PRINCIPLES AND APPLICATIONS OF ELECTRICAL ENGINEERING THIRD EDITION

PRINCIPLES AND APPLICATIONS OF ELECTRICAL ENGINEERING THIRD EDITION C H A P T E R 2 Fundamentals of Electrical Circuits Mc. Graw-Hill 1 GIORGIO RIZZONI © The Mc. Graw-Hill Companies, Inc. 2000

PRINCIPLES AND APPLICATIONS OF ELECTRICAL ENGINEERING THIRD EDITION Figure 2. 4 (a) Automotive circuits Mc. Graw-Hill 2 GIORGIO RIZZONI © The Mc. Graw-Hill Companies, Inc. 2000

PRINCIPLES AND APPLICATIONS OF ELECTRICAL ENGINEERING THIRD EDITION Figure 2. 4 (b) Equivalent electrical circuit Ibatt Ihead Itail Istart Ifan I locks Idash + Vbatt – (b) Mc. Graw-Hill 3 GIORGIO RIZZONI © The Mc. Graw-Hill Companies, Inc. 2000

PRINCIPLES AND APPLICATIONS OF ELECTRICAL ENGINEERING THIRD EDITION Figure 2. 8 (a) Electrical vehicle battery pack Vbatt 1 Vbatt 2 Vbattn 12 V 12 V DC-AC converter (electric drive) AC motor (a) Mc. Graw-Hill 4 GIORGIO RIZZONI © The Mc. Graw-Hill Companies, Inc. 2000

PRINCIPLES AND APPLICATIONS OF ELECTRICAL ENGINEERING THIRD EDITION Figure 2. 8 (b) Illustration of KVL vbatt 2 vbatt 31 + –+ – vbatt 1 + + Power converter and motor – vdrive – (b) Mc. Graw-Hill 5 GIORGIO RIZZONI © The Mc. Graw-Hill Companies, Inc. 2000

PRINCIPLES AND APPLICATIONS OF ELECTRICAL ENGINEERING THIRD EDITION i i + v – + v Load Source Figure 2. 10 Various representations of an electrical system i Power flow (a) Conceptual representation Mc. Graw-Hill VS _+ R – (b) Symbolic (circuit) representation 6 GIORGIO RIZZONI + – Car battery Headlight (c) Physical representation © The Mc. Graw-Hill Companies, Inc. 2000

PRINCIPLES AND APPLICATIONS OF ELECTRICAL ENGINEERING THIRD EDITION Figure 2. 18 Volt-ampere characteristic of a tungsten light bulb i (amps) 0. 5 0. 4 0. 3 0. 2 0. 1 – 60 – 50 – 40 – 30 – 20 – 10 0 – 0. 1 Current meter Variable voltage source Mc. Graw-Hill i – 0. 2 + – 0. 3 v – 0. 4 – 10 20 30 40 50 60 v (volts) – 0. 5 7 GIORGIO RIZZONI © The Mc. Graw-Hill Companies, Inc. 2000

PRINCIPLES AND APPLICATIONS OF ELECTRICAL ENGINEERING THIRD EDITION Figure 2. 20 The resistance element i i + l R= l A R v 1/R – A Physical resistors with resistance R. Typical materials are carbon, metal film. Mc. Graw-Hill v Circuit symbol 8 GIORGIO RIZZONI i-v characteristic © The Mc. Graw-Hill Companies, Inc. 2000

PRINCIPLES AND APPLICATIONS OF ELECTRICAL ENGINEERING THIRD EDITION Figure 2. 22 Resistor color code b 4 b b 3 2 b 1 Color bands black brown red orange yellow green 0 1 2 3 4 5 blue violet gray white silver gold 6 7 8 9 10% 5% Resistor value = ( b 1 b 2 ) 10 b 3; b 4 = % tolerance in actual value Mc. Graw-Hill 9 GIORGIO RIZZONI © The Mc. Graw-Hill Companies, Inc. 2000

PRINCIPLES AND APPLICATIONS OF ELECTRICAL ENGINEERING THIRD EDITION Figure 2. 30 R + v 1. 5 V _+ i – v The current i flows through each of the four series elements. Thus, by KVL, – + + v – R 1. 5 = v 1+ v 2+ v 3 R N R n R EQ R 3 N series resistors are equivalent to a single resistor equal to the sum of the individual resistances. R 2 R 1 Mc. Graw-Hill 10 GIORGIO RIZZONI © The Mc. Graw-Hill Companies, Inc. 2000

PRINCIPLES AND APPLICATIONS OF ELECTRICAL ENGINEERING THIRD EDITION Figure 2. 32 Parallel circuits KCL applied at this node i. S + i 1 i 2 i 3 R 1 R 2 R 3 v – The voltage v appears across each parallel element; by KCL, i S = i 1 + i 2 + i 3 Mc. Graw-Hill R 1 R 2 R 3 Rn RN REQ N resistors in parallel are equivalent to a single equivalent resistor with resistance equal to the inverse of the sum of the inverse resistances. 11 GIORGIO RIZZONI © The Mc. Graw-Hill Companies, Inc. 2000

PRINCIPLES AND APPLICATIONS OF ELECTRICAL ENGINEERING THIRD EDITION Figure 2. 36 Wheatstone bridge circuits R 1 + v. S _ a + _ R 3 va v b R 2 (a) v. S c Rx d b c R 1 a va R 2 vb R 3 b Rx d (b) Mc. Graw-Hill 12 GIORGIO RIZZONI © The Mc. Graw-Hill Companies, Inc. 2000

PRINCIPLES AND APPLICATIONS OF ELECTRICAL ENGINEERING THIRD EDITION Figure 2. 37 A force-measuring instrument F c ia + R 2 , R 3 bonded to bottom surface Beam cross section R 3 v. S va – R 2 vb R 4 h w Mc. Graw-Hill R 1 ib 13 GIORGIO RIZZONI d © The Mc. Graw-Hill Companies, Inc. 2000

PRINCIPLES AND APPLICATIONS OF ELECTRICAL ENGINEERING THIRD EDITION Figure 2. 38 Practical voltage source r. S Practical voltage source i. S + v. S _+ v. L RL – i. S = lim i S = RL r. S i. S 0 v. S r. S + R L v. S r. S max + v. S + _ v. L – The maximum (short circuit) current which can be supplied by a practical voltage source is i. S max = v. S r. S Mc. Graw-Hill 14 GIORGIO RIZZONI © The Mc. Graw-Hill Companies, Inc. 2000

PRINCIPLES AND APPLICATIONS OF ELECTRICAL ENGINEERING THIRD EDITION Figure 2. 39 Practical current source A model for practical current sources consists of an ideal source in parallel with an internal resistance. Maximum output voltage for practical current source with open-circuit load: v. S Mc. Graw-Hill max + i. S r. S v. S RL – + i. S r S v S – = i S r. S 15 GIORGIO RIZZONI © The Mc. Graw-Hill Companies, Inc. 2000

PRINCIPLES AND APPLICATIONS OF ELECTRICAL ENGINEERING THIRD EDITION Figure 2. 41 Measurement of current R 1 A A v. S + _ R 2 v. S +_ i Symbol for ideal ammeter Mc. Graw-Hill A series circuit i R 2 Circuit for the measurement of the current i 16 GIORGIO RIZZONI © The Mc. Graw-Hill Companies, Inc. 2000

PRINCIPLES AND APPLICATIONS OF ELECTRICAL ENGINEERING THIRD EDITION Figure 2. 42 Measurement of voltage R 1 + v. S + _ v 2 R 2 i – A series circuit Mc. Graw-Hill V Ideal voltmeter v. S +_ + + v 2 R 2 V v 2 – – i Circuit for the measurement of the voltage v 2 17 GIORGIO RIZZONI © The Mc. Graw-Hill Companies, Inc. 2000

PRINCIPLES AND APPLICATIONS OF ELECTRICAL ENGINEERING THIRD EDITION Figure 2. 43 Models for practical ammeter and voltmeter rm V Practical voltmeter A rm Practical ammeter Mc. Graw-Hill 18 GIORGIO RIZZONI © The Mc. Graw-Hill Companies, Inc. 2000

PRINCIPLES AND APPLICATIONS OF ELECTRICAL ENGINEERING THIRD EDITION Figure 2. 44 Measurement of power i R 1 W A + v. S _+ v 2 R 2 – Measurement of the power dissipated in the resistor R 2: P 2 = v 2 i Mc. Graw-Hill + v. S +_ V v 2 R 2 – Internal wattmeter connections 19 GIORGIO RIZZONI © The Mc. Graw-Hill Companies, Inc. 2000

PRINCIPLES AND APPLICATIONS OF ELECTRICAL ENGINEERING THIRD EDITION Figure 2. 45 Definition of a branch a i + A Branch v voltage Branch R current – rm A branch b Ideal resistor A battery Practical ammeter Examples of circuit branches Mc. Graw-Hill 20 GIORGIO RIZZONI © The Mc. Graw-Hill Companies, Inc. 2000

PRINCIPLES AND APPLICATIONS OF ELECTRICAL ENGINEERING THIRD EDITION Figure 2. 47 Definition of a node Node a Node c Node a i. S v. S Node b Examples of nodes in practical circuits Mc. Graw-Hill 21 GIORGIO RIZZONI © The Mc. Graw-Hill Companies, Inc. 2000

PRINCIPLES AND APPLICATIONS OF ELECTRICAL ENGINEERING THIRD EDITION Figure 2. 48 Definition of a loop Note how two different loops in the same circuit may include some of the same elements or branches. Loop 1 Loop 2 R R 2 i. S 1 -loop circuit 3 -loop circuit (How many nodes in this circuit? ) Loop 3 Mc. Graw-Hill R 1 v. S 22 GIORGIO RIZZONI © The Mc. Graw-Hill Companies, Inc. 2000

PRINCIPLES AND APPLICATIONS OF ELECTRICAL ENGINEERING THIRD EDITION Figure 2. 49 Definition of a mesh How many loops can you identify in this four-mesh circuit? (Answer: 14) R 4 R 3 Mesh 3 R 1 + v. S _ Mc. Graw-Hill Mesh 1 R 2 Mesh 3 23 GIORGIO RIZZONI Mesh 4 R 5 i. S © The Mc. Graw-Hill Companies, Inc. 2000