Faradays law of EMI.pptx

faradays law

1. Faraday’s Laws of Electro-magnetic Induction, Magnetic Circuits, Self and Mutual Inductance, Generation of sinusoidal voltage, Instantaneous, Average and effective values of periodic functions, Phasor representation. Introduction to 3-phase systems, Introduction to electric grids.

2. Faradays law of Electro magnetic induction Faraday’s law of electromagnetic induction (referred to as Faraday’s law) is a basic law of electromagnetism predicting how a magnetic field will interact with an electric circuit to produce an electromotive force (EMF). This phenomenon is known as electromagnetic induction.

3. Faraday’s Experiment In this experiment, Faraday takes a magnet and a coil and connects a galvanometer across the coil. At starting, the magnet is at rest, so there is no deflection in the galvanometer i.e the needle of the galvanometer is at the center or zero position. When the magnet is moved towards the coil, the needle of the galvanometer deflects in one direction.

4. When the magnet is held stationary at that position, the needle of galvanometer returns to zero position. Now when the magnet moves away from the coil, there is some deflection in the needle but opposite direction, and again when the magnet becomes stationary, at that point respect to the coil, the needle of the galvanometer returns to the zero position. Similarly , if the magnet is held stationary and the coil moves away, and towards the magnet, the galvanometer similarly shows deflection. It is also seen that the faster the change in the magnetic field, the greater will be the induced EMF or voltage in the coil.

5. Deflection in Galvanometer

6. Faraday 1 st Law Any change in the magnetic field of a coil of wire will cause an emf to be induced in the coil. This emf induced is called induced emf and if the conductor circuit is closed, the current will also circulate through the circuit and this current is called induced current. Method to change the magnetic field: By moving a magnet towards or away from the coil By moving the coil into or out of the magnetic field By changing the area of a coil placed in the magnetic field By rotating the coil relative to the magnet

7. Faraday 2 nd Law It states that the magnitude of emf induced in the coil is equal to the rate of change of flux that linkages with the coil . The flux linkage of the coil is the product of the number of turns in the coil and flux associated with the coil . E = N(d ϕ / dt )

8. Faraday’s Law Consider, a magnet is approaching towards a coil. Here we consider two instants at time T 1 and time T 2 . Flux linkage with the coil at time, T1 = N ϕ 1 wb Flux linkage with the coil at time, T2 = N ϕ 2 wb Change in flux linkage, N ( ϕ 2 – ϕ 1) Let this change in flux linkage be, ϕ = ( ϕ 2 – ϕ 1) So, the Change in flux linkage N ϕ Now the rate of change of flux linkage N( ϕ /t) Take derivative on right-hand side we will get N(d ϕ / dt ) The rate of change of flux linkage E = N(d ϕ / dt ) By Len’s Law, E = - N(d ϕ / dt ) where Flux Φ in Wb = B.A B = magnetic field strength A = area of the coil

9. How To Increase EMF Induced in a Coil By increasing the number of turns in the coil i.e N, from the formulae derived above it is easily seen that if the number of turns in a coil is increased, the induced emf also gets increased. By increasing magnetic field strength i.e B surrounding the coil- Mathematically, if magnetic field increases, flux increases and if flux increases emf induced will also get increased. Theoretically, if the coil is passed through a stronger magnetic field, there will be more lines of force for the coil to cut and hence there will be more emf induced . By increasing the speed of the relative motion between the coil and the magnet – If the relative speed between the coil and magnet is increased from its previous value, the coil will cut the lines of flux at a faster rate, so more induced emf would be produced.

10. Application of Faraday’s law Electrical equipment works on the basis of Faraday’s law just like transformers. Induction cooker works on the basis of mutual induction. Furthermore,  this happens to be the principle of Faraday’s law. By inducing an electromotive force into an electromagnetic flowmeter, the recording of the velocity of the fluids can take place. Musical instruments like electric guitar and electric violin work on the basis of Faraday’s law. The basis of Maxwell’s equation is the converse of Faraday’s laws which states that change in the magnetic field would result in a change in the electric field.

11. Inductance Inductance is the tendency of an electrical conductor to oppose a change in the electric current flowing through it. L is used to represent the inductance, and Henry is the  SI unit of inductance . 1 Henry is defined as the amount of inductance required to produce an emf of 1 volt in a conductor when the current change in the conductor is at the rate of 1 Ampere per second . Types of Inductance Inductance is classified into two types as: Self Inductance Mutual Inductance

12. Self Inductance When there is a change in the current or magnetic flux of the coil, an  electromotive force  is induced. This phenomenon is termed Self Inductance. When the current starts flowing through the coil at any instant, it is found that, that the magnetic flux becomes directly proportional to the current passing through the circuit . The relation is given as : Where L is termed as the self-inductance of the coil or the coefficient of self-inductance, the self-inductance depends on the cross-sectional area, the permeability of the material, and the number of turns in the coil. The rate of change of magnetic flux in the coil is given as ,

13. Self Inductance Formula Where , L is the self inductance in Henries N is the number of turns Φ is the magnetic flux I is the current in amperes

14. Mutual Inductance Consider two coils: P – coil (Primary coil) and S – coil (Secondary coil). A battery and a key are connected to the P-coil, whereas a galvanometer is connected across the S-coil. When there is a change in the current or  magnetic flux  linked with the two coils, an opposing electromotive force is produced across each coil, and this phenomenon is termed Mutual Inductance. This phenomenon is given by the relation : Where M is termed as the mutual inductance of the two coils or the coefficient of the mutual inductance of the two coils. The rate of change of magnetic flux in the coil is given as ,

15. Mutual Inductance Formula Where , μ  is the permeability of free space μ r  is the relative permeability of the soft iron core N is the number of turns in coil A is the cross-sectional area in m 2 l is the length of the coil in m

16. Difference between Self and Mutual Inductance Self inductance Mutual inductance In self inductance, the change in the strength of current in the coil is opposed by the coil itself by inducing an e.m.f . In mutual inductance out of the two coils one coil opposes change in the strength of the current flowing in the other coil. The induced current opposes the growth of current in the coil when the main current in the coil increases. The induced current developed in the neighboring coil opposes the growth of current in the coil when the main current in the coil increases. The induced current opposes the decay of current in the coil when the main current in the coil decreases. The induced current developed in the neighboring coil opposes the decay of the current in the coil when the main current in the coil decreases.

17. Sinusoidal waveform 1.Amplitude: It is the maximum value attained by an alternating quantity. Also called as maximum or peak value. 2.Time Period (T): It is the Time Taken in seconds to complete one cycle of an alternating quantity. 3 . Instantaneous Value: It is the value of the quantity at any instant. 4 . Frequency (f): It is the number of cycles that occur in one second. The unit for frequency is Hz or cycles/ sec.The relationship between frequency and time period can be derived as follows. Time taken to complete f cycles = 1 second Time taken to complete 1 cycle = 1/f second T = 1/f

18. Generation of sinusoidal AC voltage Consider a rectangular coil of N turns placed in a uniform magnetic field as shown in the figure. The coil is rotating in the anticlockwise direction at an uniform angular velocity of rad/sec.

19. Generation of sinusoidal AC voltage When the coil is in the vertical position, the flux linking the coil is zero because the plane of the coil is parallel to the direction of the magnetic field. Hence at this position, the emf induced in the coil is zero. When the coil moves by some angle in the anticlockwise direction, there is a rate of change of flux linking the coil and hence an emf is induced in the coil. When the coil reaches the horizontal position, the flux linking the coil is maximum, and hence the emf induced is also maximum. When the coil further moves in the anticlockwise direction, the emf induced in the coil reduces. Next when the coil comes to the vertical position, the emf induced becomes zero . After that the same cycle repeats and the emf is induced in the opposite direction. When the coil completes one complete revolution, one cycle of AC voltage is generated. The generation of sinusoidal AC voltage can also be explained using mathematical equations. Consider a rectangular coil of N turns placed in a uniform magnetic field in the position shown in the figure. The maximum flux linking the coil is in the downward direction as shown in the figure. This flux can be divided into two components, one component acting along the plane of the coil Φmaxsinωt and another component acting perpendicular to the plane of the coil Φmaxcosωt

20. Generation of sinusoidal AC voltage The component of flux acting along the plane of the coil does not induce any flux in the coil. Only the component acting perpendicular to the plane of the coil i.e . Φ maxcos ω t induces an emf in the coil. Hence the emf induced in the coil is a sinusoidal emf . This will induce a sinusoidal current in the circuit given by ∅ = 𝜙𝑚𝑎𝑥𝑐𝑜𝑠𝜔𝑡 𝑒 = −𝑁 𝑑𝜙 𝑑𝑡 = −𝑁 (𝑑 /𝑑𝑡) 𝜙𝑚𝑎𝑥𝑐𝑜𝑠𝜔𝑡 = 𝑁𝜙𝑚𝑎𝑥𝜔𝑠𝑖𝑛𝜔𝑡 = 𝐸𝑚𝑠𝑖𝑛𝜔𝑡 Hence the emf induced in the coil is a sinusoidal emf . This will induce a sinusoidal current in the circuit given by 𝑖 = 𝐼𝑚𝑠𝑖𝑛𝜔t

21. Instantaneous, Average and effective values of periodic functions Angular Frequency (ɷ): Angular frequency is defined as the number of radians covered in one second( i.e the angle covered by the rotating coil). The unit of angular frequency is rad/sec. 𝜔 = 2 𝜋/𝑇 = 2 𝜋f 1) What will be the periodic time of a 50Hz waveform and 2. what is the frequency of an AC waveform that has a periodic time of 10mS.

22. Instantaneous, Average and effective values of periodic functions The sinusoidal waveform has a different magnitude of voltage or current at the different instants of the waveform. The magnitude of the current or voltage at a particular instant is called the instantaneous value of the waveform. The average of all the instantaneous values of an alternating voltage and current over one complete cycle is known as an  average value . Average value  =  2Vp/ π = 0.637 Vp   (maximum or peak value, Vpk ) RMS value   = Vp /  0.707  Vp (maximum or peak value, Vpk )  

23. Problem 1 The equation of alternating voltage is given by ν = 325.22 𝑠𝑖𝑛314𝑡. Find RMS value Frequency Average value.

24. Single Phase Vs Three Phase A single phase system consists of just two conductors (wires): one is called the phase (sometimes line, live or hot), through which the current flows and the other is called neutral, which acts as a return path to complete the circuit.

25. 3 Phase Waveform & Phasor Representation In a single-phase AC waveforms, a single multi-turn coil rotates within a magnetic field. But if three identical coils each with the same number of coil turns are placed at an electrical angle of 120 o  to each other on the same rotor shaft, a three-phase voltage supply would be generated. A balanced three-phase voltage supply consists of three individual sinusoidal voltages that are all equal in magnitude and frequency but are out-of-phase with each other by exactly 120 o  electrical degrees. One final point about a three-phase system. As the three individual sinusoidal voltages have a fixed relationship between each other of 120 o  they are said to be “balanced” therefore, in a set of balanced three phase voltages their phasor sum will always be zero as:   V a  +  V b  +  V c  = 0

26. Single Phase Vs Three Phase In a three – phase system, we have a minimum of three conductors or wires carrying AC voltages. It is more economical to transmit power using a 3 – phase power supply when compared to a single phase power supply as a three – phase supply can transmit three times the power with just three conductors when compared to a two – conductor single – phase power supply . Types of 3 Phase connection The three – phase electric power system can be arranged in two ways. They are: Star (also called Y or Wye) and Delta (Δ ). Star and Delta Connections are the two types of connections in a 3 – phase circuits. A Star Connection is a 4 – wire system and a Delta Connection is a 3 – wire system.

27. Star Connection In a Star Connection, the 3 phase wires are connected to a common point or star point and Neutral is taken from this common point. Due to its shape, the star connection is sometimes also called as Y or Wye connection. If only the three phase wires are used, then it is called 3 Phase 3 Wire system. If the Neutral point is also used (which often it is), the it is called 3 Phase 4 Wire system. The following image shows a typical Star Connection.

28. Delta Connection In a Delta Connection, there are only 3 wires for distribution and all the 3 wires are phases (no neutral in a Delta connection).

29. Comparison of Star vs Delta Connection Sl.No . Star Connection (Y or Wye) Delta Connection ( Δ) 1 A Star Connection is a 4 – wire connection (4th wire is optional in some cases) A Delta Connection is a 3 – wire connection. 2 Two types of Star Connection systems are possible: 4 – wire 3 – phase system and 3 – wire 3 phase system. In Delta Connection, only 3 – wire 3 phase system is possible. 3 Out of the 4 wires, 3 wires are the phases and 1 wire is the neutral (which is the common point of the 3 wires). All the 3 wires are phases in a Delta Connection. 4 In a Star Connection, one end of all the three wires are connected to a common point in the shape of Y, such that all the three open ends of the three wires form the three phases and the common point forms the neutral. In a Delta Connection, every wire is connected to two adjacent wires in the form of a triangle (Δ) and all the three common points of the connection form the three phases.

30. Comparison of Star vs Delta Connection Sl.No . Star Connection (Y or Wye) Delta Connection ( Δ) 5 The Common point of the Star Connection is called Neutral or Star Point. There is no neutral in Delta Connection 6 Line Voltage (voltage between any two phases) and Phase Voltage (voltage between any of the phase and neutral) is different. Line Voltage and Phase Voltage are same. 7 Line Voltage is root three times phase voltage i.e. VL = √3 VP. Here, VL is Line Voltage and VP is Phase Voltage. Line Voltage is equal to Phase Voltage i.e. VL = VP. 8 With a Star Connection, you can use two different voltages as VL and VP are different. For example, in a 230V/400V system, the voltage between any of the phase wire and neutral wire is 230V and the voltage between any two phases is 400V. In a Delta Connection, we get only a single voltage magnitude.

31. Comparison of Star vs Delta Connection Sl.No . Star Connection (Y or Wye) Delta Connection ( Δ) 9 Line Current and Phase Current are same. Line current is root three times the phase current. In Star Connection, IL = IP. Here, IL is line current and IP is phase current. In Delta connection, IL = √3 IP 10 Total three phase Power in a Star Connection can be calculated using the following formulae. P = 3 x VP x IP x Cos(Φ) or P = √3 x VL x IL x Cos(Φ) Total three phase Power in a Delta Connection can be calculated using the following formulae. P = 3 x VP x IP x Cos(Φ) or P = √3 x VL x IL x Cos(Φ) 11 Since Line Voltage and Phase Voltage are different (VL = √3 VP), the insulation required for each phase is less in a Star Connection. In a Delta Connection, the Line and Phase Voltages are same and hence, more insulation is required for individual phases. 12 Usually, Star Connection is used in both transmission and distribution networks (with either single phase supply or three – phase. Delta Connection is generally used in distribution networks. 13 Since insulation required is less, Star Connection can be used for long distances. Delta Connections are used for shorter distances. 14 Star Connections are often used in application which require less starting current Delta Connections are often used in applications which require high starting torque.

32. Delta to Star and Star to Delta Transformation

33. Phasor Representation Phasor Diagrams are a graphical way of representing the magnitude and directional relationship between two or more alternating quantities. Phasor Diagram and Phasor Representation of a Sinusoidal waveform

34. Phase difference of a Sinusoidal Waveform and its Phasor representation

35. Phasor addition of Phasor diagrams One good use of phasors is for the summing of sinusoids of the same frequency. Sometimes it is necessary when studying sinusoids to add together two alternating waveforms, for example in an AC series circuit, that are not in-phase with each other. If they are “in-phase” that is, there is no phase shift then they can be added together in the same way as DC values to find the algebraic sum of the two vectors. For example, if two voltages of say 50 volts and 25 volts respectively are together “in-phase”, they will add or sum together to form one voltage of 75 volts (50 + 25). If however, they are not in-phase that is, they do not have identical directions or starting point then the phase angle between them needs to be taken into account so they are added together using phasor diagrams to determine their  Resultant Phasor  or  Vector Sum  by using the  parallelogram law .

36. Phasor diagram Problem Consider two AC voltages, V 1  having a peak voltage of 20 volts, and V 2  having a peak voltage of 30 volts where V 1  leads V 2  by 60 o . The total voltage, V T  of the two voltages can be found by firstly drawing a phasor diagram representing the two vectors and then constructing a parallelogram in which two of the sides are the voltages, V 1  and  V 2 . In the rectangular form, the phasor is divided up into a real part, x and an imaginary part, y forming the generalised expression  Z = x ±  jy . Definition of Complex Sinusoid

37. Definition of Complex Sinusoid So the addition of two vectors,  A  and  B  using the previous generalized expression is as follows:

38. Phasor diagram Problem - Solution Voltage, V 2  of 30 volts points in the reference direction along the horizontal zero axis, then it has a horizontal component but no vertical component as follows. Horizontal Component = 30 cos 0 o  = 30 volts Vertical Component = 30 sin 0 o  = 0 volts This then gives us the rectangular expression for voltage V 2  of:  30 + j0 Voltage , V 1  of 20 volts leads voltage, V 2  by 60 o , then it has both horizontal and vertical components as follows. Horizontal Component = 20 cos 60 o  = 20 x 0.5 = 10 volts Vertical Component = 20 sin 60 o  = 20 x 0.866 = 17.32 volts This then gives us the rectangular expression for voltage V 1  of:  10 + j17.32

39. Computing Resultant Voltage VT The resultant voltage, V T  is found by adding together the horizontal and vertical components as follows. V Horizontal  = sum of real parts of V 1  and V 2  = 30 + 10 = 40 volts V Vertical  = sum of imaginary parts of V 1  and V 2  = 0 + 17.32 = 17.32 volts Now that both the real and imaginary values have been found the magnitude of voltage, V T  is determined by simply using  Pythagoras’s Theorem  for a 90 o  triangle as follows.

40. Computing Resultant value of VT using Phasor diagram

41. Phasor Subtraction of Phasor diagrams Phasor subtraction is very similar to the above rectangular method of addition, except this time the vector difference is the other diagonal of the parallelogram between the two voltages of V 1  and V 2  as shown. This time instead of “adding” together both the horizontal and vertical components we take them away, subtraction.

42. Introduction to Electricity Grid The electrical grid is the intricate system designed to provide electricity all the way from its generation to the customers that use it for their daily needs. These systems have grown from small local designs, to stretching thousands of kilometers and connecting millions of homes and businesses today. The grid consists of countless complex interconnections, however there are three main sections—electricity generation, transmission and distribution.

43. Electricity Grid Layout

44. References [1 ] https ://www.tutorialspoint.com/ [2] https:// www.electronics-tutorials.ws/accircuits/phasors.html [3] www.wikipedia.com [4] https ://energyeducation.ca/encyclopedia/Electrical_grid