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

 To view this video please enable JavaScript, and consider upgrading to a web browser that supports HTML5 video
Save this PDF as:

Size: px
Start display at page:

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

## Transcription

1 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 circuit theory: waveform characteristics e.g. sinusoidal and non-sinusoidal waveforms, amplitude, period time, frequency, instantaneous, peak/peak-to-peak, root mean square (r.m.s), average values, form factor; determination of values using phasor and algebraic representation of alternating quantities e.g. graphical and phasor addition of two sinusoidal voltages, reactance and impedance of pure R, L and C components ac circuit measurements: safe use of an oscilloscope eg setting, handling, health and safety; measurements (periodic time, frequency, amplitude, peak/peak-to-peak, r.m.s and average values); circuits e.g. half and full wave rectifiers D.J.Dunn 1

2 1. REVISION OF BASIC A.C. THEORY 1.1 SINUSOIDAL WAVE FORMS A pure alternating current or voltage varies with time sinusoidally as shown. INSTANTANEOUS VALUES For a sinusoidal voltage and current the instantaneous value at any moment in time is given by:- v = V sin (ωt) and i = I sin (ωt) or v = V sin (2πf t) and i = I sin (2πf t) Note that this assumes that t = 0 when v or i = 0 AMPLITUDE The maximum value of volts or current is called the peak volts or current and this is the amplitude of the wave form (V and I). The peak to peak value is double the amplitude as shown on the diagram. FREQUENCY The voltage or current changes from a maximum (plus) in one direction, through zero to a maximum (minus) in the other direction. This occurs at f times a second. f is the frequency in Hertz. PERIODIC TIME 1 Hz = 1 cycle/second The time it takes to complete 1 cycle is T seconds (the periodic time). It follows that T = 1/f ANGULAR FREQUENCY If we think of the voltage and current being generated by a machine that rotates one revolution per cycle, the 1 cycle corresponds to 360 o or 2π radian. It follows that f cycles/second = 2πf radian/s and this is the angular frequency. ω = 2πf = 2π/T rad/s D.J.Dunn 2

3 AVERAGE VALUES The average value of any true alternating current or voltage is zero since half the cycle is negative and half is positive. When an average value is stated it refers to the average over one half of the cycle. This may be determined from the area under the graph as illustrated below. For a sinusoidal waveform, the blue area is exactly 2 when the angle is in radians and the peak value is 1. The mean value is value that makes the blue rectangle contain the same area as the blue area of the half cycle. In other words the green area above the average is equal to the light blue area below the rectangle. The blue area must be equal to π x average value hence the average value is 2/π = If the peak value is something other than 1 then the average is x peak value FORM FACTOR Peak Value This is defined as Form Factor Average value Hence for a sinusoidal voltage or current the form factor is π/2 = PHASE and DISPLACEMENT The sinusoidal graph is produced because we made θ = 0 when t = 0. We could choose to make θ any value at t = 0. We would then write the equations as: x = A sin(θ + ) or v = V sin(θ + ) where is the phase angle. The plot shown has x = 0 at θ = 30 o so it follows that (30 + ) = 0 and so = -30 o. If we made = 90 o we would have a cosine plot. Often periodic functions are not based about a mean of zero. For example an alternating voltage might be added to a constant (d.c.) voltage so that V = V dc + V sin(θ + ) D.J.Dunn 3

4 SELF ASSESSMENT EXERCISE No. 1 1 Mains electricity has a frequency of 50 Hz. What is the periodic time and angular frequency? (0.02 s and 314 rad/s) 2. An alternating current has a periodic time of s. What is the frequency? (400 Hz) 3. A alternating voltage has a peak to peak amplitude of 300 V and frequency of 50 Hz. What is the amplitude and average value? (150 V and V) What is the voltage at t = 0.02 s? (16.4 V) 4. An alternating current is given by the equation I = 5 sin(600t). Determine the following. i. the frequency ( Hz) ii. the periodic time ( ms) iii. the average value. (3.183 A) 5. Determine the following from the graph shown. The amplitude. The offset displacement. The periodic time. The frequency. The angular frequency. The phase angle. (Answers 5, 2, 1.57 s, 4 rad/s, Hz, 0.2 radian or 11.5 o ) D.J.Dunn 4

5 1.2 ROOT MEAN SQUARE VALUES (R.M.S.) The mean value of an alternating voltage and current is zero. Since electric power is normally calculated with P = V I it would appear that the mean power should be zero. This clearly is not true because most electric fires use alternating current and they give out power in the form of heat. When you studied Ohms' Law, you learned that electric power may also be calculated with the formulae E.P. = I 2 R or E.P. = V 2 /R These formulae work with positive or negative values since a negative number is positive when squared and power is always positive. In the case of a.c. we must use the average value of V 2 or I 2 and these are not zero. The diagram shows how a plot of V 2 or I 2 is always positive. The mean value is indicated. The mean height may be obtained by placing many vertical ordinates on it as shown. Taking a graph of current with many ordinates i 1 2, i i n 2. The mean value of the i 2 is: ( i 1 2+ i 2 2+ i in )/n If we take the square root of this, we have a value of current that can be used in the power formula. This is the ROOT MEAN SQUARE or r.m.s. value. I(r.m.s.) = ( i 1 2+ i 2 2+ i in )/n It can be shown by the use of calculus that the r.m.s. value of a sinusoidal wave form is V m / 2. We use r.m.s. values with a.c. so that we may treat some calculations the same as for d.c. When you use a voltmeter or ammeter with a.c., the values indicated are r.m.s. values. V rms = V m / 2 = 0.707V m SELF ASSESSMENT EXERCISE No The periodic time of an ac voltage is s. Calculate the frequency. (500 Hz) 2. The r.m.s. value of mains electricity is 240 V. Determine the peak voltage (amplitude). (339.5V) 3. An a.c. current varies between plus and minus 5 amps. Calculate the r.m.s. value. (3.535 A) 4. An electric fire produces 2 kw of heat from a 240 V r.m.s. supply. Determine the r.m.s. current and the peak current. (8.33 A and A) 5. An electric motor is supplied with 110 V r.m.s. at 60 Hz and produces 200W of power. Determine the periodic time, the r.m.s. current and the peak current. (16.7 ms, 1.82 A and A) D.J.Dunn 5

6 1.3 OTHER WAVE FORMS Cyclic variations may take many forms such as SQUARE, SAW TOOTH and TRIANGULAR as shown below. Square waveforms are really d.c. levels that suddenly change from plus to minus. The r.m.s. value is the same as the peak value. They are typically used for digital signal transmission. Saw tooth waves are used for scanning a cathode ray tube. The electron beam moves across the screen at a constant rate and then flies back to the beginning. Triangular waves change at a constant rate first in one direction and then the other. SELF ASSESSMENT EXERCISE No Work out the average and form factor figures for a square wave. 2. A triangular voltage has a peak value of 15 V. Work out the average value, the form factor and the r.m.s. value. Note that shape of the triangle does not make a difference so you can assume a right angle triangle to make it easier. If you cannot do the maths try plotting and working out the areas by a graphical method. (7.5V, 2 and 10.6 V) D.J.Dunn 6

7 2. REACTANCE AND IMPEDANCE Capacitors and Inductors have a property called Reactance denoted with an X. On their own they may be used with a form of Ohm s Law such that V/I = X Both V and I are r.m.s. values. The value of X depends on the frequency of the a.c. and this is why they are called REACTIVE. It should be noted that a pure capacitor and inductor does not lose any energy. A resistor on the other hand, produces resistance by dissipating energy but the value of R does not change with frequency so a resistor is a PASSIVE component. When a circuit consists of Resistance, Capacitance and Inductance, the overall impedance is denoted with a Z. The units of R, X and Z are Ohms. 2.1 CAPACITIVE REACTANCE X C When an alternating voltage is applied to a capacitor, the capacitor charges and discharges with each cycle. This means that alternating current flows in the circuit but not across the dielectric. If the frequency of the voltage is increased the capacitor must charge and discharge more quickly so the current must increase with the frequency. The r.m.s. current is directly proportional to the r.m.s. voltage V, the capacitance C and the frequency f. It follows that I rms = Constant x V rms x f x C V rms /I rms = 1/(constant x f C) The constant is 2 so V rms /I rms = X C = 1/(2 f C) Note that when f = 0, X C is infinite and when f is very large X C tends to zero. This means that a pure capacitor presents a total barrier to d.c. but the impedance to a.c. gets less and less as the frequency goes up. This makes it an ideal component for separating d.c. from a.c. If we put in a combined a.c. + d.c. signal as shown, we get out pure a.c. but with a reduced amplitude depending on the reactance. WORKED EXAMPLE No V r.m.s. applied across a capacitance of 4.7 μf. Calculate the r.m.s. current when the frequency is 20 Hz, 200 Hz and 2000 Hz SOLUTION 20 Hz 1 1 V 15 XC 1693 Ω Irms A -6 2 π f C 2 π x 20 x 4.7 x 10 XC Hz 1 1 V 15 XC Ω Irms A -6 2 π f C 2 π x 200 x 4.7 x 10 XC Hz 1 1 V 15 XC Ω Irms A -6 2 π f C 2 π x 2000 x 4.7 x 10 X 1693 C D.J.Dunn 7

8 2.2 INDUCTIVE REACTANCE X L The back e.m.f. produced by a varying current is e = - L x rate of change of current. In order to overcome the back e.m.f., a forward voltage equal and opposite is required. Hence in order to produce alternating current, an alternating voltage is needed. It can be shown that the r.m.s. voltage needed to produce an r.m.s. current is directly proportional to the current, the inductance and the frequency so that V rms = I rms (2fL) Hence V rms /I rms = X L = 2 f L Ohms Note that the reactance is zero when f = 0 and approaches infinity when f is very large. This means that a pure inductor has no impedance to d.c. but the impedance to a.c. increases directly proportional to frequency. This is the opposite affect to that of a capacitor and an inductor may be used to reduce the a.c. component of a combined a.c. and d.c. signal as illustrated. WORKED EXAMPLE No V r.m.s. applied across an inductance of 4 μh. Calculate the r.m.s. current when the frequency is 200 Hz, 200 khz and 200 MHz SOLUTION 6 V Hz XC 2π fl 2π x 20 x 4x mω Irms ka 3 X x 10 6 V khz XC 2π fl 2π x 200 x 4x Ω Irms A X V MHz XC 2π fl 2π x 2000 x 4x Ω Irms 2.98 ma X 5027 C C C D.J.Dunn 8

9 SELF ASSESSMENT EXERCISE No Calculate the reactance of a capacitor with capacitance 60 F at a frequency of 50 Hz. (53 Ω) 2. The Voltage applied to the capacitor is 110 V r.m.s. Calculate the r.m.s. current. (2.073 A) 3. A capacitor is put in a circuit to limit the r.m.s. current to 2 ma when 10 V r.m.s. at 60 Hz is placed across it. What should the value of the capacitance be? (530 nf) 4. Calculate the r.m.s. current in an inductor of 60 mh when 110 V r.m.s. is applied at 60 Hz. (4.863 A) 5. An inductor passes 20 ma rms at 12 V r.m.s. and 1000 Hz. Calculate the inductance. (95 mh) 6. Calculate the inductance of a coil 25 mm diameter, 100 mm long with 30 turns. The core has a relative permeability of ( H) Calculate the energy stored when 10 A d.c. flow. (0.555 J) Calculate the reactance for ac with a frequency of 100 Hz. (6.97 ) Calculate the r.m.s. voltage needed to make 10 A r.m.s. flow. (69.7V rms) D.J.Dunn 9

10 3. PHASOR DIAGRAMS The way a sinusoidal voltage or current varies with time is given by the following equations. v = V sin (ωt) or v = V sin (2πf t) i = I sin (ωt) or i = I sin (2πf t) V and I is the amplitude and v and i are the instantaneous values at time t. f is the frequency in Hz. ω is the angular frequency in radian/s ω = 2πf. ωt = θ and this is an angle in radian. Consider a phasor representing a sinusoidal voltage. It is a vector of length V that can be drawn at an angle θ = ωt to represent the voltage at any instant in time t. If they were drawn in succession then they would be rotating anticlockwise (positive) at ω rad/s. Starting from the horizontal position after a time t it will have rotated an angle θ = ωt. The vertical component of the phasor is v = V sin (θ) This corresponds to the value of the sinusoidal graph at that angle. When θ = π/2 radian (90 o ) the peak value is V so V is the amplitude or peak value (not the r.m.s.value). You will find some animated phasor operations at the following addresses. Requires Microsoft excel to run ADDING AND SUBTRACTING Phasors can be added or subtracted from each other in the same way as vectors. Consider two voltage phasors with the same angular frequency. The diagram shows two such phasors V 1 and V 2 but V 2 lags V 1 by angle d. This is the PHASE DIFFERENCE BETWEEN THEM. We can express the vectors as: v 1 = V 1 sin(θ) and v 2 = V 2 sin(θ - d). D.J.Dunn 10

11 If we add the two vectors we do it as shown. It is normal to draw one of the phasors horizontal as the phase difference is the same at all angles. The easiest way to add vectors is to resolve them into horizontal and vertical components. v 2 has a vertical component V 2 sin d and a horizontal component V 2 cos d The vertical component of v 2 is V 2 sin d The vertical component of v is V 2 sin d The horizontal component of v is V 1 + V cos d WORKED EXAMPLE No. 3 If v 1 = 10 sin (θ) and v 2 = 7 sin (θ - 30 o ) what is the resultant voltage? SOLUTION Let θ = 0 o when we add them. (V 1 in the horizontal position). The vertical component of v is v 2 sin d = 7 sin (-30 o ) = -3.5 (down). The horizontal component of v is V 1 + V 2 cos d = sin 30 o = The resultant voltage is ( ) = The phase angle is = tan -1 (-3.5/16.06) =-12.3 o We can express the phasor as v = sin (θ 12.3 o ) D.J.Dunn 11

12 4. CIRCUITS CONTAINING RESISTIVE AND REACTIVE COMPONENTS A.C. AND RESISTANCE When a.c. is applied to a pure resistance R, Ohm s Law applies and since it is passive it is the same at all frequencies at all moments in time. The phasors for voltage and current must rotate together. They are said to be IN PHASE AC AND INDUCTANCE This requires a basic knowledge of differentiation. The voltage required to drive a current through an inductor is v = L x rate of change of current. L is the inductance in Henries. Suppose i = I sin t The rate of change of current is obtained by differentiating di/dt = I cos(t) It follows that v = I L cos(t) and the maximum value is V = I L If V and I are plotted together we see that that V is ¼ cycle displaced and it is said that the voltage leads the current by 90 o. The voltage phasor is 90 o anticlockwise of the current phasor. D.J.Dunn 12

13 4.3 AC WITH RESISTANCE AND INDUCTANCE Now consider a.c. applied to a resistor and inductor in series as shown. The current I flows through both so this is used as the reference. The voltage over the resistance is V R = I R and on the phasor diagram this must be in the same direction as the current. The voltage over the inductor is V L = I X L and this must lead the current by 90 o and also V R by 90 o. It is not true to say that V = V L + V R because they must be treated as phasors or vectors. The resultant voltage is V S and this is the hypotenuse of a right-angled triangle so V The angle is called the phase angle and is always measured from V R. It follows that = tan -1 (V L /V R ) 2 2 V R VL D.J.Dunn 13

14 4.4. AC AND CAPACITANCE Thgis requires knowledge of integration. When a.c. is applied across a capacitor, the voltage is given by the equation v C = q/c where q is the charge stored and C is the capacitance in Farads. Since q idt then v C idt C i varies sinusoidally so that i = I sin (t) idt I ω cosω t I ω Substitute and v C cosω t C The maximum value of v C is I/c so this will be the length of the phasor representing V C. If we plot V C and I we find that V C lags the current by ¼ cycle or 90 o. This is opposite to an inductor which leads by 90 o AC WITH RESISTANCE AND CAPACITANCE Now consider a resistor and capacitor in series as shown. The voltage over the resistance is I R and on the phasor diagram this must be in the same direction as the current. It follows that V C lags V R by 90 o. It is not true to say that V s = V C + V R because they must be treated as vectors. The resultant voltage is the hypotenuse of a right-angled triangle so V s V 2 R V The angle is called the phase angle and is always measured from V R. It follows that = -tan -1 (V c /V R ) The only difference between this and the R L circuit is that V C lags V R and V L leads V R. This means that V L and V C are 180 o out of phase in a series circuit. 2 C D.J.Dunn 14

15 4.6. R L C IN SERIES The 3 voltages V R V L and V C are drawn as 3 phasors and the vector sum is found. It is convenient to draw V R horizontally but the vector diagram stays the same for all angles of rotation. Examining the small triangle, we see the vertical height is V L - V R and the horizontal length is V R. It follows that the resultant voltage is given by 2 2 V s VL Vc V and 1 V R L VC tan VR 4.7. REACTANCE AND IMPEDANCE REVISITED 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 R but for an inductor it is called inductive reactance X L and for a capacitor capacitive reactance X C. Inductive reactance increases with frequency and is given by X L = 2fL Capacitive reactance decreases with frequency and is given by X C = 1/ 2fC When current flows in a RLC circuit, the relationship between it and the resulting voltage is called the IMPEDANCE Z. Z = V/I where 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 R L C circuit may be drawn as shown with R drawn horizontally to make it easier XL XC Z X L XC R and tan R D.J.Dunn 15

16 WORKED EXAMPLE No. 4 A resistor of value 470 is connected in series with a capacitor of 22 F and an inductor of 50 mh and a voltage is applied across it. A current of 100 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 SOLUTION X L = 2πfL = 2π x 50 x 50 x 10-3 =15.71 Ω X C = 1/2πfC = 1/(2π x 50 x 22 x 10-6 ) =144.6 Ω Z X X R Ω L X C X R L C 1 o tan tan 15.3 V S = I Z = 0.1 x = 48.7 V rms SELF ASSESSMENT EXERCISE No A resistor of value 4 is connected in series with a capacitor of 47 F and an inductor of 20 μh and a voltage is applied across it. A current of 50 ma (r.m.s.) is produced. Determine the impedance, the phase angle between the voltage and current and the applied voltage when the frequency is 100 Hz. (34 Ω, o and 1.7 V) 2. A resistor of value 0.2 is connected in series with a capacitor of 4.7 F and an inductor of 5 mh and 0.5 V r.m.s. is applied across the ends. Determine the impedance, the phase angle between the voltage and current and the rms current when the frequency is 1000 Hz. (2.455 Ω, o and 204 ma) D.J.Dunn 16

### ANALYTICAL METHODS FOR ENGINEERS

UNIT 1: Unit code: QCF Level: 4 Credit value: 15 ANALYTICAL METHODS FOR ENGINEERS A/601/1401 OUTCOME - TRIGONOMETRIC METHODS TUTORIAL 1 SINUSOIDAL FUNCTION Be able to analyse and model engineering situations

### 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

### BASIC ELECTRONICS AC CIRCUIT ANALYSIS. December 2011

AM 5-202 BASIC ELECTRONICS AC CIRCUIT ANALYSIS December 2011 DISTRIBUTION RESTRICTION: Approved for Pubic Release. Distribution is unlimited. DEPARTMENT OF THE ARMY MILITARY AUXILIARY RADIO SYSTEM FORT

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

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

### 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

### 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

### 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

### 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

### 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

### 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

### 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

### 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

### 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

### 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

### 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

### 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

### 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

### 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

### Module P5.4 AC circuits and electrical oscillations

F L E X I B L E L E A R N I N G A P P R O A C H T O P H Y S I C S Module P5.4 Opening items. Module introduction.2 Fast track questions.3 Ready to study? 2 AC circuits 2. Describing alternating currents

### NZQA registered unit standard 20431 version 2 Page 1 of 7. Demonstrate and apply fundamental knowledge of a.c. principles for electronics technicians

NZQA registered unit standard 0431 version Page 1 of 7 Title Demonstrate and apply fundamental knowledge of a.c. principles for electronics technicians Level 3 Credits 7 Purpose This unit standard covers

### 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

### RESISTANCE, REACTANCE AND IMPEDANCE A Primer. Douglas Brooks, PhD UltraCAD Design, Inc. PART 2, REACTANCE

RESISTANCE, REACTANCE AND IMPEDANCE A Primer Douglas Brooks, PhD UltraCAD Design, Inc. PART 2, REACTANCE This is part 2 of a 3-part series on resistance, reactance and impedance. Most of us are familiar

### 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

### 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

### Intro to Power Lab Concepts

1 Intro to Power Lab Concepts Created by the University of Illinois at Urbana-Champaign TCIPG PMU Research Group 1 Table of Contents 1. PRE-LAB DC Power-----------------------------------------------------------------------------------

### Inductors in AC Circuits

Inductors in AC Circuits Name Section Resistors, inductors, and capacitors all have the effect of modifying the size of the current in an AC circuit and the time at which the current reaches its maximum

### PHASOR DIAGRAMS HANDS-ON RELAY SCHOOL WSU PULLMAN, WA. RON ALEXANDER - BPA

PHASOR DIAGRAMS HANDS-ON RELAY SCHOOL WSU PULLMAN, WA. RON ALEXANDER - BPA What are phasors??? In normal practice, the phasor represents the rms maximum value of the positive half cycle of the sinusoid

### 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

### 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

### 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

### Lab #4 examines inductors and capacitors and their influence on DC circuits.

Transient DC Circuits 1 Lab #4 examines inductors and capacitors and their influence on DC circuits. As R is the symbol for a resistor, C and L are the symbols for capacitors and inductors. Capacitors

### 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

### A complex number W consists of real and imaginary parts a and b respectively, and the imaginary constant j which is the square root of negative one.

eactance and Impedance A Voltage and urrent In a D circuit, we learned that the relationship between voltage and current was V=I, also known as Ohm's law. We need to find a similar law for A circuits,

### Lecture - 4 Diode Rectifier Circuits

Basic Electronics (Module 1 Semiconductor Diodes) Dr. Chitralekha Mahanta Department of Electronics and Communication Engineering Indian Institute of Technology, Guwahati Lecture - 4 Diode Rectifier Circuits

### 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.

### 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) =

### 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...

### 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

### AC Generators. Basic Generator

AC Generators Basic Generator A basic generator consists of a magnetic field, an armature, slip rings, brushes and a resistive load. The magnetic field is usually an electromagnet. An armature is any number

### 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

### 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

### CIRCUITS LABORATORY EXPERIMENT 3. AC Circuit Analysis

CIRCUITS LABORATORY EXPERIMENT 3 AC Circuit Analysis 3.1 Introduction The steady-state behavior of circuits energized by sinusoidal sources is an important area of study for several reasons. First, the

### 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

### 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...

### 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

### 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

### PHYS 2426 Engineering Physics II (Revised July 7, 2011) AC CIRCUITS: RLC SERIES CIRCUIT

PHYS 2426 Engineering Physics II (Revised July 7, 2011) AC CIRCUITS: RLC SERIES CIRCUIT INTRODUCTION The objective of this experiment is to study the behavior of an RLC series circuit subject to an AC

### 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

### Name Date Day/Time of Lab Partner(s) Lab TA

Name Date Day/Time of Lab Partner(s) Lab TA Objectives LAB 7: AC CIRCUITS To understand the behavior of resistors, capacitors, and inductors in AC Circuits To understand the physical basis of frequency-dependent

### 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

### BASIC ELECTRONICS PROF. T.S. NATARAJAN DEPT OF PHYSICS IIT MADRAS LECTURE-4 SOME USEFUL LAWS IN BASIC ELECTRONICS

BASIC ELECTRONICS PROF. T.S. NATARAJAN DEPT OF PHYSICS IIT MADRAS LECTURE-4 SOME USEFUL LAWS IN BASIC ELECTRONICS Hello everybody! In a series of lecture on basic electronics, learning by doing, we now

### 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

### Chapter 8. Introduction to Alternating Current and Voltage. Objectives

Chapter 8 Introduction to Alternating Current and Voltage Objectives Identify a sinusoidal waveform and measure its characteristics Describe how sine waves are generated Determine the various voltage and

### 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

### 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

### 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

### 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

### 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

### AC CIRCUITS - CAPACITORS AND INDUCTORS

EXPRIMENT#8 AC CIRCUITS - CAPACITORS AND INDUCTORS NOTE: Two weeks are allocated for this experiment. Before performing this experiment, review the Proper Oscilloscope Use section of Experiment #7. Objective

### ENGR 210 Lab 11 Frequency Response of Passive RC Filters

ENGR 210 Lab 11 Response of Passive RC Filters The objective of this lab is to introduce you to the frequency-dependent nature of the impedance of a capacitor and the impact of that frequency dependence

### 615xx, 616xx, 617xxx, 646x, 64xx, 65xx Series Programmable AC source

Chroma Systems Solutions, Inc. AC Power Definitions 615xx, 616xx, 617xxx, 646x, 64xx, 65xx Series Programmable AC source Keywords: Peak, RMS, Phase, Inrush Current, Power Factor, Crest Factor, Apparent

### Chapter 25 Alternating Currents

Physics Including Human Applications 554 Chapter 25 Alternating Currents GOALS When you have mastered the contents of this chapter, you will be able to achieve the following goals: Definitions Define each

### Lab #4 Capacitors and Inductors. Capacitor and Inductor Transient Response

Capacitor and Inductor Transient Response Capacitor Theory Like resistors, capacitors are also basic circuit elements. Capacitors come in a seemingly endless variety of shapes and sizes, and they can all

### Series & Parallel Impedance Parameters and Equivalent Circuits

Chroma ystems olutions, Inc. eries & arallel Impedance arameters and Equivalent Circuits Keywords: Impedance, capacitance, resistance Title: roduct Family: eries & arallel Impedance arameters and Equivalent

### Current and Temperature Ratings

Document 361-1 Current and Temperature Ratings Introduction This application note describes: How to interpret Coilcraft inductor current and temperature ratings Our current ratings measurement method and

### EXPERIMENT NUMBER 8 CAPACITOR CURRENT-VOLTAGE RELATIONSHIP

1 EXPERIMENT NUMBER 8 CAPACITOR CURRENT-VOLTAGE RELATIONSHIP Purpose: To demonstrate the relationship between the voltage and current of a capacitor. Theory: A capacitor is a linear circuit element whose

### 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

### Phasors. Phasors. by Prof. Dr. Osman SEVAİOĞLU Electrical and Electronics Engineering Department. ^ V cos (wt + θ) ^ V sin (wt + θ)

V cos (wt θ) V sin (wt θ) by Prof. Dr. Osman SEVAİOĞLU Electrical and Electronics Engineering Department EE 209 Fundamentals of Electrical and Electronics Engineering, Prof. Dr. O. SEVAİOĞLU, Page 1 Vector

Electrical Installation Calculations: Advanced This page intentionally left blank Electrical Installation Calculations: Advanced FOR TECHNICAL CERTIFICATE AND NVQ LEVEL 3 SEVENTH EDITION A. J. WATKINS

### 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

### Electrical Machines-I Prof. D. Kastha Department of Electrical Engineering Indian Institute of Technology, Kharagpur

Electrical Machines-I Prof. D. Kastha Department of Electrical Engineering Indian Institute of Technology, Kharagpur Lecture - 7 Voltage Regulation of Single Phase Transformers (Refer Slide Time: 00:59)

### EDEXCEL NATIONAL CERTIFICATE/DIPLOMA UNIT 5 - ELECTRICAL AND ELECTRONIC PRINCIPLES NQF LEVEL 3 OUTCOME 1 - D.C. CIRCUITS

EDEXCEL NATIONAL CERTIFICATE/DIPLOMA UNIT 5 - ELECTRICAL AND ELECTRONIC PRINCIPLES NQF LEVEL 3 OUTCOME - D.C. CIRCUITS Be able to use circuit theory to determine voltage, current and resistance in direct

### DOE FUNDAMENTALS HANDBOOK ELECTRICAL SCIENCE Volume 3 of 4

DOE-HDBK-1011/3-92 JUNE 1992 DOE FUNDAMENTALS HANDBOOK ELECTRICAL SCIENCE Volume 3 of 4 U.S. Department of Energy Washington, D.C. 20585 FSC-6910 Distribution Statement A. Approved for public release;

### 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

### EE 1202 Experiment #4 Capacitors, Inductors, and Transient Circuits

EE 1202 Experiment #4 Capacitors, Inductors, and Transient Circuits 1. Introduction and Goal: Exploring transient behavior due to inductors and capacitors in DC circuits; gaining experience with lab instruments.

### Lab 2: AC Measurements Capacitors and Inductors

Lab 2: AC Measurements Capacitors and Inductors Introduction The second most common component after resistors in electronic circuits is the capacitor. It is a two-terminal device that stores an electric

### Study Guide and Review for Electricity and Light Lab Final

Study Guide and Review for Electricity and Light Lab Final This study guide is provided to help you prepare for the lab final. The lab final consists of multiplechoice questions, usually two for each unit,

### Lesson 3 DIRECT AND ALTERNATING CURRENTS. Task. The skills and knowledge taught in this lesson are common to all missile repairer tasks.

Lesson 3 DIRECT AND ALTERNATING CURRENTS Task. The skills and knowledge taught in this lesson are common to all missile repairer tasks. Objectives. When you have completed this lesson, you should be able

### DIODE CIRCUITS LABORATORY. Fig. 8.1a Fig 8.1b

DIODE CIRCUITS LABORATORY A solid state diode consists of a junction of either dissimilar semiconductors (pn junction diode) or a metal and a semiconductor (Schottky barrier diode). Regardless of the type,

### Basic Electronics Prof. Dr. Chitralekha Mahanta Department of Electronic and Communication Engineering Indian Institute of Technology, Guwahati

Basic Electronics Prof. Dr. Chitralekha Mahanta Department of Electronic and Communication Engineering Indian Institute of Technology, Guwahati Module -5 Power Circuits and System Lecture - 2 Transformer

### 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

### 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,

### LABORATORY 10 TIME AVERAGES, RMS VALUES AND THE BRIDGE RECTIFIER. Bridge Rectifier

LABORATORY 10 TIME AVERAGES, RMS VALUES AND THE BRIDGE RECTIFIER Full-wave Rectification: Bridge Rectifier For many electronic circuits, DC supply voltages are required but only AC voltages are available.

### EDEXCEL NATIONAL CERTIFICATE/DIPLOMA MECHANICAL PRINCIPLES AND APPLICATIONS NQF LEVEL 3 OUTCOME 1 - LOADING SYSTEMS

EDEXCEL NATIONAL CERTIFICATE/DIPLOMA MECHANICAL PRINCIPLES AND APPLICATIONS NQF LEVEL 3 OUTCOME 1 - LOADING SYSTEMS TUTORIAL 1 NON-CONCURRENT COPLANAR FORCE SYSTEMS 1. Be able to determine the effects

### 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

### Chapter 3. Simulation of Non-Ideal Components in LTSpice

Chapter 3 Simulation of Non-Ideal Components in LTSpice 27 CHAPTER 3. SIMULATION OF NON-IDEAL COMPONENTS IN LTSPICE 3.1 Pre-Lab The answers to the following questions are due at the beginning of the lab.

### Chapter 5: Analysis of Time-Domain Circuits

Chapter 5: Analysis of Time-Domain Circuits This chapter begins the analysis of circuits containing elements with the ability to store energy: capacitors and inductors. We have already defined each of

### Experiment V: The AC Circuit, Impedance, and Applications to High and Low Pass Filters

Experiment : The AC Circuit, Impedance, and Applications to High and Low Pass Filters I. eferences Halliday, esnick and Krane, Physics, ol. 2, 4th Ed., Chapters 33 Purcell, Electricity and Magnetism, Chapter

### CAPACITIVE REACTANCE. We have already discussed the operation of a capacitor in a DC circuit, however let's just go over the main principles again.

Reading 13 Ron Bertrand VK2DQ http://www.radioelectronicschool.com CAPACITOR IN A DC CIRCUIT CAPACITIVE REACTANCE We have already discussed the operation of a capacitor in a DC circuit, however let's just

### Trigonometry for AC circuits

Trigonometry for AC circuits This worksheet and all related files are licensed under the Creative Commons Attribution License, version 1.0. To view a copy of this license, visit http://creativecommons.org/licenses/by/1.0/,

### Trigonometry for AC circuits

Trigonometry for AC circuits This worksheet and all related files are licensed under the Creative Commons Attribution License, version 1.0. To view a copy of this license, visit http://creativecommons.org/licenses/by/1.0/,

### Electrical Resonance

Electrical Resonance (R-L-C series circuit) APPARATUS 1. R-L-C Circuit board 2. Signal generator 3. Oscilloscope Tektronix TDS1002 with two sets of leads (see Introduction to the Oscilloscope ) INTRODUCTION

### 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

### 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

### 45. The peak value of an alternating current in a 1500-W device is 5.4 A. What is the rms voltage across?

PHYS Practice Problems hapters 8- hapter 8. 45. The peak value of an alternating current in a 5-W device is 5.4 A. What is the rms voltage across? The power and current can be used to find the peak voltage,

### NEON BULB OSCILLATOR EXPERIMENT

NEON BULB OSCILLATOR EXPERIMENT When we combine a neon bulb with the circuit for charging up a capacitor through a resistor, we obtain the worlds simplest active electronic circuit that does something

### R1 R2 R3. Figure1. Resistances in series V1 I. Figure 2. Equivalent circuit of figure 1 if RE= R1+R2+R3 VRE =V

Supplementary Notes for Unit 2 - Part A (Unit 3 and 4 exams also includes the topics detailed in this note) Series circuits A series circuit is a circuit in which resistors are arranged in a chain, so

### Aircraft Electrical System

Chapter 9 Aircraft Electrical System Introduction The satisfactory performance of any modern aircraft depends to a very great degree on the continuing reliability of electrical systems and subsystems.