Basic Electrical Engineering PDF - BTEE-101-18

Basic Electrical Engineering BTEE-101-18 Academic session: July- December 2024 Semester: 1st B. Tech.-CSE (P2 Group) DR NAVEEN KUMAR SHARMA ASSISTANT PROFESSOR I.K. GUJRAL PUNJAB TECHNICAL UNIVERSITY MAIN CAMPUS KAPURTHALA, PUNJAB Module 1 DC Circuits Resistors. Definition: A resist...

Basic Electrical Engineering BTEE-101-18 Academic session: July- December 2024 Semester: 1st B. Tech.-CSE (P2 Group) DR NAVEEN KUMAR SHARMA ASSISTANT PROFESSOR I.K. GUJRAL PUNJAB TECHNICAL UNIVERSITY MAIN CAMPUS KAPURTHALA, PUNJAB Module 1 DC Circuits Resistors. Definition: A resistor is an electrical component or device designed explicitly to have a certain magnitude of resistance, expressed in ohms. A resistor is a two terminal passive electrical component that represents the resistance of the electric circuit. It provides resistance to the flow of current. Further, it must operate reliably in its environment, including electric field intensity, temperature, humidity, radiation, and other effects. Some resistors are designed explicitly to convert electric energy to heat energy. Others are used in control circuits, where they modify electric signals and energy to achieve desired effects. Examples: Motor starting resistors and the resistors used in electronic amplifiers to control the overall gain and other characteristics of the amplifier. Ohm’s Law. When the current I in a conductor is steady and there are no voltages within the conductor, the value of the voltage V between the terminals of the conductor is proportional to the current I, or V=IR where the coefficient of proportionality R is called the resistance of the conductor. Cylindrical Conductors. For current directed along the axis of the cylinder, the resistance R is proportional to the length l and inversely proportional to the cross section A, or R=ρl/A (ohms), l=length of conductor, A=area of cross section where ρ (rho) is called the resistivity (or specific resistance) of the material. Changes of Resistance with Temperature. The resistance of a conductor varies with the temperature. The resistance of metals and most alloys increases with the temperature, while the resistance of carbon and electrolytes decreases with the temperature. For usual conditions, as for about 100C change in temperature, the resistance at a temperature t2 is given by Rt2 = Rt1 [ 1 + αt1 ( t2 - t1 )] Limitation of Ohms law’: It is not applicable to non-linear circuits. It is applicable to only linear circuits. Temperature must remain constant for Ohms law. E.g. all semiconductor devices are non-linear devices. Inductors An inductor is a circuit element whose behavior is described by the fact that it stores electromagnetic energy in its magnetic field. In its most elementary form, an inductor is formed by winding a coil of wire, often copper, around a form that may or may not contain ferromagnetic materials. Inductance. The property of the inductor that is useful in circuit analysis is called inductance. Inductance is defined by either of the following equations: where L coefficient of self-inductance, i current through the coil of wire, v voltage across the inductor terminals, W energy stored in the magnetic field. L=flux linkage/current (Henry). Unit of self inductance is called the henry (H). Mutual Inductance. If two coils are wound on the same coil form, or if they exist in close proximity, then a changing current in one coil will induce a voltage in the second coil. This effect forms the basis for transformers, one of the most pervasive of all electrical devices in use. Mutual inductance is always written as M. Unit of mutual inductance is called the henry (H). Capacitors Charge Storage. A capacitor is a circuit element that is described through its principal function, which is to store electric energy. This property is called capacitance. In its simplest form, a capacitor is built with two conducting plates separated by a dielectric. Q=CV coulombs. Unit of C=Farads, µFarad, nanoF, picoF Power (Unit: Watts, Kilo-Watts, Volt-Ampere). The power delivered by an electrical source to an electrical device is given by, p= vi where p power delivered, v voltage across the device and i current delivered to the device. If the device is a resistor, then the power delivered to the device is, Applicable for series circuits Power=Voltage x Current (for DC circuits) (Volt-Ampere) Power =Voltage x Current x Cosθ (for AC circuits) (Volt-Ampere) Cos θ is known as the power factor of the AC circuit (Cosθ is unit less) Applicable for parallel Energy. The energy delivered by an electrical source to an electrical device is given by, circuits where the times t1 and t2 represent the starting and ending times of the energy delivery. In SI units, the unit of energy is the joule. Note: A commonly used unit for electric energy measurement is a kilowatt hour (kWh), which is equal to 3.6 X 106 Joules. (1k=1000, 1 watt=Joules/second, 1h =3600 seconds). Students Pl. check your electricity bill and check that energy consumption every unit has been estimated in kWh. 1 kWh = 1 energy unit. Kirchhoff’s Laws. Kirchhoff’s Current Law. Kirchhoff’s Current Law states that” the algebraic sum of all the currents at any node point or a junction of a circuit is zero”. ΣI=0  1 3 Parallel=shunt. 30 V DC is the input source. 1 ohms resistor is known as load, which is connected at the output side. 1, 2, 3 and 4, these are known as nodes 2 4 In simplified way, the sum of currents approaching at any node is equal to the sum of all currents leaving that node. It is known as Kirchhoff’s current law (KCL). Kirchhoff’s Voltage Law. The second fundamental principle, abbreviated as KVL and It states that the sum of voltages around any closed path is equal to zero. In equation form, it can be written as, v1+v2+v3+…….vn = 0 DC Sources and AC Sources DC Sources. Some sources, such as batteries, deliver electric energy at a nearly constant voltage, and thus they are modeled as constant voltage sources. The term dc sources basically means direct current sources, but it has come to stand for constant sources as well. Figure shows the standard symbol for a dc source. Other sources are modeled as dc current (or constant-current) sources. + and – is known as polarity AC Sources. Most of the electric energy used in the world is passed through the stages: generation, its transmission, its distribution, and utilized in sinusoidal form. Sources of this type are frequently called ac (for alternating current) sources. Figure shows the standard symbol for an ac source. The most general expression for a voltage and current in sinusoidal form is of the type (Vm=amplitude of the voltage wave), f is the frequency Hertz, v(t), i(t) is the instantaneous value of the voltage and current respectively, α and β are the phase angle values in degrees. Effective or RMS (root mean square) Values. If a sinusoidal current i(t) flows through a resistor of R , then, over an integral number of cycles, the average power delivered to the resistor is found to be, P=I rms2 R (Watts), where Irms is the rms value of the current. Its value is given by, Irms=Im/1.414. Pavg is measured in Watts. This amount of power is identical to the amount of power that would be delivered by a constant (DC) current of Amperes. Thus, the effective value of an AC current (or voltage) is equal to the maximum value divided by. The effective value is commonly used to describe the requirements of AC systems. An alternative term is root-mean-square (rms) value. This term follows from the formal definition of effective or rms values of a function, Power Factor (cos θ). When the voltage across a device and the current through a device are given, respectively, by A computation of the average power over an integral number of cycles gives The angle (α-β), which is the phase difference between the voltage and current, is called the power factor angle. The cosine of the angle is called the power factor because it represents the ratio of the average power delivered to the product of voltage and current. Power factor (PF) is the measure of evaluating how effectively the incoming electrical power is used in an electrical system. It is defined as the ratio of Real power/Active Power (kW) to Total power/Apparent Power (kVA). If the PF is high, then we can say that more effectively the electric power is being used in an electrical system. A load with PF of 1 results most efficient loading of the system, but it is not possible to keep the unity power factor. Some reactive power is required to keep the voltage to be maintained at the receiving end of the electrical power. A high PF benefits both consumers and Power Company. Whereas Low PF indicates poor utilization of Electrical Power. In Electrical Engineering, the concept of PF is only discussed in AC circuits. Not applicable to DC circuits.  Types of Power Factor and Types of Loads There are three types of power factor in electrical science. Leading power factor (Current leads the voltage by an angle θ)- Capacitive loads (e.g. capacitor banks, synchronous motors: Both these operate at leading power factor) Lagging power factor (Current lags the voltage by an angle θ)-Inductive loads (e.g. induction motors, electric iron, electric fan: All these operate at lagging power factor) Unity power factor (Current is in same phase voltage, this means θ is zero)- Resistive loads (e.g. light, electric heaters: operate at unity power factor). In the case of AC circuit, the value of power factor always lies between the ranges 0 to 1 (0 < Cos θ < 1). where θ is the angle between V and I. Note: Unity power factor means Cos θ =1 Cos θ: It is also the ratio between resistance (R) and Total impedance (Z) of AC circuit. It has no units. Types of Electrical Power (only for AC systems). There is only 1 power in DC systems which is measured in Watts. Real power/active power=VI cos θ (Watts)-for single-phase systems Real power/active power=1.732 VI cos θ (Watts)-for three-phase systems Reactive power= VI sin θ (VaR=Volt Ampere Reactive) -for single-phase systems, Reactive power= 1.732 VI sin θ (VaR=Volt Ampere Reactive) -for three-phase systems θ Apparent power/Total power= VI (Volt-Ampere) Cos θ = Real power /apparent power = KW/KVA or W/VA Reactive power (VaR=Volt ampere reactive) represents electrical energy stored in the coil that then flows back to the grid. Ideal coils do not consume any electrical energy, but create a significant electric current. Real power is the power actually consumed due to the resistive load Apparent power is the power the grid must be able to withstand. Unit of real power is Watt, while apparent power unit is VA (Volt Ampere) Impedance Triangle: Term impedance is applicable only for AC circuits, not for DC circuits. For DC circuits, we have Resistance (R ohms), because there is no inductance or reactance in DC circuits. When dealing with DC circuits the only thing that opposes current is the resistance in the circuit. AC adds a component that opposes current as well. This is called reactance (in Ohms, denoted by Ω) and it runs 90 degrees to the circuit resistance. This means it is not possible to add them together arithmetically; it has to be done using the Pythagoras’ theorem. When you add these two together, you get a total opposition to current flow called impedance (in Ohms). The triangle that is created when adding the resistance to the reactance is known as an impedance triangle.  In an impedance triangle, the resistance (r) is always on the bottom of the triangle, the reactance (x) always goes on the side and the hypotenuse is always the impedance (z). XL = ω L (in Ohms), L=self inductance measured in Henry Xc = 1/ω C (in Ohms), C=capacitance in Farads ω=2πf f=frequency in Hertz For DC circuits, f=0 so there is no inductance or reactance in DC circuits. f is applicable only for AC circuits. Cos θ = R/Z=power factor in terms of impedance Impedance, Z= R + j X (ohms)= Impedance is a complex quantity. ◦ If X is positive, it is inductive reactance XL ◦ If X is negative, it is capacitive reactance XC Units of Z, R and X is same and is ohms Few advantages of maintaining high power factor (Cos θ) Improved voltage profile Reduction in variable losses in the system Inductive reactance Xl θ Capacitive reactance Xc Capacitive load (Xc) Electrical Network: Any possible combination of various electric elements (Resistor, Inductor, Capacitor, Voltage source, Current source) connected in any manner what so ever is called an electrical network. We may classify circuit elements in two categories, passive and active elements. Electrical Circuit: An electric circuit is a closed energized electric network. It means circuit must have closed path with energy sources. From the above example, we can say that fig 1 and fig 2 are electric networks but only fig 2 is electric circuit. It means, electric circuit is always an electric network but electric network may or may not be an electric circuit. Active Element: The elements that supply energy to the circuit is called active element and the network containing these sources together with other circuit elements are known as active network. Examples of active elements include voltage and current sources, generators, and electronic devices that require power supplies. A transistor is an active circuit element, meaning that it can amplify power of a signal. Passive Element: The element 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 is called passive element, and the network containing these elements without energy sources are known as passive network. Examples are resistor, inductor, capacitor, transformer etc. Energy Sources (Voltage and Current Sources): There are two types of energy sources namely Voltage Sources and Current Sources. Independent Voltage Source: A hypothetical generator which maintains its value of voltage independent of the output current. It can be represented as: Ideal DC Voltage Source Practical DC Voltage Source If the value of internal resistance will be zero, then the voltage source is called as ideal voltage source. The V-I characteristics for ideal and practical voltage source V-I Characteristic of Voltage Source Independent Current Source: A generator which maintains its output current independent of the voltage across its terminals. It can be represented as: Ideal DC Current Source Practical DC Current Source if the value of internal resistance will be infinity, then the current source is called as ideal current source. The V-I characteristics for ideal and practical current source V-I Characteristic of Current Source Bilateral Elements: If by reversing the terminal connections of an element in a circuit, the circuit response remains same. Such elements are known as bilateral elements. Examples are Resistor, Inductor, Capacitor etc. Unilateral Elements: If by reversing the terminal connections of an element in a circuit, the circuit response gets change. Such elements are called as unilateral elements. Examples are Voltage Source, Current Source, Diode etc. Sign Convention: If take voltage rise with positive (+) sign then voltage drop will be taken with negative (-) sign or vice-versa. When current direction will be from negative terminal to positive terminal, voltage will rise and vice-versa. In all the passive elements current entering terminal is taken as positive and current leaving terminal is taken as negative. According to KVL in the above circuit diagram: 1. Node: A node of a network is an equipotential surface at which two or more circuit elements are joined. 2. Junction: A junction is that point in an electric circuit where three or more elements are joined. So, the junction is always a node but node may or may not be a junction. 3. Loop: A loop is any closed path of the electric network. 4. Mesh: A mesh is the most elementary form of loop, and it cannot be further subdivided into other loops. So, we can say that mesh is always a loop but loop may or may not be a mesh. 5. Lumped Network: A network in which physically separate resistors, capacitors and inductors can be represented. 6. Distributed Network: One in which resistors, capacitors, and inductors cannot be physically separated and individually isolated as separate elements. For example, Transmission Line