BEEE Unit-1 PDF

23EEE102 BASIC ELECTRICAL AND ELECTRONICS Unit-I: Review of Electrical Engineering Dr. K.B. Badri Narayanan Assistant Professor (Sr. Gr.) Department of Mechanical Engineering Amrita School of Engineering, Chennai campus  Potential difference When th...

23EEE102 BASIC ELECTRICAL AND ELECTRONICS Unit-I: Review of Electrical Engineering Dr. K.B. Badri Narayanan Assistant Professor (Sr. Gr.) Department of Mechanical Engineering Amrita School of Engineering, Chennai campus  Potential difference When these protons, neutrons and electrons are together within the atom they are happy and stable. But if we separate them from each other they want to reform and start to exert a potential of attraction called a potential difference. Electrical current Now if we create a closed circuit these loose electrons will start to move and drift back to the protons due to their attraction creating a flow of electrons. This flow of electrons is called an electrical current. The electrons do not flow freely through the circuit as the material they move through creates a restriction to the electron flow. This restriction is called resistance. All basic electrical or electronic circuits consist of three separate but very much related electrical quantities called: Voltage, ( v ), Current, ( i ) and Resistance, ( Ω ). As energy has the ability to do work this potential energy can be described as the work required in joules to move electrons in the form of an electrical current around a circuit from one point or node to another. Electrical current-Cont. In DC circuit theory, electrical Current, ( I ) is the movement or flow of electrical charge and is measured in Amperes, symbol i, for intensity). It is the continuous and uniform flow (called a drift) of electrons (the negative particles of an atom) around a circuit that are being “pushed” by the voltage source. In reality, electrons flow from the negative (–ve) terminal to the positive (+ve) terminal of the supply and for ease of circuit understanding conventional current flow assumes that the current flows from the positive to the negative terminal. Current (I) Current is measured in Amps and an amp or ampere is defined as the number of electrons or charge (Q in Coulombs) passing a certain point in the circuit in one second, (t in Seconds). Current that flows in a single direction is called Direct Current, or D.C. and current that alternates back and forth through the circuit is known as Alternating Current, or A.C. Whether AC or DC current only flows through a circuit when a voltage source is connected to it with its “flow” being limited to both the resistance of the circuit and the voltage source pushing it.  Voltage ( V ) In Dc circuit theory, voltage, ( V ) is the potential energy of an electrical supply stored in the form of an electrical charge. Voltage can be thought of as the force that pushes electrons through a conductor and the greater the voltage the greater is its ability to “push” the electrons through a given circuit. A voltage source that is unchanging and constant over time is called a DC Voltage. While a voltage source that varies periodically in amplitude over time is called an AC voltage. Whether an AC or DC supply, voltage is measured in volts, with one volt being defined as the electrical pressure required to force an electrical current of one ampere through a resistance of one Ohm. Resistance ( R ) Resistance is the capacity of a material to resist or prevent the flow of current or, more specifically, the flow of electric charge within a circuit. The circuit element which does this perfectly is called the “Resistor”. Resistance is a circuit element measured in Ohms, Greek symbol ( Ω, Omega ) with prefixes used to denote Kilo-ohms ( kΩ = 103Ω ) and Mega-ohms ( MΩ = 106Ω ). Note that resistance cannot be negative in value only positive. The relationship between Voltage, ( v ) and Current, ( i ) in a circuit of constant Resistance, ( R ) The reciprocal of resistance ( 1/R ) called Conductance. In other words we can also present current flow as being: i = 1/R * v. Thus high values of conductance implies a good conductor such as copper while low values of conductance implies a bad conductor such as wood. Quantity Symbol Unit of Measure Abbreviation Voltage V or E Volt V Current I Ampere A Resistance R Ohms Ω  Ohm’s Law By knowing any two values of the Voltage, Current or Resistance quantities we can use Ohms Law to find the third missing value. To find the Voltage, ( V ) [ V = I x R ] V (volts) = I (amps) x R (Ω) To find the Current, ( I ) [I=V÷R] I (amps) = V (volts) ÷ R (Ω) To find the Resistance, ( R ) [ R = V ÷ I ] R (Ω) = V (volts) ÷ I (amps) Electrical Power in Circuits Electrical Power, ( P ) in a circuit is the rate at which energy is absorbed or produced within a circuit. A source of energy such as a voltage will produce or deliver power while the connected load absorbs it. Light bulbs and heaters for example, absorb electrical power and convert it into either heat, or light, or both. The higher their value or rating in watts the more electrical power they are likely to consume. To find the Power (P) [ P = V x I ] P (watts) = V (volts) x I (amps) The Power Triangle Ohms Law Matrix Table Ohms Law Example No1 For the circuit shown below find the Voltage (V), the Current (I), the Resistance (R) and the Power (P). Resistance [ R = V ÷ I ] = 24 ÷ 2 = 12 Ω P=? Power [ P = V x I ] = 24 x 2 = 48W R=? Electrical Energy in Circuits Electrical Energy is the capacity to do work, and the unit of work or energy is the joule ( J ). Electrical energy is the product of power multiplied by the length of time it was consumed. So if we know how much power, in Watts is being consumed and the time, Kirchhoff’s Law Kirchhoffs Current Law or KCL, states that the “total current or charge entering a junction or node is exactly equal to the charge leaving the node as it has no other place to go except to leave, as no charge is lost within the node“. In other words the algebraic sum of ALL the currents entering and leaving a node must be equal to zero, I(exiting) + I(entering) = 0. Kirchhoff’s Voltage Law or KVL Kirchhoffs Voltage Law or KVL, states that “in any closed loop network being driven by a voltage source, the total voltage around the loop is equal to the sum of all the voltage drops within the same loop” which is equal to zero. In other words the algebraic sum of all voltage sources and voltage drops within a closed loop must be equal to zero since the algebraic sum of the voltage drops equals the algebraic sum of the voltage sources. Common DC Circuit Theory Terms: Circuit – a circuit is a closed loop conducting path in which an electrical current flows. Path – a single line of connecting elements or sources. Node – a node is a junction, connection or terminal within a circuit were two or more circuit elements are connected or joined together giving a connection point between two or more branches. A node is indicated by a dot. Branch – a branch is a single or group of components such as resistors or a source which are connected between two nodes. Loop – a loop is a simple closed path in a circuit in which no circuit element or node is encountered more than once. Mesh – a mesh is a single closed loop series path that does not contain any other paths. There are no loops inside a mesh Kirchhoffs Circuit Law Example Using Kirchhoffs Current Law At node A : I1 + I2 = I3 At node B : I3 = I1 + I2 Using Kirchhoffs Voltage Law, KVL As : I3 = I1 + I2 The current flowing in resistor R3 is given as : - Loop 1 is given as : 10 = R1 I1 + R3 I3 = 10I1 + 40I3 0.143 + 0.429 = 0.286 Amps and the voltage across the resistor R3 is given Loop 2 is given as : 20 = R2 I2 + R3 I3 = 20I2 + 40I3 as : 0.286 x 40 = 11.44 volts The negative sign for I1 means that the direction of current Loop 3 is given as : 10 – 20 = 10I1 – 20I2 flow initially chosen was wrong, but never the less still valid. In fact, the 20v battery is charging the 10v battery. As I3 is the sum of I1 + I2 we can rewrite the equations as; Eq. No 1 : 10 = 10I1 + 40(I1 + I2) = 50I1 + 40I2 Eq. No 2 : 20 = 20I2 + 40(I1 + I2) = 40I1 + 60I2 “Simultaneous Equations” that can be reduced by subtraction to give us the values of I1 and I2 Substitution of I1 in terms of I2 gives us the value of I1 as -0.143 Amps Substitution of I2 in terms of I1 gives us the value of I2 as +0.429 Amps Voltage Dividers Voltage dividers are also known as potential dividers, because the unit of voltage, the “Volt” represents the amount of potential difference between two points. A voltage or potential divider is a simple passive circuit that takes advantage of the effect of voltages being dropped across components which are connected in series. The potentiometer, which is a variable resistor with a sliding contact, is the most basic example of a voltage divider as we can apply a voltage across its terminals and produce an output voltage in proportion to the mechanical position of its sliding contact The simplest, easiest to understand, and most basic form of a passive voltage divider network is that of two resistors connected together in series. This basic combination allows us to use the Voltage Divider Rule to calculate the voltage drops across each series resistor. Resistive Voltage Dividers Here the circuit consists of two resistors connected together in series: R1, and R2. Since the two resistors are connected in series, it must therefore follow that the same value of electric current must flow through each resistive element of the circuit as it has nowhere else to go. Thus providing an I*R voltage drop across each resistive element. Apply Kirchhoff’s Voltage Law, (KVL)  The current flowing through the series network is simply I = V/R following Ohm’s Law. Since the current is common to both resistors, (IR1 = IR2) we can calculate the voltage dropped across resistor, R2 in the above series circuit as being: Likewise for resistor R1 as being:  Voltage Dividers Example No1 How much current will flow through a 20Ω resistor connected in series with a 40Ω resistor when the supply voltage across the series combination is 12 volts dc. Also calculate the voltage drop produced across each resistor. Voltage Dividers Example No2 Calculate the noload voltage output for each tapping point of the voltage divider circuit above if the series-connected resistive network is connected to a 15 volt DC supply. Calculate the noload voltage output from between points B and E. Capacitive Voltage Divider Capacitive Voltage Divider circuits produce voltage drops across capacitors connected in series to a common AC supply. Generally capacitive voltage dividers are used to “step-down” very high voltages to provide a low voltage output signal which can then be used for protection or metering. Nowadays, high frequency capacitive voltage dividers are used more in display devices and touch screen technologies found in mobile phones and tablets. Unlike resistive voltage divider circuits which operate on both AC and DC supplies, voltage division using capacitors is only possible with a sinusoidal AC supply. This is because the voltage division between series connected capacitors is calculated using the reactance of the capacitors, XC which is dependent on the frequency of the AC supply. Capacitive Reactance Formula Where: Xc = Capacitive Reactance in Ohms, (Ω) π (pi) = a numeric constant of 3.142 ƒ = Frequency in Hertz, (Hz) C = Capacitance in Farads, (F) Therefore by knowing the voltage and frequency of the AC supply, we can calculate the reactances of the individual capacitors, substitute them in the above equation for the resistive voltage divider rule, and obtain the corresponding voltage drops across each capacitor as shown. Using the two capacitors of 10uF and 22uF in the series circuit above, we can calculate the rms voltage drops across each capacitor in terms of their reactance when connected to a 100 volts, 50Hz rms supply. Inductive Voltage Dividers As its name suggests, Inductive Voltage Dividers create voltage drops across inductors or coils connected together in series to a common AC supply. An inductive voltage divider can consist of a single winding or coil which is divided into two sections where the output voltage is taken from across one of the section, or from two individual coils connected together. The most common example of an inductive voltage divider is the auto-transformer with multiple tapping points along its secondary winding. When used with steady state DC supplies or with sinusoids having a very low frequency, approaching 0 Hz, inductors act as a short circuit. This is because their reactance is almost zero allowing any DC current to easily pass through them, so like the previous capacitive voltage divider network, we must perform any inductive voltage division using a sinusoidal AC supply.  Inductive Reactance Formula Where: If we know the voltage and frequency of the AC supply, we can XL = Inductive Reactance in Ohms, (Ω) calculate the reactances of the two inductors and use them along π (pi) = a numeric constant of 3.142 with the voltage divider rule to obtain the voltage drops across ƒ = Frequency in Hertz, (Hz) each inductor as shown. L = Inductance in Henries, (H) Using the two inductors of 10mH and 20mH in the series circuit above, we can calculate the rms voltage drops across each capacitor in terms of their reactance when connected to a 60 volts, 200Hz rms supply. Current Divider Current Dividers are parallel circuits in which the source or supply current divides into a number of parallel paths. In a parallel connected circuit, all the components have their terminals connected together sharing the same two end nodes. This results in different paths and branches for the current to flow or pass along. However, the currents can have different values through each component. The main characteristic of parallel circuits is that while they may produce different currents flowing through different branches, the voltage is common to all the connected paths. That is VR1 = VR2 = VR3 … etc. Therefore the need to find the individual resistor voltages is eliminated allowing branch currents to be easily found with Kirchhoff’s Current Law, (KCL) and of course Ohm’s Law. Resistive Current Divider Here this basic current divider circuit consists of two resistors: R1, and R2 in parallel which splits the supply or source current IS between them into two separate currents IR1 and IR2 before joining together again and returning back to the source. As the source or total current equals the sum of the individual branch currents, then the total current, IT flowing in the circuit is given by Kirchoffs current law KCL as being:  As the same voltage, (V) is present across each resistive element, we can find the current flowing through each resistor in terms of this common voltage as it is simply V = I*R following Ohm’s Law. So solving for the voltage (V) across the parallel combination gives us: Solving for IR1 gives: Substitute Likewise, solving for IR2 gives: Substitute Current Dividers Example No1 A 20Ω resistor is connected in parallel with a 60Ω resistor. If the combination is connected across a 30 volts battery supply, find the current flowing through each resistor and the total current supplied by the source. Current Dividers Example No2 Three resistors are connected together to form a current divider circuit as shown below. If the circuit is fed from a 100 volts supply with a capacity of 1.5kW. Calculate the individual branch currents using the current division rule. Faraday’s Law 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. Faraday’s law states that a current will be induced in a conductor which is exposed to a changing magnetic field. Lenz’s law of electromagnetic induction states that the direction of this induced current will be such that the magnetic field created by the induced current opposes the initial changing magnetic field which produced it. The direction of this current flow can be determined using Fleming’s right-hand rule. Similarly if a conductor is forcefully brought under a magnetic field, there will be an induced current in that conductor. The direction of this force can be found using Fleming’s Right Hand Rule. 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. 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. Conclusion: From this experiment, Faraday concluded that whenever there is relative motion between a conductor and a magnetic field, the flux linkage with a coil changes and this change in flux induces a voltage across a coil. Michael Faraday formulated two laws on the basis of the above experiments. These laws are called Faraday’s laws of electromagnetic induction. 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. An electric current flowing through a conductor creates a magnetic field around it. The strength of the field depends upon the magnitude of the current. The generated magnetic field follows any changes in the current, and from Faraday’s law of induction, we know that changing the magnetic field induces an electromotive force in the conductor. Considering this principle, inductance is defined as the ratio of the induced voltage to the rate of change of current causing it. The electronic component designed to add inductance to a circuit is an inductor. Factors Affecting Inductance Number of Wire Turns in the Coil Inductance is greater when the number of turns of wire in the coil is greater. More coils of wires indicate a greater amount of magnetic field force for a given amount of coil current. Coil Area Inductance is proportional to the coil area. Greater the coil area, the greater the inductance. Greater coil area presents less opposition to the formation of magnetic field flux for a given amount of field force Core Material The greater the magnetic permeability of the core to which the coil is wrapped around, the greater the inductance. Coil Length The longer the coil’s length, the lesser the inductance. The shorter the coil’s length, the greater the inductance. Types of Inductance Inductance is classified into two types as: ✓ 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. Where L is termed as the self-inductance of the coil It depends on the cross-sectional area, the permeability of the Where: material, and the number of turns in the coil. L is in Henries μο is the Permeability of Free The rate of change of magnetic flux in the coil is given as Space (4.π.10-7) N is the Number of turns A is the Inner Core Area (πr 2) in m2 Self Inductance Formula ℓ is the length of the Coil in metres