1 ELEC130 Electrical Engineering 1 Week 2 Module 1 Introductory Circuit Techniques

23-Feb-99Lecture 22 Software zElectronic Workbench: Simulation Software Faculty PC’s Rm. ES210 - Go to Diomedes yLogin: cstudentnumber yPassword: access keys on students card + daymonth (ddmm) of birth zTopClass: Class Discussion & Notices yUsername: first name.last name yPassword: date of birth ddmmyy z first name.last

23-Feb-99Lecture 23 Administration Items zLaboratory & Tutorials start THIS WEEK yA couple of corrections have been given to the Tutors and Laboratory demonstrators zQuiz 1 - Week 3 - Lecture NEXT MONDAY yWill cover to the end of Module 1 which will be completed next lecture before the quiz. zSurvey zSubject Home Page: - through Dept. Pages

23-Feb-99Lecture 24 Last week zChargeSymbol: Q q(t) Units: Coulombs or C zCurrent Symbol: I i(t) Units: Amperes or A zVoltageSymbol: V v(t) Units: Volts or V zPowerSymbol: P p(t) Units: Watts or W zResistanceSymbol: RUnits: Ohms or  (I = Q / t Amps & V = P.t / Q volts ) P = V. I Watts V = R. I Ohms

23-Feb-99Lecture 25 Conventions zCurrent - positive charge flow - through element zVoltage - measured across an element zPower 3 A - 3 A = +_+_ I Circuit or element v(t) _ I Absorbing power Delivering power I v(t)

23-Feb-99Lecture 26 Resistance zMaterial - resistivity   R = .l / A yPoor conductor  is large e.g. plastics, wood yGood conductors  is small e.g. copper, gold, aluminium zResistance - the most common materials used are: ycarbon composition ynickel chromium ywire wound (for high power applications) zCan be physically small (10mm long) or large (>1m), can be fixed or variable

23-Feb-99Lecture 27 Resistance zCommon - are small fixed with colour coded values:

23-Feb-99Lecture 28 Resistance zCharge tends to flow from a higher voltage (potential) to a lower voltage zDetermine direction of the current. If not labelled - GUESS the direction. zPotential of resistor where the current enters is positive and leaves is negative. z(If guess is wrong - just get negative voltage for an answer) 4 V 10  I + _

23-Feb-99Lecture 29 Conductance zSometimes easier to use inverse of resistance called conductance zSymbol: G zUnits:Siemens S (mhos) zG = R -1 ze.g. 2  = 0.5 S zNB: Useful when resistors are connected in parallel

23-Feb-99Lecture 210 Some Analogies zChargeVolume (of gas) zVoltagePressure zCurrentFlow Rate zResistanceConstriction

23-Feb-99Lecture 211 Series and Parallel Elements zSeries elements have the same current zShare voltage z Parallel elements have the same voltage z Share current i a (t) i c (t) i b (t)i(t) + v(t) - i(t) + v a (t) - + v b (t) - + v c (t) - + v(t) -

23-Feb-99Lecture 212 Kirchoff’s Voltage Law zThe sum of the voltages around a closed path is zero:  (closed path) V = 0 zConvention is to move around a closed loop in a clockwise direction zAnalogy - Walk around campus zHow do you specify the polarity of voltages in the circuit?

23-Feb-99Lecture 213 Kirchoffs Voltage Law - example + - I R1R1 R2R2 V1V1 +_+_ V2V2 +_+_ VsVs z Example: If V s = 12 V and R 1 = R 2, then V 1 = V 2 = 6 V

23-Feb-99Lecture 214 Series Resistance zVzV s = V 1 + V 2 + …….+ V nwhere e.g. V 1 = R 1 I by Ohm’s Law zVzV s = R 1 I + R 2 I + …….+ R n I zVzV s = (R 1 + R 2 + …….+ R n )I zTzThus R eq = R 1 + R 2 + …….+ R n I + - VsVs + V n - RnRn + V 2 - R2R2 + V 1 - R1R1

23-Feb-99Lecture 215 Lecture Exercise I VXVX + -

23-Feb-99Lecture 216 Kirchoff’s Current Law zTotal charge (current) accumulating at a node is zero:  (entering) I -  (leaving) I = 0 zConvention is current entering a node is positive and leaving a node is negative zAnalogy - road intersection zHow do you specify the direction of current if it is not given?

23-Feb-99Lecture 217 Kirchoff’s Current Law - example I 1 + I 3 - I 2 = 0 node I1I1 I2I2 I3I3

23-Feb-99Lecture 218 Parallel resistance zIzI s = I 1 + I 2 + …..+ I n z[z[ I = V. 1/R = V G ] zIzI s = VG 1 + VG VG n zIzI s = V (G 1 + G G n ) zIzI s = V G eq zGzG eq = G 1 + G G n z1z1 /R eq = 1/R 1 + 1/R /R n IsIs R2R2 R1R1 +V_+V_ RnRn I1I1 I2I2 InIn

23-Feb-99Lecture 219 Two Parallel Resistors z1/R eq = 1/R 1 + 1/R 2 = (R 1 + R 2 )/ R 1.R 2 zR eq = R 1.R 2 / (R 1 + R 2 ) VsVs R2R2 R1R1 I1I1 I2I2 +-+-

23-Feb-99Lecture 220 Current Division z NB: more current flows through path of lesser resistance R2R2 R1R1 I1I1 I2I VsVs +_+_

23-Feb-99Lecture 221 Voltage Division VsVs + - I R1R1 R2R2 V1V1 +_+_ V2V2 +_+_

23-Feb-99Lecture 222 Series Sources zIdeal independent voltage sources in series add algebraically zNB cases of parallel voltage sources are not resolvable. WHY? + - I V1V1 V2V2 V3V3 VnVn - V R + R I

23-Feb-99Lecture 223 Parallel Sources zIdeal independent current sources in parallel add algebraically zNB cases of series current sources are not resolvable. WHY? InIn I3I3 I2I2 I1I1 R +V_+V_ ITIT

23-Feb-99Lecture 224 Example z R 2 and R 3 are effectively open circuited and therefore can be omitted z R 7 and R 8 are short circuited, and can be omitted

23-Feb-99Lecture 225 Example continues

23-Feb-99Lecture 226 Wye Delta Transformations z Need to find equivalent resistance to determine current. HOW? (They are not in series, not in parallel) z Use Y to  transformation

23-Feb-99Lecture 227 Equating Resistance's zResistance between X - Y zIn   R a // (R b + R c ) zIn Y  R 1 + R 3 RbRb RaRa RcRc R1R1 R2R2 R3R3 X X Y Y Z Z

23-Feb-99Lecture 228 Solving simultaneously …. zTo obtain R 1, R 2, R 3 in terms of R a, R b, R c zand vice versa

23-Feb-99Lecture 229 Example cont. X Y Z Y XZ

23-Feb-99Lecture 230 Linearity zA linear circuit is one that contains only linear elements. zResistors, Voltage & Current sources, Inductors and Capacitors are linear elements. zAn example of a nonlinear element is a lamp or a diode. A diode allows current to flow freely in one direction, but blocks the flow of current in the other. zPower is not linear due to V 2 or I 2 !

23-Feb-99Lecture 231 Superposition zWhat to do when there is more than one source in a circuit? zSUPERPOSITION - If a linear circuit is excited by more than one independent source, then the total response is simply the sum of the responses of the individual sources. zHow do you temporarily remove sources? yVoltage source by a short circuit yCurrent sources by an open circuit

23-Feb-99Lecture 232 Superposition example +-+- VsVs R1R1 R2R2 R3R3 IsIs IR2IR2