Exploring Electrical Engineering: Principles and Applications

1. USE OF ICT IN EDUCATION FOR ONLINE AND BLENDED LEARNING-IIT BOMBAY BIRLA INSTITUTE OF TECHNOLOGY MESRA, RANCHI ASSIGNMENT( MODULE BASIC ELECRICAL) Submitted by: RC_1331_Birla Institute of Technology, Mesra Dr. Deepak Kumar(Group Leader) Dr. Vikas Kumar Gupta

2. INTRODUCTION & HISTORY • Electrical engineering is the study of generation, transmission and distribution of power. • Earlier it included electronic engineering, which has obtained an identity of its own only in the recent years. In most cases, both of these disciplines are offered through a combined course of study. • Electrical engineering gained recognition in the 19th century . Many contributed in its growth, notable among them are Nikola Tesla , Thomas Alva Edison etc.

3. Applications of Electrical Engineering • The primary objective of electrical engineering is to supply electricity safely to consumers. This includes both, the design of electrical appliances as well as suitable wiring system. • Industrial automation and automobile control system design are also a part of electrical engineering. • In Signal processing, principles of electrical engineering is used to modify signals to obtain the required output . • Principles of electrical engineering are also used in Telecommunication engineering, which deals with the transmission of information through different channels to enable communication.

4. Resistance • The electrical resistance of an electrical element is the opposition to the passage of an electric current through that element. • The SI unit of electrical resistance is the ohm (Ω). • The resistance (R) of an object is defined as the ratio of voltage across it to current through it, while the conductance (G) is the inverse. • i.e. R=V/I, G=I/V • A resistor limits current flow.

5. Inductance • An electric current I flowing around a circuit produces a magnetic field and hence a magnetic flux Φ through the circuit. • The ratio of the magnetic flux to the current is called the inductance of the circuit. Inductance is measured in Henry (H) L = Ø/I 1H = 1Wb/A • An inductor stores energy in a magnetic field. When the magnetic field collapses in the coil, it liberates its energy.

6. Capacitor • Capacitance is the ability of a body to store an electrical charge. • If the charges on the plates are +q and −q, and V gives the voltage between the plates, then the capacitance is given by C= q / V • Capacitance is measured in farads, symbol F. However 1F is very large, so prefixes (multipliers) are used to show the smaller values.

7. Basic Elements & Introductory Concepts • Electrical Network is a combination of various electric elements (Resistor, Inductor, Capacitor, Voltage source, Current source) connected in any manner what so ever. • Passive Elements are the elements which receives energy (or absorbs energy) and then either converts it into heat (R) or stored it in an electric (C) or magnetic (L ) field. • Active Elements are the elements that supply energy to the circuit is called active element. Examples: voltage and current sources, generators, and electronic devices that require power supplies. • Bilateral Elements conducts current in both directions with same magnitude . Example: Resistors, Inductors, Capacitors. • Unilateral Element allow conduction of current in one direction. Example: Diode, Transistor etc. • The behaviour of output signal on the application of input signal to a system is called response of the system.

8. Resistor , Diode Fig1.1 Ex. Of Bilateral & Unilateral Element

9. Linear and Nonlinear Circuits • Linear Circuit: A linear circuit is one whose parameters do not change with voltage or current. More specifically, a linear system is one that satisfies (i) homogeneity property (ii) additive property (See Fig. 1.2 ) • Non-Linear Circuit: A non-linear system is that whose parameters change with voltage or current. Non-linear circuit does not obey the homogeneity and additive properties. • A circuit is linear if and only if its input and output can be related by a straight line passing through the origin Otherwise, it is a nonlinear system. (See Fig. 1.2) • Potential Energy Difference: The voltage or potential energy difference between two points in an electric circuit is the amount of energy required to move a unit charge between the two points.

10. V-I Characteristics of Linear and Non-Linear Elements Fig1.2 V-I Characteristics

11. Basic Definitions • Node- A node is a point where two or more components are connected together. This point is usually marked with dark circle or dot. Generally, a point, or a node in an circuit specifies a certain voltage level with respect to a reference point or node. • Branch- A branch is a conducting path between two nodes in a circuit containing the electric elements. These elements could be sources, resistances, or other elements. • Loop- A loop is any closed path in an electric circuit i.e., a closed path or loop in a circuit is a contiguous sequence of branches which starting and end points for tracing the path are, in effect, the same node and touches no other node more than once. • Mesh- A mesh is a special case of loop that does not have any other loops within it or in its interior.

12. Kirchhoff’s Laws • Kirchhoff's laws are analytical tools to obtain the currents and voltages in both, direct-current and alternating current system. • Kirchhoff’s Current Law (KCL): KCL states that at any node (junction) in a circuit the algebraic sum of currents entering and leaving a node at any instant of time must be equal to zero. Here currents entering and currents leaving the node must be assigned opposite algebraic signs . • Kirchhoff’s Voltage Law (KVL): It states that in a closed circuit, the algebraic sum of all source voltages must be equal to the algebraic sum of all the voltage drops. • Voltage drop is encountered when current flows in an element (resistance or load) from the higher-potential terminal toward the lower potential terminal. Voltage rise is encountered when current flows in an element (voltage source) from lower potential terminal (or negative terminal of voltage source) toward the higher potential terminal (or positive terminal of voltage source). Kirchhoff’s voltage law is explained with the help of fig 1.4(b) .

13. Illustration of Kirchhoff's Current Law Fig. 1.4(a) Illustrate the KCL

14. Illustration of Kirchhoff’s Voltage Laws Fig 1.4(b) Illustrate the KVL

15. Independent & Dependent Sources • Independent Sources are those where the generated voltage (Vs) or the generated current (Is) are not affected by the load connected across the source terminals or across any other element that exists elsewhere in the circuit or external to the source. • Dependent Sources are those source voltage or current depends on a voltage across or a current through some other element elsewhere in the circuit. In general, dependent source is represented by a diamond shaped symbol as not to confuse it with an independent source. • Classification of dependent sources: (i) Voltage-controlled voltage source (VCVS) (ii) Current-controlled voltage source (ICVS) (iii) Voltage-controlled current source(VCIS) (iv) Current-controlled current source(ICIS)

16. Dependent Sources Fig. 1.5 Ideal Dependent (Controlled) Sources

17. Dependent Sources • When the value of the source (either voltage or current) is controlled by a voltage somewhere else in the circuit, the source is said to be voltage-controlled source. • When the value of the source (either voltage or current) is controlled by a current somewhere else in the circuit, the source is said to be current-controlled source. • KVL and KCL laws can be applied to networks containing dependent sources. Source conversions, from dependent voltage source models to dependent current source models, or visa-versa, can be employed as needed to simplify the network.

18. Mesh Current Method Fig. 1.6 Circuit for Mesh Current Method

19. Mesh analysis • The analysis of a dc network by writing a set of simultaneous algebraic equations (based on KVL only) in which the variables are currents, known as mesh analysis or loop analysis. • Step-1: Draw the circuit on a flat surface with no conductor crossovers. • Step-2: Label the mesh currents (I) carefully in a clockwise direction. • Step-3: Write the mesh equations by inspecting the circuit (No. of independent mesh (loop) equations=no. of branches (b) - no. of principle nodes (n) + 1). Note: • If possible, convert current source to voltage source. • Otherwise, define the voltage across the current source and write the mesh equations as if these source voltages were known. Augment the set of equations with one equation for each current source expressing a known mesh current or difference between two mesh currents. • Mesh analysis is valid only for circuits that can be drawn in a two-dimensional plane in such a way that no element crosses over another.

20. Node voltage analysis • The Node voltage analysis can be used to solve any linear circuit. In Nodal analysis, KCL equations are used to form equations. • Step-1: Identify all nodes in the circuit. Select one node as the reference node (assign as ground potential or zero potential) and label the remaining nodes as unknown node voltages with respect to the reference node. • Step-2: Assign branch currents in each branch. (The choice of direction is arbitrary). • Step-3: Express the branch currents in terms of node assigned voltages. • Step-4: Write the standard form of node equations by inspecting the circuit. (No of node equations = No of nodes (N) – 1). • Step-5: Solve a set of simultaneous algebraic equation for node voltages and ultimately the branch currents.

21. Node voltage analysis Remarks: • Sometimes it is convenient to select the reference node at the bottom of a circuit or the node that has the largest number of branches connected to it. • One usually makes a choice between a mesh and a node equations based on the least number of required equations.

22. Node voltage analysis Fig. 1.7 Circuit for Node Voltage Analysis

23. Node voltage analysis • KCL equation at node 1 • KCL equation at node 2

24. KCL equation at node 3 • In general, for the ith node the KCL equations can be written as

25. Delta – Wye Connection • Delta and Wye connections are one of the basic connections. • They are named depending on their shapes. • These three terminal networks can be redrawn as four-terminal networks . • We can convert delta connection to wye connection and vice versa. Fig. 1.8 Resistances connected in (a) Delta and (b) Star configurations

26. Delta(Δ)-Star(Y) conversion and Star-Delta conversion The formulas for star-delta conversion The formulas for delta-star conversion The formulas here are given in terms of resistances but the same can be applied for complex circuits also by replacing resistances by impedances.

27. Delta(Δ)-Star(Y) conversion and Star-Delta conversion • The equivalent star (Wye) resistance connected to a given terminal is equal to the product of the two Delta (Δ) resistances connected to the same terminal divided by the sum of the Delta (Δ) resistances (see fig. 1.8). • The equivalent Delta (Δ) resistance between two-terminals is the sum of the two star (Wye) resistances connected to those terminals plus the product of the same two star (Wye) resistances divided by the third star (Wye (Y)) resistance (see fig. 1.8 ).

28. Thank You