Lecture 3 Alternating Current Basics & Single-Phase AC Generator PDF

Lecture 3: Alternating current basics and single-phase AC generator Electrical or electronics circuit elements There are two types of elements within an electrical or electronics circuit: 1. Active elements. An active element is one that is capable of continuously supplyi...

Lecture 3: Alternating current basics and single-phase AC generator Electrical or electronics circuit elements There are two types of elements within an electrical or electronics circuit: 1. Active elements. An active element is one that is capable of continuously supplying energy to a circuit, such as a battery, a generator, an operational amplifier, etc. 2. Passive Elements. A passive element on the other hand are physical elements such as resistors, capacitors, inductors, etc., which cannot generate electrical energy by themselves but only consume it. Electrical Sources Source is a device that supplies electrical power to a circuit in the form of a voltage source or a current source. The objective of a power supply is to power the load with the proper voltage and current. The power at the input and output can be either alternating current (AC) or direct current (DC): 1. Alternating current (AC) occurs when the electric current periodically inverts its direction. AC is the method used to deliver electricity through power transmission lines to homes and businesses. 2. Direct current (DC) occurs when the current flows in one constant direction. It usually comes from batteries, solar cells, or from AC/DC converters. DC is the preferred type of power for electronic devices. Therefore, if AC is the type of power delivered to your house and DC is the type of power you need to charge your phone, you are going to need an AC/DC power supply in order to convert the AC voltage coming in from the power grid to the DC voltage needed to charge your mobile phone’s battery. Electric Generator A generator is a mechanical device that converts mechanical energy into electrical energy. The electricity generated at various power plants is produced by the generators installed there. When a coil spins in a magnetic field or moves relative to a magnet, it generates an electromotive force (emf) or potential difference. The emf is caused by a phenomenon known as electromagnetic induction. Faraday’s Laws of Electromagnetic Induction H.C. Oersted scientist was a Danish physicist and chemist, in 1820, discovered electromagnetism and demonstrated that electric currents produce a magnetic field. Faraday noted this and in 1821, predict that If electricity could produce magnetism, why couldn't magnetism produce electricity. By 1831, he was able to prove this and through his experiment was able to explain that these magnetic fields were lines of force. These lines of force would cause a current to flow in a coil of wire, when the coil is rotated between the poles of a magnet. This action then shows that the coils of wire being cut by lines of magnetic force, in some strange way, produces electricity. These experiments convincingly demonstrated the discovery of electromagnetic induction in the production of electric current, by a change in magnetic intensity. Faraday’s law of electromagnetic induction, also known as Faraday’s law, is the basic law of electromagnetism which helps us predict how a magnetic field would interact with an electric circuit to produce an electromotive force (EMF). Their core principle is that electricity can create magnetism, and, conversely, magnetism can generate electricity. The electromagnetic induction, is the fundamental operating principle of transformers, inductors, solenoids, electric motors and generators. Faraday’s first law Faraday’s first law of electromagnetic induction states that “Whenever a conductor is placed in a varying magnetic field, an electromotive force is induced. If the conductor circuit is closed, a current is induced, which is called induced current.” Faraday’s Second Law Faraday’s second law of electromagnetic induction states that “the magnitude of induced EMF in a coil is directly proportional to the rate of change of flux linking to 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. The equation for calculating the emf is: EMF = − (number of coils x change in flux linkage) ÷ change in time Where, E = Induced EMF, N = the number of turns of coil, dΦ = Change in flux linkage, dt = Change in time. Magnetic flux is a quantity which signifies how much of a magnetic field passes perpendicularly through some area. For example, the amount of magnetic flux through a rotating coil will vary as the coil rotates in the magnetic field. It is a maximum when the magnetic field lines are perpendicular to the coil area. It is at a minimum when the magnetic field lines are parallel to the coil area. Magnetic flux is defined as the product of the magnetic flux density and the cross-sectional area perpendicular to the direction of the magnetic flux density. Magnetic flux is defined by the symbol Φ (greek letter ‘phi’). It is measured in units of Webers (Wb). Magnetic flux can be calculated using the equation: Φ = BA Where, Φ = magnetic flux (Wb), B = magnetic flux density (T) and A = cross-sectional area (m2). The magnetic flux is maximized when the magnetic field lines and the area through which they are passing through are perpendicular When magnetic flux is not completely perpendicular to area A, then the component of magnetic flux density B perpendicular to the area is taken. The equation then becomes: Φ = BA cos(θ) Where: θ = angle between magnetic field lines and the line perpendicular to the plane of the area (often called the normal line) (degrees) The magnetic flux increases as the angle between the field lines and the normal decreases. This means the magnetic flux is: Maximum = BA when cos(θ) =1 therefore θ = 0o. The magnetic field lines are perpendicular to the plane of the area Minimum = 0 when cos(θ) = 0 therefore θ = 90o. The magnetic fields lines are parallel to the plane of the area An E.M.F is induced in a circuit when the magnetic flux linkage changes with respect to time. This means an E.M.F is induced when there is: 1. A changing magnetic flux density B 2. A changing cross-sectional area A 3. A change in angle θ Magnetic Flux Linkage The magnetic flux linkage is a quantity commonly used for solenoids which are made of N turns of wire The flux linkage is defined as: The product of the magnetic flux and the number of turns of the coil It is calculated using the equation: Flux linkage = ΦN = BAN Where, Φ = magnetic flux (Wb), N = number of turns of the coil, B = magnetic flux density (T) and A = cross-sectional area (m2). The flux linkage ΦN has the units of Weber turns (Wb turns) How To Increase EMF Induced in a Coil Faraday’s experiments showed that the induced EMF depends on only a few factors. A) The induced EMF is directly proportional to the change in the magnetic flux (ΦB). 1. The magnetic flux (ΦB) can be altered by a change in the magnetic field strength (B). By changing the magnitude of the magnetic field within the coil, changing B will change the magnetic flux Φ. Increasing the magnetic field strength around the coil boosts the magnetic flux, thus enhancing the induced EMF. Theoretically, a stronger magnetic field means the coil intersects more lines of force, resulting in greater EMF. Increasing the magnetic flux density will increase the maximum E.M.F. (amplitude) and have no effect on the frequency. ΦB =B A cos θ 2. The magnetic flux (ΦB) can be altered by changing the area of the coil (A) within the magnetic field, changing the area A will also change the magnetic flux Φ. ΦB =B A cos θ 3. The magnetic flux (ΦB) can be altered by changing the angle between the direction of the magnetic field and the plane of the coil (θ). Since the coil is perpendicular to the magnetic field, the angle θ is 0 degrees. If we change the angle, it will affect the flux. ΦB =B A cos θ B) The induced EMF can be altered by increasing the speed of the relative motion between the coil and the magnet. EMF is greatest when the relative speed between the coil and magnet is increased from its previous value, so, the change in time Δt is smallest—that is, EMF is inversely proportional to Δt. The induced emf is increased when run the wires through the gap at a faster velocity (the coil will cut the lines of flux at a faster rate). Increasing the speed of rotation will increase the frequency and the maximum E.M.F. (amplitude). C) The induced EMF can be altered by increasing the number of turns in the coil. it is easily seen that from the formulae N (the number of turns of coil). If a coil has N turns, an EMF will be produced that is N times greater than for a single coil, so that EMF is directly proportional to N. Lenz's law states that the direction of the electric current induced in a conductor by a changing magnetic field is such that the magnetic field created by the induced current opposes changes in flux of the initial magnetic field. It is named after physicist Heinrich Lenz, who formulated it in 1834. It is a qualitative law that specifies the direction of induced current, but states nothing about its magnitude. Lenz's law is contained in the rigorous treatment of Faraday’s law of induction (the magnitude of EMF induced in a coil is proportional to the rate of change of the magnetic flux), where it finds expression by the negative sign: 𝑑 𝚽𝐁 𝐸 = −𝑁 𝑑𝑡 which indicates that the induced electromotive force (E) and the rate of change in magnetic flux (d ΦB) have opposite signs. Magnetic field due to a straight wire Magnetic fields are formed wherever a current flows, such as in straight wires. The magnetic field lines around a straight wire are made up of concentric circles centered on the wire. A circular field pattern indicates that the magnetic field around a current-carrying wire has no poles. The right-hand grip rule can be used to work out the direction of the magnetic field. Right-hand grip rule 1: The rule states that if a straight conductor carrying current is held in the right hand such that the thumb is pointed in the direction of the current, then the direction in which your fingers encircle the wire gives the direction of the magnetic lines of force around the wire. This rule is also known as the right-hand thumb rule. The direction of the field around a current-carrying wire can be determined using the right- hand grip rule The field lines are clockwise or anticlockwise around the wire, depending on the direction of the current. Reversing the current reverses the direction of the field. The direction of the magnetic field can be determined using the right-hand grip rule. This is determined by pointing the right-hand thumb in the direction of the current in the wire and curling the fingers onto the palm. The direction of the curled fingers represents the direction of the magnetic field lines around the wire. For example, if the current is travelling vertically upwards, the magnetic field lines will be directed anticlockwise, as seen from directly above the wire. Note: the direction of the current is taken to be the conventional current i.e. from positive to negative, not the direction of electron flow. Explanation of Lenz’s Law Lenz’s law can be understood with the help of the diagrams where an insulated coil and a static and solid bar magnet. It clearly shows that when the magnet bar (in movement) is near to the coil, it cuts or links to the large portion of flux whereas, the rate of flux linkage is less in case when magnet bar moves away from the coil. Let’s see how it works When both the bar magnet and coil are in static position, no current flowing or induced EMF. Opposition to flux change 𝑬𝒙𝒂𝒎𝒑𝒍𝒆 𝒂: Bar magnet approaches the loop with the north pole facing the loop As the bar magnet approaches the loop, the magnetic field ⃗⃗⃗ 𝐵 points towards the left and its magnitude increase with time at the location of the loop. Thus, the magnitude of the loop magnetic flux 𝜱𝑩 also increases. The induced current flow in the counterclockwise (CCW) direction, so ⃗ 𝑖 opposes the magnetic field 𝐵 that the induced magnetic field 𝐵 ⃗⃗⃗.  ⃗ 𝑛𝑒𝑡 = 𝐵 Then the net field 𝐵 ⃗ −𝐵 ⃗ 𝑖. The induced current is thus trying to prevent flux 𝜱𝑩 from increasing. remember that it was the increase 𝜱𝑩 that is generated the induced current in the first place. 𝑬𝒙𝒂𝒎𝒑𝒍𝒆 𝒃: Bar magnet moves away from the loop with north pole facing the loop. As the bar magnet moves away from the loop, the magnetic field 𝐵 ⃗⃗⃗ points towards the left and its magnitude decreases with time at the location of the loop. Thus, the magnitude of the loop magnetic flux 𝜱𝑩 also decreases. The induced current flow in the clockwise (CW) direction so ⃗ 𝑖 adds to the magnetic field 𝐵 that the induced magnetic field 𝐵 ⃗⃗⃗. ⃗ 𝑛𝑒𝑡 = 𝐵 The net field 𝐵 ⃗ +𝐵 ⃗ 𝑖. The induced current is thus trying to prevent 𝜱𝑩 from decreasing. remember that it was decreased in 𝜱𝑩 that generated the induced current in the first place 𝑬𝒙𝒂𝒎𝒑𝒍𝒆 𝒄: Bar magnet approaches the loop with south pole facing the loop. As the bar magnet approaches the loop, the magnetic field ⃗⃗⃗ 𝐵 points towards the right and its magnitude increases with time at the location of the loop. Thus, the magnitude of the loop magnetic flux 𝜱𝑩 also increases. the induced current slow in the clockwise (CW) direction so ⃗ 𝑖 oppose the magnetic field 𝐵 that the induced magnetic field 𝐵 ⃗⃗⃗. ⃗ 𝑛𝑒𝑡 = 𝐵 The net field 𝐵 ⃗ −𝐵 ⃗ 𝑖. The induced current is thus trying to prevent 𝜱𝑩 from increasing. Remember that it was the increase in 𝜱𝑩 that generated the induced current in the first place.  𝑬𝒙𝒂𝒎𝒑𝒍𝒆 𝒅: Bar magnet moves away from the loop with south pole facing the loop. As the bar magnet moves away from the loop, the magnetic field ⃗⃗⃗𝐵 points towards the right and its magnitude decreases with time adds the location of the loop. Thus, the magnitude of the loop magnetic flux 𝜱𝑩 also decreases. The induced current flow in the counterclockwise (CCW) direction so that the induced magnetic field ⃗𝑩 ⃗ 𝒊 adds to the magnetic field ⃗⃗⃗ 𝐵. ⃗⃗ 𝒏𝒆𝒕 = 𝑩 The net field 𝑩 ⃗⃗ + 𝑩 ⃗⃗ 𝒊. the induced current is thus trying to prevent 𝜱𝑩 from decreasing. remember that it was the decrease 𝜱𝑩 that generated in the induced current in the first place. The E.M.F and flux linkage are 90° out of phase Fleming’s Right Hand Rule It may be used to identify the direction of the induced current produced in the coil: “Stretch the thumb, first finger, and center finger of your right hand such that they are perpendicular to each other. The first finger points in the direction of the magnetic field, the thumb in the direction of conductor velocity, and the middle finger in the direction of induced current.” The coil of the electric generator is spun in a magnetic field to generate induced current. The resultant induced current fluctuates in amplitude and direction at a rate of thousands of times per second. Alternating current is the name given to this sort of energy (AC). AC Generator (Alternators) An AC single phase generator is an electric generator that uses mechanical energy to create into alternating form of electric energy. Mechanical energy is supplied to the AC Generator through steam turbines, gas turbines, falling water and combustion engines. Principle of AC Generator Following Faraday’s laws, It works on the principle of electromagnetic induction, the generator produces voltage when an armature comprising winding coils over a metal core rotates in a magnetic field produced by two magnets or between the poles of a horseshoe-type magnet. Alternating electrical power in the form of alternating voltage and current is the output. AC generators function on Faraday’s law of electromagnetic induction states that electromotive force (EMF or voltage) is created in a current-carrying wire that cuts a uniform magnetic field. Rotating a conducting coil in a static magnetic field or rotating the magnetic field enclosing the stationary conductor can both be used to accomplish this. Because it is easier to extract induced alternating current from a stationary armature coil than from a revolving coil. The EMF generated is determined by the number of armature coil turns, magnetic field intensity, and rotating field speed. Construction: It consists of the following main ports 1) Field Magnet: it is a strong horseshoe-type permanent magnet with concave poles.  2) Armature: This generator produces voltage in one single wave. 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. This component largely comprises of wire coils large enough to handle the generator’s full-load current. ABCD is a rectangular armature coil. It consists of a large number of turns of insulated copper wire wound on a soft iron cylindrical core. The coil is mounted on a rotor shaft. 3) Rotor- The rotor is the rotating component of the generator. The axle is rotated by an external force (Mechanical energy). The rotor is driven by the generator’s prime mover. It can be rotated about an axis perpendicular to the magnetic field of the field magnet. 4) Prime Mover- The prime mover is the component that drives the axle of the AC generator. It is an external force (Mechanical energy) such as steam turbines, gas turbines, falling water, combustion engines or a motor might all be used as the prime mover. 5) Slip Rings- Slip rings are electrical connectors that transport electricity from and to an AC generator’s rotor. They are primarily used to transfer electricity from a fixed device to a revolving one. There are two brass rings, S1 and S2 rigidly connected to the two ends of the armature coil. As the coil rotates, slip rings also rotate about the same axis of rotation. The brushes are in constant electrical contact with the slip rings. 6) Brushes: there are two graphite rods B1 and B2 which are kept pressed against the slip rings S1 and S2. Through these brushes, the current induced in the armature coil is sent to the external circuit. Working of an AC Generator The flux linkage of the armature varies continually as it revolves between the poles of the magnet on an axis perpendicular to the magnetic field. As shown in figure, suppose the armature coil ABCD is in the horizontal position. Now the coil is rotated clockwise. The coil cut the magnetic lines of force. The arm AB moves upwards while the arm CD moves downwards. According to Fleming’s right hand rule the induced current flow from A to B in arm AB and C to D in arm CD. i.e: the induced current flows along ABCD. The induced current flows in the circuit through brush B2 to B1. After half the rotation of the armature, the arm CD moves upwards, and AB moves downwards. The induced current now flows in the reverse direction. i.e. along DCBA. The current flows from B1 to B2. Thus, the direction of current in the external circuit changes after every half rotation such a current which changes its direction after equal intervals of time is called alternating current. This device is called AC generators. Fleming’s Right-Hand Rule can be used to determine the direction of the induced current.