M.I.E.T ENGG COLLEGE DEPT OF EEE M.I.E.T. ENGINEERING COLLEGE (Approved by AICTE and Affiliated to Anna University Chennai) TRICHY – PUDUKKOTTAI ROAD, TIRUCHIRAPPALLI – 620 007 DEPARTMENT OF ELECTRICAL AND ELECTRONICS ENGINEERING COURSE MATERIAL GE6252 Basic Electrical and Electronics Engineering I YEAR - II SEMESTER II – SEM – BASIC ELECTRICAL & ELECTRONICS ENGG M.I.E.T ENGG COLLEGE DEPT OF EEE UNIT – I ELECTRIC CIRCUITS AND MEASUREMENTS BASIC DEFINITIONS OF ELECTRICITY: The electron or the electrons revolving in outermost orbit are hence loosely held to the nucleus. Such a shell is called the valence shell .and Such electrons are called valence electrons. In some atom such valence electrons are so loosely bound to the nucleus that at room temperature the additional energy imported to the valence electrons causes them to escape from the shell and exists as free electrons. Such free electrons constitute the flow of electric current. CURRENT: The current can be defined as rate of flow of charge in an electric circuit or in any medium in which charges are subjected to an external electric field. I = Q / t ampere OHM ‘s LAW : At constant temperature, the voltage difference across the two ends of the conductor is directly proportional to the current flowing through the conductor. V = R I I R V II – SEM – BASIC ELECTRICAL & ELECTRONICS ENGG M.I.E.T ENGG COLLEGE DEPT OF EEE KIRCHOFF’s LAW: KIRCHHOFF’s CURRENT LAW (KCL): “At a junction, total current flowing towards the junction is equal to total current flowing away from the junction.” Simply, the algebraic sum of current meeting at a junction or node is zero. ∑I = 0. Applying KCL, at a junction a. I1 + I3 = I2 + I4 +I5 I1 – I2 + I3 – I4 – I5 = 0 KIRCHOFF’s VOLTAGE LAW (KVL): “In any closed network , the algebraic sum of the voltage drops across the circuit elements is equal to the algebraic sum of the e.m.f ‘s in the path.”Simply, in a closed network, potential rise equal to potential drop. ∑V= 0. STEADY STATE SOLUTION OF DC CIRCUITS: They are two solutions in DC circuits 1. Voltage division in series resistive circuit 2. Current division in parallel resistive circuit II – SEM – BASIC ELECTRICAL & ELECTRONICS ENGG M.I.E.T ENGG COLLEGE DEPT OF EEE VOLTAGE DIVISION IN SERIES RESISTIVE CIRCUIT: Consider a series circuit of two resistors R1 and R2 connected to source of V volts. As two resistors are connected in series flowing through both the resistors is same i.e., then applying KVL we get V= IR1 + IR2 Therefore I = V/ R1 + R2 Total voltage applied is equal to the sum of voltage drops VR1 and VR2 across R1 and R2 respectively. VR1 = I.R1 VR1 = {V / R1+ R2) .R1 VR1 = ( R1 / R2 ) .V Similarly VR2 = I .R2 VR2 = (V/ R1+ R2).R2 VR2 = (R2 / R1 + R2) .V So this circuit is a voltage divider circuit. CURRENT DIVISION IN PARALLEL RESISTIVE CIRCUIT: I1 R I I2 R 2 V II – SEM – BASIC ELECTRICAL & ELECTRONICS ENGG M.I.E.T ENGG COLLEGE DEPT OF EEE Consider a parallel circuit of two resistor R1 and R2 connected across a source of V volts. Current through R1 is I1 and R2 is I2 , while total current drawn from source is I I = I1 + I2 but I1 = V /R1 and I2 = V / R2 V = I1R1 =I2R2 i.e., V = I1 R1 =I2R2 I 1 = I2 (R2 /R1) Substituting value of I1 in eqn I = I2 (R2/R1) + I2 = I2(R2/R1 +1) I = I2 (R1 +R2 / R1) I2 = I(R1/R1+ R2) Now, I1= I – I2 = I –(R1 / R1+R2) I I1 = (R1 + R2 –R1/R1+R2) I I1 = I (R2 / R1+R2) Note : Current through a resistor = (incoming Current) * Opposite branch resistance / total loop resistance Voltage across a resistor = (applied voltage ) * Voltage of that branch resistance / Total loop resistance INTRODUCTION OF AC CIRCUITS : Alternating current is the current which changes its magnitude and direction (polarity) at regular interval of time. II – SEM – BASIC ELECTRICAL & ELECTRONICS ENGG M.I.E.T ENGG COLLEGE DEPT OF EEE AC WAVEFORM: The waveforms of most alternating currents are curves representing gradual changes in voltage and current. i.e., first increasing in one direction upto a maximum value and decreases to zero .Then it will increase in the other direction upto the maximum value. The graph representing the manner in which an alternating current (or) voltage changes with respect to time is known as waveform or wave shape. ADVANTAGES OF AC SUPPLY: 1. By using AC supply , it is possible to step up (or) step down the voltage to the required value, by the transformer. 2. When a high voltage is transmitted, in the transmission line, the current will be Minimum. Hence the I2R loss in the conductor will be minimum and therefore Transmission system will be efficient and economical. GENERATION OF AC VOLTAGES: Emf induced the different situation : (I) Moving the conductor across the lines of force V ,velocity of conductor. Magnetic flux lines In this case maximum flux will be cuts by the conductor .So e = BlV v II – SEM – BASIC ELECTRICAL & ELECTRONICS ENGG M.I.E.T ENGG COLLEGE DEPT OF EEE Where , e= induced emf , (v) B= flux density , (Wb /m2) l = length of the conductor (m/sec) V = velocity of conductor (m/sec ) (ii) Moving the conductor parallel to the lines of force. V , velocity of conductor In this case , no flux lines will cut the conductor .So , e = 0 V (iii) Moving the conductor in such a way making an angle ‘’ 0 ‘ ‘ with the lines of force. In this case , Velocity (V) can be resolved in to two components. (i) Across the magnetic flux = Vsin teta (ii) Along (parallel ) to the magnetic flux = Vcos teta Therefore total induced emf , e = BlV sin teta + Blv cost eta When the conductor is parallel to magnetic flux lines , the e = 0 So , II – SEM – BASIC ELECTRICAL & ELECTRONICS ENGG M.I.E.T ENGG COLLEGE DEPT OF EEE e = BlV sin teta Volts. EQUATION OF ALTERNATING EMF AND CURRENT: N Φm X X ‘ S For the derivation of the equation of an alternating quantity , consider single turn , 2 pole alternator. The coil is rotated with constant angular velocity in the uniform magnetic field of density B Wb / m2 in the anti clockwise direction as shown in fig In position 1 , the coil lines in the plane of reference axis XOX 1.At this position maximum flux (Φm) will be linking the coil. After ‘t ‘ second , the coil is rotated through an angel θ radians as shown in fig. In position 2 , the maximum flux (Φm) can be resolved in to two components. (i) Component Φm cos ώt perpendicular to the plane of the coil. Due to this ,there will be maximum flux cutting in the coil and hence emf . induced in the coil. (ii) Component Φm sin ώt is parallel to the plane of the coil. Component does not induced emf in the coil. According to Faraday’s law of electro magnetic induction , an emf induced in the coil is given by, II – SEM – BASIC ELECTRICAL & ELECTRONICS ENGG M.I.E.T ENGG COLLEGE DEPT OF EEE e = -N dΦ/dt Where , N = number of turns Φ = Flux linkage. N = l e = -d/ dt Φm cos ώt e = - Φm ( - sin ώt). Ώ e = ώ Φm sin ώtV (2.1) When θ = λ0 degree , maximum emf will be induced in the coil. Em = ώ Φm(1) = ώ Φm V (2.2) Sub the equation 2.1 in 2.2 e = Emsin ώt e = Emsin θ therefore the equation of alternating emf induced in a coil is given by e = Em sin ώt (or ) V = Vm sin ώtV Equating of alternating current induced ina coil is i = Im sinώtA From the above equation , it is clear that the instantaneous values of voltage and current veries as the sine function of the time (t) or angle.Because of this reason only it is called as sinusoidal voltage / sinusoidal current. II – SEM – BASIC ELECTRICAL & ELECTRONICS ENGG M.I.E.T ENGG COLLEGE DEPT OF EEE VARIOUS TYPES OF WAVEFORMS: The various types of waveforms are shown i,v i , v T t Triangle waveform Rectangular waveform II – SEM – BASIC ELECTRICAL & ELECTRONICS ENGG M.I.E.T ENGG COLLEGE DEPT OF EEE Trapezoidal Waveform ROOT MEAN SQUARE (RMS ) OR EFFECTIVE VALUE OF AN ALTERNATING QUANTITY When a current through a resistor, heat is produced irrespective of the direction of current flow. The heat produced by an alternating current of maximum value (Imax) will not be equal to the heat produced by a direct current of Imax amperes. The RMS value of an alternating quantity is defined as the AC value of current flowing through a given resistance for a given time produces the same amount of heat as produced by the direct current when flowing through the same resistance for the same time. GRAPHICALMETHOD: II – SEM – BASIC ELECTRICAL & ELECTRONICS ENGG M.I.E.T ENGG COLLEGE DEPT OF EEE SIMPLE AC CIRCUITS. An AC circuit may contain any one or two or all of the following three circuit elements. 1.Resistance 2.Inductance 3.Capacitance. POWER AND POWER FACTOR: Power : Pav = Average power consumed by R ,L, C Pav = I2R Pav = I (IR) P = IVR P= IVcosø P= VI cosø W. POWER TRIANGLE: P= VI cosø ø S = VI Q = VI sinø Q = VI S = Vt cosø ø P= VI cosø Xc > XL POWER FACTOR: It is defined as the cosine angle between voltage and current. Power Factor = True Power / Apparent Power = VI cos ø/ VI Power Factor = cos ø II – SEM – BASIC ELECTRICAL & ELECTRONICS ENGG M.I.E.T ENGG COLLEGE DEPT OF EEE If current lags volume, power factor is said to be lagging .If current leads voltage Power factor is said to be leading.