltage at resonance. If we increase, we reduce the peak. D.J.Dunn 8

9 PAAE esonance in a parallel circuit occurs when B = B C and the resulting admittance is G = / We will find the result is the same and f o π C WOKED EXAMPE No. 4 A series circuit comprises of a resistance of 5 Ω, a capacitor of nf and an inductor of 5 μh. Calculate the resonant frequency and the current at resonance when V rms is applied. Calculate the Q factor at resonance. SOUTION fo π C π 5 x 0-6 x x MHz I = V/Z = V/ = /5 = 0. A Q C = /f o C == /( x.59 x 0 6 x 5 x x 0-9 ) = 0 Q = f o / = 0 SEF ASSESSMENT EXECISE No. 4. A series circuit has = 60 mh, = 5 and C = 5 nf. The supply is V ac. Calculate: i. the resonant frequency (5.3 khz) ii. the voltage over each component. (V = 0.33 A, V C = 66 V, V = 66 A) iii. the Q factor for the capacitor and inductor at resonance. (33.3). A parallel circuit has = 40 mh, = k and C = 0 nf. The supply is V ac. Calculate: i. the resonant frequency (7.96 khz) ii. the current in each component. (I = ma, I C = ma, I = ma) D.J.Dunn 9

10 5. DYNAMIC ESISTANCE Any inductor is made from a coil of conducting material, usually copper and so has a resistance. We can idealise such an inductor as a resistance in series with pure inductor. This also applies to a series and circuit. The phasor diagram is as shown and it follows that the impedance of the coil is: Z The admittance of the coil is S Y S X Z The phase angle is found from tan() = X / S Now suppose that a capacitor is placed in parallel with the circuit. The phasor diagram using the admittance is shown. At resonance the inductive and capacitive admittance are equal so the impedance of the circuit is resistive. This is called the DYNAMIC ESISTANCE D. At resonance capacitive and inductive components are equal so the conductance is G = Y S cos() BC YSsin( ) XC YS XC sin( ) cos( ) G YS cos( ) D XC sin( ) XC tan( ) XC X π f D XC tan( ) D π f C C WOKED EXAMPE No. 5 A pure inductance of 50 μh is connected in series with a resistance of 5Ω. A capacitance of 470 nf is connected in parallel as shown. Determine the dynamic resistance and the resonant frequency. If a sinusoidal voltage of 5 V rms is applied at the resonant frequency, what are the rms currents in the inductor and the capacitor? Determine the current Q factor for each. SOUTION 6 50 x0 D Ω 9 C 470 x0 x 5 At resonance X c = X so fo π C -6 π 50x0 x 470 x 0 X C Ω - π foc (8955)(470 x0 9 ) I C = 5/7.865 = 0.8 A rms Hz D.J.Dunn 0

11 For an inductor and resistor in series -6 Z S X π fo (8955)(50 x0 ) Ω This is no surprise because the circuit is resonant. Z X S Z s = 8.55 Ω I = 5/8.55 = 0.7 A rms X The impedance of the whole network is the dynamic resistance so I = 5/63.83 = A rms Q C = 0.8/0.078 = Q = 0.7/0.078 = 3.44 SEF ASSESSMENT EXECISE No. 5 A pure inductance of 00 μh is connected in series with a resistance of 0.5Ω. A capacitance of 900 nf is connected in parallel as shown. A sinusoidal voltage of 0 V rms is applied at the resonant frequency. Determine the resonant frequency, the dynamic resistance and the current Q factor for the capacitor and inductor. (Answers 863 Hz, Ω, 9.8 and 9.8) D.J.Dunn

12 6 FITES You have seen that capacitors and inductors produce reactance that varies with frequency. If we use a suitable circuit containing both we can filter out unwanted components of mixed signals. The diagram shows a OW and HIGH PASS FITE. The high pass filter allows frequencies above a certain value to pass while those below are attenuated. The low pass filter allows low frequencies through but attenuates high frequencies. emember capacitive reactance reduces with frequency but inductive reactance increases. The design of the filter depends on the frequencies of interest. One use of a low pass filter is to smooth out direct current with an ac ripple on it and remove mains hum from an audio signal. ow and high pass filters may be designed with a capacitor and resistor as shown. The time constant C is important in determining the useful frequencies. The characteristics of a typical low pass filter are shown. How fast the voltage drops away after the cut off point depends on the design and in particular the Q factor. Other filters are used to either stop a band of frequencies within a range or either side of a range. These are called BAND PASS and BAND STOP. The diagram shows a band pass filter design and characteristic. The band width is the frequency range between the cut off point on either side of the filter. The sharpness of the filter depends on the steepness of the sides. An example of a band pass filter is in radios where the frequencies either side of the frequency required are removed. Another example is in signal multiplexing like multiple telephone signals on one line might be removed leaving only the one required. A band stop filter does the opposite by filtering out a particular range of frequencies. For example a notch filter used in radios will be tuned with a high Q factor to prevent one particular frequency interfering with the rest. The diagram opposite shows a high Q notch filter. D.J.Dunn

EDEXCEL NATIONAL CERTIFICATE/DIPLOMA UNIT 5 - ELECTRICAL AND ELECTRONIC PRINCIPLES NQF LEVEL 3 OUTCOME 4 - ALTERNATING CURRENT

EDEXCEL NATIONAL CERTIFICATE/DIPLOMA UNIT 5 - ELECTRICAL AND ELECTRONIC PRINCIPLES NQF LEVEL 3 OUTCOME 4 - ALTERNATING CURRENT EDEXCEL NATIONAL CERTIFICATE/DIPLOMA UNIT 5 - ELECTRICAL AND ELECTRONIC PRINCIPLES NQF LEVEL 3 OUTCOME 4 - ALTERNATING CURRENT 4 Understand single-phase alternating current (ac) theory Single phase AC

More information

Chapter 12. RL Circuits. Objectives

Chapter 12. RL Circuits. Objectives Chapter 12 RL Circuits Objectives Describe the relationship between current and voltage in an RL circuit Determine impedance and phase angle in a series RL circuit Analyze a series RL circuit Determine

More information

LCR Series Circuits. AC Theory. Introduction to LCR Series Circuits. Module 9. What you'll learn in Module 9. Module 9 Introduction

LCR Series Circuits. AC Theory. Introduction to LCR Series Circuits. Module 9. What you'll learn in Module 9. Module 9 Introduction Module 9 AC Theory LCR Series Circuits Introduction to LCR Series Circuits What you'll learn in Module 9. Module 9 Introduction Introduction to LCR Series Circuits. Section 9.1 LCR Series Circuits. Amazing

More information

Practice Problems - Chapter 33 Alternating Current Circuits

Practice Problems - Chapter 33 Alternating Current Circuits Multiple Choice Practice Problems - Chapter 33 Alternating Current Circuits 4. A high-voltage powerline operates at 500 000 V-rms and carries an rms current of 500 A. If the resistance of the cable is

More information

Reactance and Impedance

Reactance and Impedance Reactance and Impedance Capacitance in AC Circuits Professor Andrew H. Andersen 1 Objectives Describe capacitive ac circuits Analyze inductive ac circuits Describe the relationship between current and

More information

Chapt ha e pt r e r 12 RL Circuits

Chapt ha e pt r e r 12 RL Circuits Chapter 12 RL Circuits Sinusoidal Response of RL Circuits The inductor voltage leads the source voltage Inductance causes a phase shift between voltage and current that depends on the relative values of

More information

Direct versus Alternating Current Things We Can Measure

Direct versus Alternating Current Things We Can Measure Phil Sherrod W4PHS Direct versus Alternating Current Things We Can Measure Direct Current (DC) Alternating Current (AC) Voltage Voltage (peak, RMS) Current Current (peak, effective) Power True power, Apparent

More information

EXPERIMENT 4:- MEASUREMENT OF REACTANCE OFFERED BY CAPACITOR IN DIFFERENT FREQUENCY FOR R-C CIRCUIT

EXPERIMENT 4:- MEASUREMENT OF REACTANCE OFFERED BY CAPACITOR IN DIFFERENT FREQUENCY FOR R-C CIRCUIT Kathmandu University Department of Electrical and Electronics Engineering BASIC ELECTRICAL LAB (ENGG 103) EXPERIMENT 4:- MEASUREMENT OF REACTANCE OFFERED BY CAPACITOR IN DIFFERENT FREQUENCY FOR R-C CIRCUIT

More information

Basic Electrical Theory

Basic Electrical Theory Basic Electrical Theory Impedance PJM State & Member Training Dept. PJM 2014 10/24/2013 Objectives Identify the components of Impedance in AC Circuits Calculate the total Impedance in AC Circuits Identify

More information

RADIO AMATEUR EXAM GENERAL CLASS

RADIO AMATEUR EXAM GENERAL CLASS RAE-Lessons by 4S7VJ 1 RADIO AMATEUR EXAM GENERAL CLASS By 4S7VJ CHAPTER- 3 3.1 REACTANCE (X) When a.c. voltage applied to a capacitor or an inductor the current (r.m.s.) is proportional to the voltage

More information

Physics 9 Fall 2009 Homework 9 - Solutions

Physics 9 Fall 2009 Homework 9 - Solutions . Chapter 36 - Exercise 5. Physics 9 Fall 2009 Homework 9 - s What are V R and V C if the emf frequency in the figure is 0 khz? The voltage are V R = IR, and V C = IX C, where the capitative reactance

More information

Prof. Anchordoqui Problems set # 11 Physics 169 May 5, 2015

Prof. Anchordoqui Problems set # 11 Physics 169 May 5, 2015 rof. Anchordoqui roblems set # hysics 69 May 5, 5. A semicircular conductor of radius.5 m is rotated about the axis A at a constant rate of rev/min (Fig. ). A uniform magnetic field in all of the lower

More information

Chapter 10. RC Circuits. Objectives

Chapter 10. RC Circuits. Objectives Chapter 10 RC Circuits Objectives Describe the relationship between current and voltage in an RC circuit Determine impedance and phase angle in a series RC circuit Analyze a series RC circuit Determine

More information

LRC Circuits. Purpose. Principles PHYS 2211L LAB 7

LRC Circuits. Purpose. Principles PHYS 2211L LAB 7 Purpose This experiment is an introduction to alternating current (AC) circuits. Using the oscilloscope, we will examine the voltage response of inductors, resistors and capacitors in series circuits driven

More information

LCR Parallel Circuits

LCR Parallel Circuits Module 10 AC Theory Introduction to What you'll learn in Module 10. The LCR Parallel Circuit. Module 10.1 Ideal Parallel Circuits. Recognise ideal LCR parallel circuits and describe the effects of internal

More information

ALTERNATING CURRENTS

ALTERNATING CURRENTS ALTERNATING CURRENTS VERY SHORT ANSWER QUESTIONS Q-1. What is the SI unit of? Q-2. What is the average value of alternating emf over one cycle? Q-3. Does capacitor allow ac to pass through it? Q-4. What

More information

ε rms ε substation HOMEWORK #11 Chapter 29

ε rms ε substation HOMEWORK #11 Chapter 29 HOMEWOK # hapter 9 5 f the frequency in the circuit in Figure 9-8 is doubled, the capacitive reactance of the circuit will (a) double, (b) not change, (c) halve, (d) quadruple. Determine the oncept The

More information

Chapter 15 10/14/2014

Chapter 15 10/14/2014 Chapter 15 Analyze series and parallel ac circuits to find Voltage Current Power Total impedance, admittance Apply known circuit theories Kirchhoff s current, voltage laws Voltage or current divider rule

More information

Chapter 13. RLC Circuits and Resonance

Chapter 13. RLC Circuits and Resonance Chapter 13 RLC Circuits and Resonance Impedance of Series RLC Circuits A series RLC circuit contains both inductance and capacitance Since X L and X C have opposite effects on the circuit phase angle,

More information

ECE215 Lecture 16 Date:

ECE215 Lecture 16 Date: Lecture 16 Date: 20.10.2016 Bode Plot (contd.) Series and Parallel Resonance Example 1 Find the transfer function H(ω) with this Bode magnitude plot Example 2 Find the transfer function H(ω) with this

More information

L-C-R Series and parallel Resonance

L-C-R Series and parallel Resonance Page o 6 L-C-R Series and parallel Resonance Aim :- To study the requency response and to ind resonant requencies o L-C-R series and parallel circuits. Also to ind the quality actor and band width in L-C-R

More information

Three phase circuits

Three phase circuits Three phase circuits THREE PHASE CIRCUITS THREE-PHASE ADVANTAGES 1. The horsepower rating of three-phase motors and the kva rating of three-phase transformers are 150% greater than single-phase motors

More information

Electronic Components. Electronics. Resistors and Basic Circuit Laws. Basic Circuits. Basic Circuit. Voltage Dividers

Electronic Components. Electronics. Resistors and Basic Circuit Laws. Basic Circuits. Basic Circuit. Voltage Dividers Electronics most instruments work on either analog or digital signals we will discuss circuit basics parallel and series circuits voltage dividers filters high-pass, low-pass, band-pass filters the main

More information

Chapter 13. RLC Circuits and Resonance. Objectives

Chapter 13. RLC Circuits and Resonance. Objectives Chapter 13 RLC Circuits and Resonance Objectives Determine the impedance of a series RLC circuit Analyze series RLC circuits Analyze a circuit for series resonance Analyze series resonant filters Analyze

More information

Chapter 22: Alternating current. What will we learn in this chapter?

Chapter 22: Alternating current. What will we learn in this chapter? Chapter 22: Alternating current What will we learn in this chapter? Contents: Phasors and alternating currents Resistance and reactance Series R L C circuit Power in ac-circuits Series resonance Parallel

More information

Lesson 27. (1) Root Mean Square. The emf from an AC generator has the time dependence given by

Lesson 27. (1) Root Mean Square. The emf from an AC generator has the time dependence given by Lesson 27 () Root Mean Square he emf from an AC generator has the time dependence given by ℇ = ℇ "#$% where ℇ is the peak emf, is the angular frequency. he period is he mean square value of the emf is

More information

FUNDAMENTALS OF ENGINEERING (FE) EXAMINATION

FUNDAMENTALS OF ENGINEERING (FE) EXAMINATION January 8, 008 1:55 Appc Sheet number 1 Page number 77 magenta black A P P E N D I X C FUNDAMENTALS OF ENGINEERING (FE) EXAMINATION C.1 INTRODUCTION The Fundamentals of Engineering (FE) examination 1 is

More information

Laboratory #2: AC Circuits, Impedance and Phasors Electrical and Computer Engineering EE University of Saskatchewan

Laboratory #2: AC Circuits, Impedance and Phasors Electrical and Computer Engineering EE University of Saskatchewan Authors: Denard Lynch Date: Aug 30 - Sep 28, 2012 Sep 23, 2013: revisions-djl Description: This laboratory explores the behaviour of resistive, capacitive and inductive elements in alternating current

More information

Chapter 21 Band-Pass Filters and Resonance

Chapter 21 Band-Pass Filters and Resonance Chapter 21 Band-Pass Filters and Resonance In Chapter 20, we discussed low-pass and high-pass filters. The simplest such filters use RC components resistors and capacitors. It is also possible to use resistors

More information

Network Analysis (Subject Code: 06ES34) Resonance

Network Analysis (Subject Code: 06ES34) Resonance NEWS RESULTS FORUMS Network Analysis (Subject Code: 06ES34) Resonance Introduction Resonance Classification of Resonance Circuits Series Resonance Circuit Parallel Resonance Circuit Frequency Response

More information

Vectors and Phasors. A supplement for students taking BTEC National, Unit 5, Electrical and Electronic Principles. Owen Bishop

Vectors and Phasors. A supplement for students taking BTEC National, Unit 5, Electrical and Electronic Principles. Owen Bishop Vectors and phasors Vectors and Phasors A supplement for students taking BTEC National, Unit 5, Electrical and Electronic Principles Owen Bishop Copyrught 2007, Owen Bishop 1 page 1 Electronics Circuits

More information

1. Effective voltage is given by expression

1. Effective voltage is given by expression Chapter 07 A C CIRCUITS 1. Effective voltage is given by expression 1) Ve = Vo/ 2 2) Ve = 2 Vo 3) Vo/π 4) π Vo Effective voltage isrms voltage Answer is (1) 2. A coil having zero resistance is connected

More information

Extra Questions - 1. 1. What current will flow in a 20Ω resistor when it is connected to a 50V supply? a) 0.4A b) 1.6A c) 2.5A

Extra Questions - 1. 1. What current will flow in a 20Ω resistor when it is connected to a 50V supply? a) 0.4A b) 1.6A c) 2.5A Extra Questions - 1 1. What current will flow in a 20Ω resistor when it is connected to a 50V supply? a) 0.4A b) 1.6A c) 2.5A 2. A current of 500mA flows in a resistance of 12Ω. What power is dissipated

More information

Alternating Current. Asist. Prof. Dr. Aytaç Gören Asist. Prof. Dr. Levent Çetin

Alternating Current. Asist. Prof. Dr. Aytaç Gören Asist. Prof. Dr. Levent Çetin Asist. Prof. Dr. Aytaç Gören Asist. Prof. Dr. Levent Çetin 30.10.2012 Contents Alternating Voltage Phase Phasor Representation of AC Behaviors of Basic Circuit Components under AC Resistance, Reactance

More information

Eðlisfræði 2, vor 2007

Eðlisfræði 2, vor 2007 [ Assignment View ] [ Pri Eðlisfræði 2, vor 2007 31. Alternating Current Circuits Assignment is due at 2:00am on Wednesday, March 21, 2007 Credit for problems submitted late will decrease to 0% after the

More information

Inductive and Capacitive Reactance

Inductive and Capacitive Reactance Inductive and Capacitive Reactance Course No: E04-005 Credit: 4 PDH A. Bhatia Continuing Education and Development, Inc. 9 Greyridge Farm Court Stony Point, NY 10980 P: (877) 322-5800 F: (877) 322-4774

More information

Resonant and cut-off frequencies Tuned network quality, bandwidth, and power levels Quality factor

Resonant and cut-off frequencies Tuned network quality, bandwidth, and power levels Quality factor Chapter 20 Resonant and cut-off frequencies Tuned network quality, bandwidth, and power levels Quality factor ECET 207 AC Circuit Analysis, PNC 2 1 20.1-20.7 A condition established by the application

More information

Electrical Fundamentals - Reactance and Impedance

Electrical Fundamentals - Reactance and Impedance PDHonline Course E239 (4 PDH) Electrical Fundamentals - Reactance and Impedance Instructor: A. Bhatia, B.E. 2012 PDH Online PDH Center 5272 Meadow Estates Drive Fairfax, VA 22030-6658 Phone & Fax: 703-988-0088

More information

Chapter 12. RL Circuits ISU EE. C.Y. Lee

Chapter 12. RL Circuits ISU EE. C.Y. Lee Chapter 12 RL Circuits Objectives Describe the relationship between current and voltage in an RL circuit Determine impedance and phase angle in a series RL circuit Analyze a series RL circuit Determine

More information

Transistor Tuned Amplifiers

Transistor Tuned Amplifiers 5 Transistor Tuned Amplifiers 389 Transistor Tuned Amplifiers 5. Tuned Amplifiers 5. Distinction between Tuned Amplifiers and other Amplifiers 5.3 Analysis of Parallel Tuned Circuit 5.4 Characteristics

More information

Basic AC Reactive Components IMPEDANCE

Basic AC Reactive Components IMPEDANCE Basic AC Reactive Components Whenever inductive and capacitive components are used in an AC circuit, the calculation of their effects on the flow of current is important. EO 1.9 EO 1.10 EO 1.11 EO 1.12

More information

EXPERIMENT 5: SERIES AND PARALLEL RLC RESONATOR CIRCUITS

EXPERIMENT 5: SERIES AND PARALLEL RLC RESONATOR CIRCUITS EXPERIMENT 5: SERIES AND PARALLEL RLC RESONATOR CIRCUITS Equipment List S 1 BK Precision 4011 or 4011A 5 MHz Function Generator OS BK 2120B Dual Channel Oscilloscope V 1 BK 388B Multimeter L 1 Leeds &

More information

Chapter 9: Ideal Transformer. 10/9/2003 Electromechanical Dynamics 1

Chapter 9: Ideal Transformer. 10/9/2003 Electromechanical Dynamics 1 Chapter 9: Ideal Transformer 10/9/003 Electromechanical Dynamics 1 Introduction Transformers are one of the most useful electrical devices provides a change in voltage and current levels provides galvanic

More information

Circuits with inductors and alternating currents. Chapter 20 #45, 46, 47, 49

Circuits with inductors and alternating currents. Chapter 20 #45, 46, 47, 49 Circuits with inductors and alternating currents Chapter 20 #45, 46, 47, 49 RL circuits Ch. 20 (last section) Symbol for inductor looks like a spring. An inductor is a circuit element that has a large

More information

LCR Meter Measurement Accuracy

LCR Meter Measurement Accuracy LCR Meter Measurement Accuracy Introduction LCR meters make taking L, C and R measurements very easy. One can simply hook up the test component between the clip terminals and get the reading on the display

More information

Characterizing Resonant Series RLC Circuits : Two Challenging Experiments Using Either LabView. Software of National Instruments or VEE of Hewlett

Characterizing Resonant Series RLC Circuits : Two Challenging Experiments Using Either LabView. Software of National Instruments or VEE of Hewlett Characterizing Resonant Series RLC Circuits : Two Challenging Experiments Using Either LabView Software of National Instruments or VEE of Hewlett Packard Software for Data Acquisition Via the GPIB Bus

More information

3 Phase Power Basics. Thomas Greer Executive Director Engineering Services TLG Services

3 Phase Power Basics. Thomas Greer Executive Director Engineering Services TLG Services 3 Phase Power Basics Thomas Greer Executive Director Engineering Services TLG Services Agenda Terminology Basic Electrical Circuits Basic Power Calculations Why This Electricity Stuff? To Become an Electrical

More information

Simple Harmonic Motion: AC circuits: alternating current electricity

Simple Harmonic Motion: AC circuits: alternating current electricity Simple Harmonic Motion: AC circuits: alternating current electricity Alternating current (AC) circuits explained using time and phasor animations. Impedance, phase relations, resonance and RMS quantities.

More information

The W5JCK Guide to the Mathematic Equations Required for the Amateur Extra Class Exam

The W5JCK Guide to the Mathematic Equations Required for the Amateur Extra Class Exam The W5JCK Guide to the Mathematic Equations Required for the Amateur Extra Class Exam This document contains every question from the Extra Class (Element 4) Question Pool* that requires one or more mathematical

More information

Diodes have an arrow showing the direction of the flow.

Diodes have an arrow showing the direction of the flow. The Big Idea Modern circuitry depends on much more than just resistors and capacitors. The circuits in your computer, cell phone, Ipod depend on circuit elements called diodes, inductors, transistors,

More information

Resonance. Objectives

Resonance. Objectives Resonance Objectives Determine the impedance of a series RLC circuit Analyze series RLC circuits Analyze a circuit for series resonance Analyze series resonant filters Analyze parallel RLC circuits Analyze

More information

Alternating Current RL Circuits

Alternating Current RL Circuits Alternating Current RL Circuits Objectives. To understand the voltage/current phase behavior of RL circuits under applied alternating current voltages, and. To understand the current amplitude behavior

More information

Filters & Wave Shaping

Filters & Wave Shaping Module 8 AC Theory Filters & Wave Shaping Passive Filters & Wave Shaping What you'll learn in Module 8. Module 8 Introduction Recognise passive filters with reference to their response curves. High pass,

More information

Chapter 11. Inductors. Objectives

Chapter 11. Inductors. Objectives Chapter 11 Inductors Objectives Describe the basic structure and characteristics of an inductor Discuss various types of inductors Analyze series inductors Analyze parallel inductors Analyze inductive

More information

Chapter 12 Driven RLC Circuits

Chapter 12 Driven RLC Circuits hapter Driven ircuits. A Sources... -. A ircuits with a Source and One ircuit Element... -3.. Purely esistive oad... -3.. Purely Inductive oad... -6..3 Purely apacitive oad... -8.3 The Series ircuit...

More information

Chapter 29 Alternating-Current Circuits

Chapter 29 Alternating-Current Circuits hapter 9 Alternating-urrent ircuits onceptual Problems A coil in an ac generator rotates at 6 Hz. How much time elapses between successive emf values of the coil? Determine the oncept Successive s are

More information

Online Homework 10 Solution

Online Homework 10 Solution Onle Homework Solution Phasors Explaed n this problem, you will answer some basic questions about phasors and prepare to use them the analysis o various A circuits. n parts A - consider the our phasors

More information

Experiment 10 Inductors in AC Circuits

Experiment 10 Inductors in AC Circuits Experiment 1 Inductors in AC Circuits Preparation Prepare for this week's experiment by looking up inductors, self inductance, enz's aw, inductive reactance, and R circuits Principles An inductor is made

More information

Understanding Power Factor and How it Affects Your Electric Bill. Presented by Scott Peele PE

Understanding Power Factor and How it Affects Your Electric Bill. Presented by Scott Peele PE Understanding Power Factor and How it Affects Your Electric Bill Presented by Scott Peele PE Understanding Power Factor Definitions kva, kvar, kw, Apparent Power vs. True Power Calculations Measurements

More information

Alternating-Current Circuits

Alternating-Current Circuits hapter 1 Alternating-urrent ircuits 1.1 A Sources... 1-1. Simple A circuits... 1-3 1..1 Purely esistive load... 1-3 1.. Purely Inductive oad... 1-5 1..3 Purely apacitive oad... 1-7 1.3 The Series ircuit...

More information

RESONANCE AND FILTERS

RESONANCE AND FILTERS 1422-1 RESONANCE AND FILTERS Experiment 5, Current in a Parallel Resonant Circuit, For more courses visit www.cie-wc.edu OBJECTIVES: 1. To verify by experiment, that the line current (I line ) is at its

More information

Einstein Classes, Unit No. 102, 103, Vardhman Ring Road Plaza, Vikas Puri Extn., Outer Ring Road, New Delhi , Ph. : ,

Einstein Classes, Unit No. 102, 103, Vardhman Ring Road Plaza, Vikas Puri Extn., Outer Ring Road, New Delhi , Ph. : , 1 EMI & AC 1. Derive an expression for the impendance of a coil in AC ciruit. A current of 1.1 A flows through a coil when connected to a 110 V DC. When 110 V AC of 50 Hz is applied to the same coil, only

More information

Critical thin-film processes such as deposition and etching take place in a vacuum

Critical thin-film processes such as deposition and etching take place in a vacuum WHITEPAPER INTRODUCING POWER SUPPLIES AND PLASMA Critical thin-film processes such as deposition and etching take place in a vacuum SYSTEMS chamber in the presence of a plasma. A plasma is an electrically

More information

Series and Parallel Resonant Circuits

Series and Parallel Resonant Circuits Seies and Paallel Resonant icuits OBJETIVE To detemine the esonant fequency, self-inductance and the quality facto of the coil in the seies and paallel cicuits. PRINIPE A coil of self-inductance is connected

More information

AC Power Basics REAL, REACTIVE, AND APPARENT POWER

AC Power Basics REAL, REACTIVE, AND APPARENT POWER AC Power Basics Power in an electric circuit is the rate of flow of energy past a given point of the circuit. In AC circuits, energy storage elements such as inductance and capacitance may result in periodic

More information

Basic Electrical Theory

Basic Electrical Theory Basic Electrical Theory Power Principles and Phase Angle PJM State & Member Training Dept. PJM 2014 10/24/2013 Objectives At the end of this presentation the learner will be able to; Identify the characteristics

More information

2. A conductor of length 2m moves at 4m/s at 30 to a uniform magnetic field of 0.1T. Which one of the following gives the e.m.f. generated?

2. A conductor of length 2m moves at 4m/s at 30 to a uniform magnetic field of 0.1T. Which one of the following gives the e.m.f. generated? Extra Questions - 2 1. A straight length of wire moves through a uniform magnetic field. The e.m.f. produced across the ends of the wire will be maximum if it moves: a) along the lines of magnetic flux

More information

Impedance Matching and Matching Networks. Valentin Todorow, December, 2009

Impedance Matching and Matching Networks. Valentin Todorow, December, 2009 Impedance Matching and Matching Networks Valentin Todorow, December, 2009 RF for Plasma Processing - Definition of RF What is RF? The IEEE Standard Dictionary of Electrical and Electronics Terms defines

More information

ε: Voltage output of Signal Generator (also called the Source voltage or Applied

ε: Voltage output of Signal Generator (also called the Source voltage or Applied Experiment #10: LR & RC Circuits Frequency Response EQUIPMENT NEEDED Science Workshop Interface Power Amplifier (2) Voltage Sensor graph paper (optional) (3) Patch Cords Decade resistor, capacitor, and

More information

EE 221 AC Circuit Power Analysis. Instantaneous and average power RMS value Apparent power and power factor Complex power

EE 221 AC Circuit Power Analysis. Instantaneous and average power RMS value Apparent power and power factor Complex power EE 1 AC Circuit Power Analysis Instantaneous and average power RMS value Apparent power and power factor Complex power Instantaneous Power Product of time-domain voltage and time-domain current p(t) =

More information

First Year (Electrical & Electronics Engineering)

First Year (Electrical & Electronics Engineering) Z PRACTICAL WORK BOOK For The Course EE-113 Basic Electrical Engineering For First Year (Electrical & Electronics Engineering) Name of Student: Class: Batch : Discipline: Class Roll No.: Examination Seat

More information

Filter Considerations for the IBC

Filter Considerations for the IBC application note AN:202 Filter Considerations for the IBC Mike DeGaetano Application Engineering July 2013 Contents Page Introduction 1 IBC Attributes 1 Damping and 2 Converter Bandwidth Filtering 3 Filter

More information

EDEXCEL NATIONAL CERTIFICATE/DIPLOMA UNIT 67 - FURTHER ELECTRICAL PRINCIPLES NQF LEVEL 3 OUTCOME 1 TUTORIAL 1 - DIRECT CURRENT CIRCUIT THEOREMS

EDEXCEL NATIONAL CERTIFICATE/DIPLOMA UNIT 67 - FURTHER ELECTRICAL PRINCIPLES NQF LEVEL 3 OUTCOME 1 TUTORIAL 1 - DIRECT CURRENT CIRCUIT THEOREMS EDEXCE NATIONA CERTIFICATE/DIPOMA UNIT 67 - FURTHER EECTRICA PRINCIPES NQF EVE 3 OUTCOME 1 TUTORIA 1 - DIRECT CURRENT CIRCUIT THEOREMS Unit content 1 Be able to apply direct current (DC) circuit analysis

More information

AC Impedance and High-Pass Filters

AC Impedance and High-Pass Filters Lab 7 AC Impedance and High-Pass Filters In this lab you will become familiar with the concept of AC impedance and apply it to the frequency response of a high-pass filter. 7.1 AC Impedance Just as Ohm

More information

FREQUENCY RESPONSE AND PASSIVE FILTERS LABORATORY. We start with examples of a few filter circuits to illustrate the concept.

FREQUENCY RESPONSE AND PASSIVE FILTERS LABORATORY. We start with examples of a few filter circuits to illustrate the concept. FREQUENCY RESPONSE AND PASSIVE FILTERS LABORATORY In this experiment we will analytically determine and measure the frequency response of networks containing resistors, AC source/sources, and energy storage

More information

RLC Resonant Circuits

RLC Resonant Circuits C esonant Circuits Andrew McHutchon April 20, 203 Capacitors and Inductors There is a lot of inconsistency when it comes to dealing with reactances of complex components. The format followed in this document

More information

Power Factor Vs. Crest Factor: Critical Application Quantities Nicholas Piotrowski, Associated Power Technologies

Power Factor Vs. Crest Factor: Critical Application Quantities Nicholas Piotrowski, Associated Power Technologies Power Factor Vs. Crest Factor: Critical Application Quantities Nicholas Piotrowski, Associated Power Technologies Introduction Two critical quantities to specify when dealing with AC power sources are

More information

Chapter 35 Alternating Current Circuits

Chapter 35 Alternating Current Circuits hapter 35 Alternating urrent ircuits ac-ircuits Phasor Diagrams Resistors, apacitors and nductors in ac-ircuits R ac-ircuits ac-ircuit power. Resonance Transformers ac ircuits Alternating currents and

More information

7.1 POWER IN AC CIRCUITS

7.1 POWER IN AC CIRCUITS C H A P T E R 7 AC POWER he aim of this chapter is to introduce the student to simple AC power calculations and to the generation and distribution of electric power. The chapter builds on the material

More information

Characteristics of Crystal Units and Oscillation Circuit

Characteristics of Crystal Units and Oscillation Circuit Characteristics of Crystal Units and Oscillation Circuit 1. Characteristics of crystal units The thickness of crystal vibrator of the AT cut crystal unit as described in the previous page differs depending

More information

Electrical Circuits I Lecture 1

Electrical Circuits I Lecture 1 Electrical Circuits I Lecture Course Contents Basic dc circuit elements, series and parallel Networks Ohm's law and Kirchoff's laws Nodal Analysis Mesh Analysis Source Transformation

More information

AS91526: Demonstrate understanding of electrical systems Level 3 Credits 6

AS91526: Demonstrate understanding of electrical systems Level 3 Credits 6 AS956: Demonstrate understanding of electrical systems Level 3 redits 6 This achievement standard involves demonstrating understanding of electrical systems. Achievement riteria Achievement Achievement

More information

Basic Electrical Technology Dr. L. Umanand Department of Electrical Engineering Indian Institute of Science, Bangalore. Lecture - 33 3 phase System 4

Basic Electrical Technology Dr. L. Umanand Department of Electrical Engineering Indian Institute of Science, Bangalore. Lecture - 33 3 phase System 4 Basic Electrical Technology Dr. L. Umanand Department of Electrical Engineering Indian Institute of Science, Bangalore Lecture - 33 3 phase System 4 Hello everybody. So, in the last class we have been

More information

Module Title: Electrotechnology for Mech L7

Module Title: Electrotechnology for Mech L7 CORK INSTITUTE OF TECHNOLOGY INSTITIÚID TEICNEOLAÍOCHTA CHORCAÍ Autumn Examinations 2012 Module Title: Electrotechnology for Mech L7 Module Code: ELEC7007 School: School of Mechanical, Electrical and Process

More information

April 8. Physics 272. Spring Prof. Philip von Doetinchem

April 8. Physics 272. Spring Prof. Philip von Doetinchem Physics 272 April 8 Spring 2014 http://www.phys.hawaii.edu/~philipvd/pvd_14_spring_272_uhm.html Prof. Philip von Doetinchem philipvd@hawaii.edu Phys272 - Spring 14 - von Doetinchem - 218 L-C in parallel

More information

Experiment 16 ANALOG FOURIER ANALYSIS. Experiment setup 4. Prelab problems 6. Experiment procedure 7. Appendix A: an effective high-q filter A-1

Experiment 16 ANALOG FOURIER ANALYSIS. Experiment setup 4. Prelab problems 6. Experiment procedure 7. Appendix A: an effective high-q filter A-1 16-i Experiment 16 ANALOG FOURIER ANALYI Introduction 1 Theory 1 Experiment setup 4 Prelab problems 6 Experiment procedure 7 Appendix A: an effective high-q filter A-1 16-ii 16-1 1/31/14 INTRODUCTION In

More information

Lecture Notes ELE A6

Lecture Notes ELE A6 ecture Notes EE A6 Ramadan El-Shatshat Three Phase circuits 9/12/2006 EE A6 Three-phase Circuits 1 Three-phase Circuits 9/12/2006 EE A6 Three-phase Circuits 2 Advantages of Three-phase Circuits Smooth

More information

Chapter 10. RC Circuits ISU EE. C.Y. Lee

Chapter 10. RC Circuits ISU EE. C.Y. Lee Chapter 10 RC Circuits Objectives Describe the relationship between current and voltage in an RC circuit Determine impedance and phase angle in a series RC circuit Analyze a series RC circuit Determine

More information

Physics 6C, Summer 2006 Homework 2 Solutions

Physics 6C, Summer 2006 Homework 2 Solutions Physics 6C, Summer 006 Homework Solutions All problems are from the nd edition of Walker. Numerical values are different for each student. Chapter 3 Problems. Figure 3-30 below shows a circuit containing

More information

The electrical energy is almost exclusively

The electrical energy is almost exclusively CHAPTER CHAPTER 6 Power Factor Improvement 6.1 Power Factor 6.2 Power Triangle 6.3 Disadvantages of Low Power Factor 6.4 Causes of Low Power Factor 6.5 Power Factor Improvement 6.6 Power Factor Improvement

More information

APJ ABDUL KALAM TECHNOLOGICAL UNIVERSITY. EE100 Basics of Electrical

APJ ABDUL KALAM TECHNOLOGICAL UNIVERSITY. EE100 Basics of Electrical APJ ABDUL KALAM TECHNOLOGICAL UNIVERSITY EE100 Basics of Electrical SAMPLE QUESTION PAPER Maximum Marks 100 Part- A (10 questions) Attempt all the questions 10*4=40 1. We have two identical 10 V electromotive

More information

Power Factor Correction for Power Systems First Semester Report Spring Semester 2007

Power Factor Correction for Power Systems First Semester Report Spring Semester 2007 Power Factor Correction for Power Systems First Semester Report Spring Semester 2007 by Pamela Ackerman Prepared to partially fulfill the requirements for EE401 Department of Electrical and Computer Engineering

More information

UNIVERSITY of PENNSYLVANIA DEPARTMENT of ELECTRICAL and SYSTEMS ENGINEERING ESE206 - Electrical Circuits and Systems II Laboratory.

UNIVERSITY of PENNSYLVANIA DEPARTMENT of ELECTRICAL and SYSTEMS ENGINEERING ESE206 - Electrical Circuits and Systems II Laboratory. UNIVERSITY of PENNSYLVANIA DEPARTMENT of ELECTRICAL and SYSTEMS ENGINEERING ESE06 - Electrical Circuits and Systems II Laboratory. Objectives: Transformer Lab. Comparison of the ideal transformer versus

More information

Parallel Inductor-Resistor-Capacitor (RLC) Circuits

Parallel Inductor-Resistor-Capacitor (RLC) Circuits Parallel Inductor-Resistor-Capacitor (RLC) Circuits Session 4b for Basic Electricity A Fairfield University E-Course Powered by LearnLinc 7/9/2002 Basic Electricity 1 Module: Basic Electronics (AC Circuits

More information

APPLICATION NOTE - 018

APPLICATION NOTE - 018 APPLICATION NOTE - 018 Power Transformers Background Power Transformers are used within an AC power distribution systems to increase or decrease the operating voltage to achieve the optimum transmission

More information

Chapter 11. Inductors ISU EE. C.Y. Lee

Chapter 11. Inductors ISU EE. C.Y. Lee Chapter 11 Inductors Objectives Describe the basic structure and characteristics of an inductor Discuss various types of inductors Analyze series inductors Analyze parallel inductors Analyze inductive

More information

UNIVERSITY OF NORTH CAROLINA AT CHARLOTTE. Department of Electrical and Computer Engineering

UNIVERSITY OF NORTH CAROLINA AT CHARLOTTE. Department of Electrical and Computer Engineering UNIVERSITY OF NORTH CAROLINA AT CHARLOTTE Department of Electrical and Computer Engineering Experiment No. 9 - Resonance in Series and parallel RLC Networks Overview: An important consideration in the

More information

RF POWER AMPLIFIERS - TANK CIRCUITS & OUTPUT COUPLING

RF POWER AMPLIFIERS - TANK CIRCUITS & OUTPUT COUPLING 1 of 6 RF POWER AMPLIFIERS - TANK CIRCUITS & OUTPUT COUPLING by Lloyd Butler VK5BR The output tuning and coupling of the final RF amplifier is an important part of the transmitter. It is designed to load

More information

Lesson Plan. Inductive Reactance Electronics

Lesson Plan. Inductive Reactance Electronics Inductive Reactance Electronics Lesson Plan Performance Objective Upon completion of the lesson, students will be able to demonstrate an understanding of inductive reactance through satisfactory completion

More information

Calculations for Electrical Installations - 2

Calculations for Electrical Installations - 2 Calculations for Electrical Installations - 2 Contents Preface vii Use of calculators 1 Simple transposition of formulae 3 SI units 5 Conductor colour identification 7 Alternating current circuit

More information