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ECE 201 Electrical Networks I module 1-module 5 summary
notes (Basic Electrical Engineering) Arizona State University
SYLLABUS
Module – 1 1a. D.C.Circuits: Ohm‟s Law and Kirchhoff‟s Laws, analysis of series, parallel and series- parallel circuits excited by independent voltage sources. Power and Energy. Illustrative examples. 1b. Electromagnetism : Review of field around a conductor, coil, magnetic flux and flux density, magneto motive force and magnetic field intensity, reluctance and permeability, definition of magnetic circuit and basic analogy between electric and magnetic circuits. 5 Hours Electromagnetic induction : Definition of Electromagnetic Induction, Faradays Laws, Fleming‟s right hand rule, Lenz‟s Law, Statically and dynamically induced emf. Concept of self- inductance, mutual inductance and coefficient of coupling. Energy stored in magnetic field. Illustrative examples. Force on current carrying conductor placed in a magnetic field, Fleming‟s left hand rule. 5 Hours Module – 2 2a. D.C.Machines: Working principle of D.C.Machine as a generator and a motor. Types and constructional features. Types of armature windings, Emf equation of generator, relation between induced emf and terminal voltage with an enumeration of brush contact drop and drop due to armature reaction. Illustrative examples, neglecting armature reaction. Operation of D.C. motor, back emf and its significance, torque equation. Types of D.C. motors, characteristics and applications. Necessity of a starter for D.C. motor. Illustrative examples on back emf and torque. 7 Hours 2b. Measuring Instruments : Construction and Principle of operation of dynamometer type wattmeter and single phase induction type energy meter. 3 Hours
Module – 3 3a.Single-phase A.C. Circuits : Generation of sinusoidal voltage, frequency of generated voltage, definition and numerical values of average value, root mean square value, form factor and peak factor of sinusoidally varying voltage and current, phasor representation of alternating quantities. Analysis, with phasor diagrams, of R, L, C, R-L, R-C and R-L-C circuits and, parallel and series- parallel circuits. Real power, reactive power, apparent power and power factor. Illustrative examples. 7 Hours 3b. Domestic Wiring: Service mains, meter board and distribution board. Brief discussion on concealed conduit wiring. Two-way and three-way control. Elementary discussion on Circuit protective devices: fuse and Miniature Circuit Breaker (MCB‟s). Electric shock, precautions against shock–Earthing, Earth leakage circuit breaker (ELCB) and Residual current circuit breaker (RCCB). 3 Hours Module – 4 4a. Three Phase Circuits : Necessity and advantages of three phase systems, generation of three phase power. Definition of Phase sequence, balanced supply and balanced load. Relationship between line and phase values of balanced star and delta connections. Power in balanced three- phase circuits, measurement of power by two-wattmeter method. Determination power factor using wattmeter readings. Illustrative examples. 6 Hours 4b. Three Phase Synchronous Generators : Principle of operation, Types and constructional features, Advantages of rotating field type alternator, Synchronous speed, Frequency of generated voltage,Emf equation. Concept of winding factor (excluding the derivation of distribution and pitch factors). Illustrative examples on emf equation. 4 Hours Module – 5 5a. Single Phase Transformers: Necessity of transformer, Principle of operation and construction of single-phase transformers (core and shell types). Emf equation, losses, variation losses with respect to load, efficiency, Condition for maximum efficiency, Voltage regulation and its significance (Open Circuit and Short circuit tests, equivalent circuit and phasor diagrams are excluded). Illustrative problems on emf equation and efficiency only. 6 Hours
CONTENTS
Sl. No
TOPICS PAGE NO.
Module-1: 1a) DC Circuits 1b) Electromagnetism
Module-2: 2 a) D.C.Machines 2 b) Measuring Instruments
Module- 3 3a) Single-phase A.C. Circuits 3 b) Domestic Wiring
Module- 4 4 a) Three Phase Circuits 4 b) Three Phase Synchronous Generators
Module- 5 5 a) Single Phase Transformers 5 b) Three Phase Induction Motors
MODULE –
1. D. C. Circuits
Ohm‟s Law : the current flowing through the electric the electric circuit is directly proportional to the potential difference across the circuit and inversely proportional to the resistance of the circuit, provided the temperature remains constant. The limitations of the Ohm‟s law are,
- It is not applicable to the nonlinear devices such as diodes, zener diodes, voltage regulators ect.
- It does not hold good for non-metallic conductors such as silicon carbide. The law for such conductors is given by, V = K Im^ where k, m are constants. ( I ) Current is what flows on a wire or conductor like water flowing down a river. Current flows from negative to positive on the surface of a conductor. Current is measured in (A) amperes or amps. ( E ) Voltage Ohm's Law defines the relationships between (P) power, (E) voltage, (I) current, and (R) resistance. One ohm is the resistance value through which one volt will maintain a current of one ampere is the difference in electrical potential between two points in a circuit. It's the push or pressure behind current flow through a circuit, and is measured in (V) volts. ( R ) Resistance determines how much current will flow through a component. Resistors are used to control voltage and current levels. A very high resistance allows a small amount of current to flow. A very low resistance allows a large amount of current to flow. Resistance is measured in ohms.
at junction point = 0 StateandexplainKirchhoff’slaws. Kirchhoff‟s current law: The law can be stated as, The total current flowing towards a junction point is equal to the total current flowing y from that junction point. The word algebraic means considering the signs of various currents. Sign convention : Currents flowing towards a junction point are assumed to be positive whie currents flowing away from a junction point assumed to be negative. e.g. Refer to Fig. 1, currents I 1 and I 2 are positive while I 3 and I 4 are negative. Applying KCL, at junction 0 = 0 I 1 + I 2 - I 3 - I 4 = 0 i.e. I 1 + I 2 = I 3 + I 4 The law is very helpful in network simplification.
Around a closed path= 0 Kirchhoff’svoltagelaw: “In any network, the algebraic sum of the voltage drops across the circuit elements of any closed path (or loop or mesh) is equal to the algebraic sum of the e.m.f s in the path” In other words, “the algebraic sum of all the branch voltages, around any closed path or closed loop is always zero.” The law states that if one starts at a certain point of a closed path and goes on tracing and noting all the potential changes (either drops or rises), in any one particular direction, till the starting point reached again, he must be at the same potential with which he started tracing a closed path. Sum of all the potential rises must be equal to sum of all the potential drops while tracing any closed path of the circuit. The total change in potential along a closed path is always zero. This law is very useful in loop analysis of the network. A circuit consists of two parallel resistors having resistance of 20 and 30 respectively connected in series with 15 .If current through 15 resistor is 3 A, Resistance Resistance is the property of a component which restricts the flow of electric current. Energy is used up as the voltage across the component drives the current through it and this energy appears as heat in the component.
Note that the combined resistance in parallel will always be less than any of the individual resistances. ( P ) Power is the amount of current times the voltage level at a given point measured in wattage or watts. electrical energy - energy made available by the flow of electric charge through a conductor; "they built a car that runs on electricity" measured in k Watt Hour Energy=VItKWhour Faraday’sLaws: 1 st^ law: Whenever magnetic flux linking with a coil changes with time an emf is induced in that coil or whenever a moving conductor cuts the magnetic flux, an emf is induced in the conductor. 2 nd^ law: The magnitude of the induced emf is equal to the product of the number of turns of the coil and the rate of change of flux linkage. Lenz’s law : It states that the direction of an induced emf produced by the electromagnetic induction is such that it sets up a current which always opposes the cause that is responsible for inducing the emf. In short the induced emf always opposes the cause producing it which is represented by negative sign, mathematically in its expression Consider a solenoid as shown in Fig.1. Let a bar magnet is moved towards coil such that N-pole of magnet is facing a coil which will circulate the current through the coil. According to Lenz‟s law, the direction of current due to induced emf is so as to oppose the cause. The cause is motion of bar magnet towards coil So emf will set up a current through coil in such a way that the end of solenoid facing bar magnet will become N-pole. Hence two like poles will face each other experiencing force of repulsion which is opposite to the motion of bar magnet as shown in the above
Fleming’srules:
- Fleming‟sRighthandrule: This rule helps in deciding the direction of the induced emf. Hold the right hand thumb, fore finger and the middle finger set at right angles to each other and the thumb points the direction of the motion of the conductor and the fore finger points the direction of the field and the middle finger points the direction of the induced emf.
- Fleming’sLefthandrule : This rule helps in deciding the direction of force acting on a conductor.
Dynamically induced e.m.f. The change in the flux linking with a coil, conductor or circuit can be brought about by its motion relative to magnetic field. This is possible by moving flux with respect to coil conductor or circuit or it is possible by moving conductor, coil, circuit with respect to stationary magnetic flux. Such an induced e.m.f. which is due to physical movement of coil, conductor with respect to flux or movement of magnet with respect with to stationary coil, conductor is called dynamically induced e.m.f. or motional induced e.m.f. This type of induced e.m.f. is available in the rotating machines such as alternators, generator etc. Self inductance : According to Lenz‟s law the direction of this induced e.m.f. will be so as to oppose the cause producing it. The cause is the current I hence self-induced e.m.f will try to set up a current which is in opposite direction to that of current I. When current is increased, self-induced e.m.f. reduces the current tries to keep to its original value. If current is decreased, self-induced e.m.f. increases the current and tries to maintain it back to its original value. So any change in current through coil is opposed by the coil. This property of the coil which opposes any change in the current passing through it is called self-inductance or only inductance. It is analogous to electrical inertia or electromagnetic inertia. The formula for self-inductance is given by, L = It can be defined as flux linkages per ampere current in it. Its unit is Henry (H) Expressions for coefficient of self-inductance (L): L = But = = ∴ L =
∴ L = henries Now s ∴
L =
L = = Henries Where l = length of magnetic circuit a = area of cross-section of magnetic circuit which flux is passing. Derive an Expression for energy stored in the inductor: Let the induced e.m.f. in a coil be, e = -L This opposes a supply voltage. So supply voltage „V‟ supplies energy to overcome this, which ultimately gets stored in the magnetic field. ∴ V = -e = - = L Power supplied = V × I = L × I Energy supplied in time dt is, E = power x time = L x I x dt = L di x I joules. This is energy supplied for a change in current of dI but actually current changes from zero to I. ∴ Integrating above total energy stored is, E = State i) Fleming’s right hand rule, and ii) Fleming’s left hand rule. And Mention their applications. Fleming’s right hand rule : The Fleming‟s left hand rule is used to get direction of force experienced by conductor carrying current placed in magnetic field while Fleming‟s right hand rule can be used to get direction of induced e.m.f. when conductor is moving at right angles to the magnetic field.
= Rate Applications: Fleming‟s right hand rule is used to get the direction of induced emf in case of generators and alternators while left hand rule is used to get the direction of torque induced in motors. Mutual inductance: Magnitude of mutually induced e.m.f Let N 1 = Number of turns of coil A N 2 = Number of turns of coil B I 1 = Current flowing through coil A ∅ 1 = Flux produced due to current I 1 in webers. ∅ 2 = Flux linking with coil B According to Faraday‟s law, the induced e.m.f. in coil B is, e2 = Negative sign indicates that this e.m.f will set up a current which will oppose the change of flux linking with it. Now ∅ 2 = If permeability of the surroundings is assumed constant then ∅ 2 ∝ I 1 and hence ∅∕I 1 is constant. ∴ Rate of change of of change of current I 1 ∴ ∴
∴ Here is called co efficient of mutual inductance dented by M Volts Coefficient of mutual inductance is defined as the property by which e.m.f gets induced in the second coil because of change in current through first coil. Coefficient of mutual inductance is defined as the property by which e.m.f gets induced in the second coil because of change in current through first coil. Coefficient of mutual inductance is also called mutual inductance. It is measured in Henries. Definitions of mutual inductance and its unit:
- The coefficient of mutual inductance is defined as the flux linkages of the coil per ampere current in other coil.
- It can also be defined as equal to e.m.f induced in volts in one coil when current in other coil changes uniformly are rate of one ampere per second. Similarly its unit is defined as follows:
- Two coils which are magnetically coupled are said to have mutual inductance of one hence when a current of one ampere flowing through one coil produces a flux linkage of one Weber turn in the other coil.
- Two coils which are magnetically coupled are said to have mutual inductance of one Henry when a current changing uniformly at the rate of one ampere per second in one coil, induces as e.m.f of one volts in the other coil. Expressions of the mutual inductance (M):
- ∅ 2 is the part of the flux ∅ 1 produced due to I 1. Let K 1 be the fraction of ∅ 1 which is linkage with coil B. ∴
K=
I 1 = current through first coil I 2 = current through by first coil 1 =^ flux^ produced by^ first^ coil 2 =^ flux^ produced by^ second^ coil M = and M = Multiplying the two expressions, M × M = × M 2 = K 1 K 2 But = L 1 = self-inductance of first coil And = L 2 = self-inductance of second coil M 2 = K 1 K 2 L 1 L 2 M = Let K = = coefficient of coupling M = K
MODULE –
2a. D.C.Machines: A machine which works on direct current is defined as a D.C.Machine. D.C.Machines are of two types. (i) D.C.Generator and (ii) D.C.Motor. Sl.No. D.C. Generator D.C.Motor 1 Definition: A generator is a rotating machine which converts mechanical energy into electrical energy Definition: A motor is a machine which converts electrical energy into mechanical energy 2 Principle: Whenever a coil is rotated in a magnetic field an e.m.f. will be induced in this coil and is given by e=BlvSinθ volts/coil side where, B=The flux density in Tesla, l=the active length of the coil side in meters, v=the velocity with which the coil is moved in meters/sec and θ is the angle between the direction of the flux and the direction of rotation of the coil side. Principle: Whenever a current coil is placed under a magnetic field the coil experiences a mechanical force, and is given by F= BIlSinθ Newtons/coil side. Where, I is the current through the coil in ampere. 3 The direction of the emf induced is fixed by applying the Fleming‟s right hand rule The direction of the force acting is fixed by applying the Fleming‟s left hand rule. Types and constructional features Salient parts of a D.C.machine are: Field system (poles) Coil arrangement (armature) Commutator Brushes Yoke
