1 0 ALTERNATING VOLTAGES AND CURRENT Bakiss Hiyana

1. 0 ALTERNATING VOLTAGES AND CURRENT Bakiss Hiyana binti Abu Bakar JKE, POLISAS BHAB 1

COURSE LEARNING OUTCOME Explain AC circuit concept and their analysis using AC circuit law. 2. Apply the knowledge of AC circuit in solving problem related to AC electrical circuit. 1. BHAB 2

CHAPTER CONTENT Understand alternating current Understand the generation of an alternating current Use oscilloscope to measure waveforms Understand the basic circuits laws of resistive AC circuits ALTERNATING VOLTAGE AND CURRENT Understand a phasor to represent a sine wave BHAB Understand a sinusoidal voltage and current values Understand angular measureme nt of a sine wave 3

1. 1 UNDERSTAND ALTERNATING CURRENT 1. 1. 1 DIFFERENTIATE BETWEEN DIRECT CURRENT AND ALTERNATING CURRENT DC AC The flow of electrical charge is only in one direction The movement of electrical charge periodically reverses directions. The output voltage will remain essentially constant over time AC source of electrical power charges constantly in amplitude & regularly changes polarity BHAB 4

1. 1. 2 EXPLAIN WHY AC IS USED IN PREFERENCE TO DC DC CRITERIA When a large amount of electrical energy is required, it is much difficult to generate DC (Expensive) Difficult to convert voltage DC does get used in some local commercial applications COST AC When a large amount of electrical energy is required, it is much economical & easier to generate & transmit AC (Cheaper) CONVERT -Easy to change AC voltage to a VOLTAGE higher @ low voltage using transformer. -Easy to convert to DC USAGE -AC is the form in which electrical power is delivered to business & residences. - AC may also converted into electromagnetic waves (radio waves) which can radiate @ travel through space. (wireless). BHAB - Use extensively in electronic to carry information from 1 point to another. 5

1. 1. 3 LIST THE SOURCES OF ALTERNATING CURRENT DC AC -Alternating current generator -Generating plant -Wind power station - Dry cell battery -Solar cell -Car battery **WHERE IS AC USED? - In any application where a large quantities of power are needed. BHAB 6

1. 2 UNDERSTAND THE GENERATION OF ALTERNATING CURRENT 1. 2. 1 EXPLAIN FARADAY’S & LENZ’S LAW INVOLVED IN GENERATING AC CURRENT - Faraday’s Law: Any change in the magnetic environment of a coil of wire will cause a voltage (emf) to be induced in the coil. - Lenz’s Law: There is an induced current in a closed conducting loop if and only if the magnetic flux through the loop is changing. The direction of the induced current is such that the induced magnetic field always opposes the change in the flux. BHAB 7

Generation of a sine wave: - Sinusoidal voltages are produced by ac generators and electronic oscillators. - 2 way to generate AC current: (a) Conductor rotates in a constant magnetic field, a sinusoidal wave is generated When the loop is moving perpendicular to the lines of flux, the maximum voltage is induced. A B C D When the conductor is moving parallel with the lines of flux, no voltage is induced. BHAB 8

(b) Conductor remain constant whole the magnetic field moved. - A bar magnet passes through a coil When magnet’s S-pole is leaving the coil, induced I flows in such a direction as to produce a N-pole to oppose the leaving of magnet. BHAB The induced I become zero. I is about to change direction. When magnet’s N-pole is moving into coil, induced I flows in such a direction as to produce a N-pole to oppose the approaching of magnet. 9

- Induced Voltage: the voltage produced within the conductor. - The voltage induced in a conductor is directly proportional to the rate at which the conductor cuts the magnetic lines of forces. 3. The length of the conductor in the field -The longer the conductor, the greater the induced voltage coz longer conductor cut more line of force as it moves through the field. Factor affected the amount of voltage induced 4. The angle at which the conductor cuts the field. -If the conductor moves at a right angle with respect to the field, maximum amount of voltage is induced. BHAB 1. The strength of magnetic field -Stronger magnetic field will result in more lines of force, induced voltage will higher. 2. The speed of conductor movement -The faster the conductor moves, the greater the induced voltage coz it cut more lines of force in a given period of time, voltage increase. 10

1. 2. 2 DRAW AC WAVEFORMS PRODUCED BY A SIMPLE ALTERNATING CURRENT GENERATOR ( 1 LOOP 2 POLE MAGNET ) � Generators convert rotational energy to electrical energy. When a conductor is in a magnetic field and either the field or the conductor moves, an emf (voltage) is induced in the conductor. This effect is called electromagnetic induction. � A loop of wire rotating in a magnetic field produces a voltage which constantly changes in amplitude and direction. � The waveform produced is called a sine wave and is a graphical picture of alternating current (ac). One complete revolution (360°) of the conductor produces one cycle of ac. � The cycle is composed of two alternations: a positive alternation and a negative alternation. One cycle of ac in one second is equal to 1 hertz (1 Hz). BHAB 11

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Basic Single Coil AC Generator BHAB 14

AC GENERATOR: - The AC generator has slip rings that pick up the induces voltage through a complete relation cycle. - The induced voltage is related to the number of lines f flux cut. - When the loop in moving parallel with the lines of flux, no voltage is induced. - When the loop in moving perpendicular to the lines of flux, the maximum voltage is induced. BHAB 15

MULTI POLE AC GENERATOR: - By increasing the number of poles, the number of cycle per revolution can be increased. BHAB 16

1. 2. 3 DEVELOP AN EQUATION OF A SINUSOIDAL WAVEFORM, e = Em sin ( ωt + θ ) � Em = is the peak voltage @ current. (unit: volt @ A). � ω = is the angular frequency (unit: radians per second; rads) � The angular frequency is related to the physical frequency, (unit = hertz), which represents the number of cycles per second , by the equation. � t = is the time (unit: second). � θ = the phase, specifies where in its cycle the oscillation begin at t= 0. BHAB 17

Basic trigonometry: BHAB 18

Sinusoidal equation: θ BHAB 19

1. 3 UNDERSTAND A SINUSOIDAL VOLTAGE AND CURRENT VALUES 1. 3. 1 DEFINE FREQUENCY, PERIOD, PEAK VALUE OR AMPLITUDE AND THEIR RELATIONS. FREQUENCY: - Frequency ( f ) is the number of cycles that a sine wave completes in one second. - Frequency is measured in hertz (Hz). - The more cycles completed in 1 sec, the higher the frequency. - Relationship between frequency (f) & period (T) is f = 1/T 1. 0 s If 3 cycles of a wave occur in one second, the frequency is 3. 0 Hz BHAB 20

- The period and frequency are reciprocals of each other. AND - Thus, if you know one, you can easily find the other. If the period is 50 ms, the frequency is 0. 02 MHz = 20 k. Hz. BHAB 21

PERIOD: - The time required for a sine wave to complete 1 full cycle is called a period (T). - A cycle consists of 1 complete +ve and 1 complete –ve alternation. - The period of sine wave can be measured between any 2 corresponding points on the waveform. AMPLITUDE@ PEAK VALUE (Vp/Ip): - The amplitude is the maximum value of a voltage or current. - The amplitude of a sine wave is only measured from the center to the maximum point. The amplitude (A) of this sine wave 20 is V A The period is 50. 0 ms T BHAB 22

PEAK TO PEAK VALUE: - The voltage @ current from the +ve and –ve peak. - The peak to peak values are represented as Vpp @ Ipp. - Where: Vpp = 2 Vp @ Ipp = 2 Ip VPP BHAB 23

1. 3. 2 DATERMINE THE VARIOUS VOLTAGE AND CURRENT VALUES OF A SINE WAVE a. b. - - INSTANTANEOUS VALUE AT ANY POINT: The instantaneous values of a sine wave voltage @ current are different at any different point along the curve, having +ve and –ve value. Represent as: v @ I RMS VALUE: The rms ( root mean square ) value @ effective value of a sinusoidal voltage is equal to the dc voltage that produces the same amount of heat in a resistance as does the sinusoidal voltage. V rms = 0. 707 Vp NOTE: I rms = 0. 707 Ip 0. 707 = 1_ √ 2 BHAB 24

c. - AVERAGE VALUE: By definition, the average value is as 0. 637 times the peak value The average value is the total area under the half cycle curve divided by the distance in radians of the curve along the horizontal axis. Vavg = 0. 637 Vp @ 2/π Vp Iavg = 0. 637 Ip @ 2/π Ip The peak voltage of this waveform is 20 V. The rms voltage is VP Vavg Vrms 14. 1 V. The average value for the sinusoidal voltage is 12. 7 V. BHAB 25

d. - FORM FACTOR: Rms value _ Average value = 1. 11 e. - PEAK FACTOR: Peak value____ 0. 707 peak value @ BHAB maximum value rms value = 1. 414 26

1. 3. 3 CALCULATE MEAN VALUE, RMS VALUE AND PEAK FACTOR FOR A GIVEN WAVEFORM: EXAMPLE: Mean/ average value Rms value = = = 0. 637 Vp = 0. 637. 20 V = 12. 74 V = 0. 707 Vp = 0. 707. 20 V = 14. 14 V BHAB Peak factor = = Vp / rms value = 20 V / 14. 14 = 1. 414 27

SUMMARY FORMULA UNIT Frequency Hz Period Sec Amplitude Vp @ Ip Volt @ A 2 x Vp @ 2 x Ip Volt @ A RMS value 0. 707 x Vp @ 0. 707 x Ip Volt @ A Average value 0. 637 x Vp @ 0. 637 x Ip Volt @ A Peak to Peak value Form Factor RMS value__ Average value = 1. 11 - Peak Factor Peak value__ RMS value = 1. 414 - BHAB 28

1. 4 UNDERSTAND ANGULAR MEASUREMENT OF A SINE WAVE 1. 4. 1 SHOW TO MEASURE A SINE WAVE IN TERMS OF ANGLES - Angular measurements can be made in degrees (o) or radians. BHAB 29

1. 4. 1 SHOW TO MEASURE A SINE WAVE IN TERMS OF ANGLES • As angle A increases, the values of the trigonometric functions of A undergo a periodic cycle from 0, to a maximum of 1, down to a minimum of -1, and back to 0. • There are several ways to express the measure of the angle A. One way is in degrees, where 360 degrees defines a complete circle. • Another way to measure angles is in a unit called the radian, where 2π radians defines a complete circle. BHAB 30

- If we now plot the sine of the angle measured in radians along the Cartesian coordinate system, we see that we again get the characteristic rise and fall. - If you look closely at this graph you will see that the wave crosses the x-axis at multiples of 3. 1416… – the value of pi. One full wave is completed at the value 6. 2832…, or 2π, exactly the circumference of the unit circle. BHAB 31

1. 4. 2 DEFINE RADIAN - The Radian, (rad) is defined mathematically as a quadrant of a circle where the distance subtended on the circumference equals the radius (r) of the circle. - There are 360 o or 2 radians in one complete revolution. - Since the circumference of a circle is equal to 2π x radius, so 1 radian = 360 o/2π = 57. 3 o. - Radian = the standard unit of angular measurement. BHAB 32

1. 4. 3 CONVERT RADIANS TO DEGREE - Because there are 2 radians in one complete revolution and 360 o in a revolution, the conversion between radians and degrees is easy to write. - To find the number of radians, given the number of degrees: - To find the number of degrees, given the radians: BHAB 33

1. 4. 4 DETERMINE THE PHASE ANGLE OF A SINE WAVE Phase shift: - The phase of a sine wave is an angular measurement that specifies the position of a sine wave relative to a reference. - To show that a sine wave is shifted to the left or right of this reference, a term is added to the equation given previously. Where, θ = phase shift BHAB 34

Example of a wave that lags the reference: …and the equation has a negative phase shift v = 30 V sin ( t - 45 o) Notice that a lagging sine wave is below the axis at 0 o BHAB 35

Example of a wave that leads the reference: Notice that a leading sine wave is above the axis at 0 o v = 30 V sin ( t + 45 o) …and the equation has a positive phase shift BHAB 36

1. 5 UNDERSTAND A PHASOR TO REPRESENT A SINE WAVE 1. 5. 1 DEFINE PHASOR - A phasor is a straight line drawn in such a way that its length is related to the amplitude of the sine wave represented, and its angular position relative to other phasors is related to the phase difference between the quantities. - Phase denotes the particular point in the cycle of a waveform, measured as an angle in degrees. BHAB 37

1. 5. 2 EXPLAIN HOW PHASORS ARE RELATED TO THE SINE WAVE FORMULA - The sine wave can be represented as the projection of a vector rotating at a constant rate. This rotating vector is called a phasor. - The phasor represented by the arrow is rotating in an anticlockwise direction about the centre origin point, describing the sine wave as it rotates. - Phasors allow AC calculations to use basic trigonometry. The sine function in trigonometry is the ratio of the opposite side of a right triangle to the adjacent side. BHAB 38

1. 5. 3 DRAW A PHASOR DIAGRAM Phasor Diagram a. At any point in time, the length of the red dotted line represents the instantaneous value of the wave. b. The length of the phasor represents the amplitude of the wave. c. The angle of the phasor gives the phase of the waveform. d. Increments in phasor angle in the circular diagram are equivalent to time or angle increments along the horizontal axis of the waveform diagram. e. So with this addition of angular information, the phasor gives a relatively simple way to show the complex relationships that exist between sine waves in an ac circuit. BHAB 39

- The position of a phasor at any instant can be expressed as a positive angle, measured counterclockwise from 0 or as a negative angle equal to - 360. positive angle of negative angle of - 360 phasor BHAB 40

1. 5. 4 DISCUSS ANGULAR VELOCITY - When a phasor rotates through 360 or 2 radians, one complete cycle (since 1 revolution = 360°) - In 1 second, phasor will rotate through f revolutions @ through f x 360° - In calculation, it is more common to use angular unit RADIAN (rad) where 360° = 2π rads. - The phasor therefore rotate through 2π f radians per second. - The velocity of rotation is called the angular velocity ( ). = 2 f (Note that this angular velocity is expressed in radians per second. ) BHAB 41

1. 6 UNDERSTAND THE BASIC CIRCUIT LAWS TO RESISTIVE AC CIRCUIT 1. 6. 1 APPLY OHM’S LAW TO RESISTIVE CIRCUITS WITH AC SOURCES - The voltage V across a resistor is proportional to the current I travelling through it. - This is true at all times: V = RI. ohm law BHAB 42

1. 6 UNDERSTAND THE BASIC CIRCUIT LAWS TO RESISTIVE AC CIRCUIT 1. 6. 1 APPLY OHM’S LAW TO RESISTIVE CIRCUITS WITH AC SOURCES - The voltage V across a resistor is proportional to the current I travelling through it. - This is true at all times: V = RI. ohm law BHAB 43

1. 6. 2 APPLY KIRCHHOFF’S VOLTAGE LAW AND CURRENT LAW TO RESISTIVE CIRCUITS WITH AC SOURCES � Kirchhoff's Voltage and Current Laws apply to all AC circuits as well as DC circuits. Kirchhoff's Current Law: - The sum of current into a junction equals the sum of current out of the junction. - i 2 + i 3 = i 1 + i 4 - The sum of all currents at a node must equal to zero. BHAB 44

1. 6. 2 APPLY KIRCHHOFF’S VOLTAGE LAW AND CURRENT LAW TO RESISTIVE CIRCUITS WITH AC SOURCES Kirchhoff's Voltage Law: - The algebraic sum of the voltage (potential) differences in any loop must equal zero. - Example: V 1 + V 2 – Vs = 0 BHAB 45

1. 6. 3 DETERMINE POWER IN RESISTIVE AC CIRCUITS - In a direct current circuit the power is equal to the voltage times the current, or P = E X I. - The TRUE POWER depends upon the phase angle between the current and voltage. - True power of a circuit is the power actually used in the circuit. - Measured in watts. BHAB 46

1. 6. 3 DETERMINE POWER IN RESISTIVE AC CIRCUITS - Note that the waveform for power is always positive, never negative for this resistive circuit. - This means that power is always being dissipated by the resistive load, and never returned to the source as it is with reactive loads. BHAB 47

Example: • In this example, the current to the load would be 2 amps. • The power dissipated at the load would be 240 watts. • Because this load is purely resistive (no reactance), the current is in phase with the voltage, and calculations look similar to that in an equivalent DC circuit. BHAB 48

Example: Calculate the current and power consumed in a single phase 240 V AC circuit by a heating element which has an impedance of 60 Ohms. Also draw the corresponding phasor diagram. � The Active power consumed by the AC resistance is calculated as: � The corresponding phasor diagram is given as: BHAB 49

Example: � A sinusoidal voltage supply defined as: V(t) = 100 x cos(ωt + 30 o) is connected to a pure resistance of 50 Ohms. Determine its impedance and the value of the current flowing through the circuit. Draw the corresponding phasor diagram. Converting this voltage from the time-domain expression into the phasor-domain expression gives us: Applying Ohms Law gives us: The corresponding phasor diagram will be BHAB 50

1. 7 USE AN OSCILLOSCOPE TO MEASURE WAVEFORMS 1. 7. 1 IDENTIFYCOMMON OSCILLOSCOPE CONTROLS BHAB 51

- The oscilloscope is divided into four main sections. BHAB 52

Trigger BHAB 53

Horizontal BHAB 54

Vertical BHAB 55

Display BHAB 56

QUIZ 1. In North America, the frequency of ac utility voltage is 60 Hz. The period is a. 8. 3 ms b. 16. 7 ms c. 60 ms d. 60 s BHAB 57

2. The amplitude of a sine wave is measured. . a. at the maximum point b. between the minimum and maximum points c. at the midpoint d. anywhere on the wave BHAB 58

3. Which property of a sine wave does the length of a phasor represent? a. Frequency b. Phase c. Amplitude d. Instantaneous value BHAB 59

4. In the equation v = Vp sin ωt ± q , the letter v stands for the a. peak value b. average value c. rms value d. instantaneous value BHAB 60

V 1 5. Give the suitable sinusoidal equation for waveform V 1 above a. V 1 = 30 sin ωt b. V 1 = 30 sin ωt + 45° c. V 1 = 30 sin ωt - 45° d. V 1 = 30 sin ωt ± 45° BHAB 61

6. The number of radians in 90 o is a. /2 b. c. 2 /3 d. 2 BHAB 62

7. For the waveform shown, the same power would be delivered to a load with a dc voltage of a. 21. 2 V b. 37. 8 V c. 42. 4 V d. 60. 0 V BHAB 63

8. A control on the oscilloscope that is used to set the desired number of cycles of a wave on the display is a. volts per division control b. time per division control c. trigger level control d. horizontal position control BHAB 64