1. © The McGraw-Hill Companies, Inc. 2000 McGraw-Hill 1 PRINCIPLES AND APPLICATIONS OF ELECTRICAL ENGINEERING THIRD EDITION G I O R G I O R I Z Z O N I C H A P T E R 2 Fundamentals of Electrical Circuits

2. © The McGraw-Hill Companies, Inc. 2000 McGraw-Hill 2 PRINCIPLES AND APPLICATIONS OF ELECTRICAL ENGINEERING THIRD EDITION G I O R G I O R I Z Z O N I Overview This chapter deals with: The definition of current, voltage and power Voltage and current sources, dependent sources Resistance: Linear and Nonlinear Equivalent of series and parallel resistance Measuring devices, voltmeter, ammeter,..

3. © The McGraw-Hill Companies, Inc. 2000 McGraw-Hill 3 PRINCIPLES AND APPLICATIONS OF ELECTRICAL ENGINEERING THIRD EDITION G I O R G I O R I Z Z O N I Current, Voltage, Power Definition Electrons are the main element that their flow makes electric current. Convention: The opposite direction of electron flow is defined the positive direction of current(By Ben Franklin) since the charge of electron is negative. The charge of electron is:1.6*10 -19 Coulomb

4. © The McGraw-Hill Companies, Inc. 2000 McGraw-Hill 4 PRINCIPLES AND APPLICATIONS OF ELECTRICAL ENGINEERING THIRD EDITION G I O R G I O R I Z Z O N I Current, Voltage, Power Definition Coulomb is the unit of charge and each coulomb charge is equivalent to the charge of 6.25*10 18 electron. Electric current is the flow of electric charges, the unit of electric current is ampere (A). Each ampere is equivalent to the flow of one coulomb in one second: I=Q/t

5. © The McGraw-Hill Companies, Inc. 2000 McGraw-Hill 5 PRINCIPLES AND APPLICATIONS OF ELECTRICAL ENGINEERING THIRD EDITION G I O R G I O R I Z Z O N I Current, Voltage, Power Definition For example if a capacitor charges with one ampere, in one second the increase in capacitor charge will be one coulomb dQ=I*dt I=dQ/dt Electric charges make electric field in their vicinity, so moving other charges in this field requires energy.

6. © The McGraw-Hill Companies, Inc. 2000 McGraw-Hill 6 PRINCIPLES AND APPLICATIONS OF ELECTRICAL ENGINEERING THIRD EDITION G I O R G I O R I Z Z O N I Current, Voltage, Power Definition If for moving the unit of charge(Coulomb) from point A to point B requires one Joule energy, we say the potential between point A and B is one Volt. 1 volt = 1 joule/coulomb The power is defined as energy per time Power=energy/time=energy/charge*charge/ time=V*I So P=V*I

7. © The McGraw-Hill Companies, Inc. 2000 McGraw-Hill 7 PRINCIPLES AND APPLICATIONS OF ELECTRICAL ENGINEERING THIRD EDITION G I O R G I O R I Z Z O N I Voltage, Current source and Load The voltage source generate voltage and the current comes out of its positive terminal. The current source generate current and the current comes out its positive terminal. The load consumes electric power and the current goes in its positive terminal.

8. © The McGraw-Hill Companies, Inc. 2000 McGraw-Hill 8 PRINCIPLES AND APPLICATIONS OF ELECTRICAL ENGINEERING THIRD EDITION G I O R G I O R I Z Z O N I

9. © The McGraw-Hill Companies, Inc. 2000 McGraw-Hill 9 PRINCIPLES AND APPLICATIONS OF ELECTRICAL ENGINEERING THIRD EDITION G I O R G I O R I Z Z O N I

10. © The McGraw-Hill Companies, Inc. 2000 McGraw-Hill 10 PRINCIPLES AND APPLICATIONS OF ELECTRICAL ENGINEERING THIRD EDITION G I O R G I O R I Z Z O N I

11. © The McGraw-Hill Companies, Inc. 2000 McGraw-Hill 11 PRINCIPLES AND APPLICATIONS OF ELECTRICAL ENGINEERING THIRD EDITION G I O R G I O R I Z Z O N I

12. © The McGraw-Hill Companies, Inc. 2000 McGraw-Hill 12 PRINCIPLES AND APPLICATIONS OF ELECTRICAL ENGINEERING THIRD EDITION G I O R G I O R I Z Z O N I

13. © The McGraw-Hill Companies, Inc. 2000 McGraw-Hill 13 PRINCIPLES AND APPLICATIONS OF ELECTRICAL ENGINEERING THIRD EDITION G I O R G I O R I Z Z O N I

14. © The McGraw-Hill Companies, Inc. 2000 McGraw-Hill 14 PRINCIPLES AND APPLICATIONS OF ELECTRICAL ENGINEERING THIRD EDITION G I O R G I O R I Z Z O N I

15. © The McGraw-Hill Companies, Inc. 2000 McGraw-Hill 15 PRINCIPLES AND APPLICATIONS OF ELECTRICAL ENGINEERING THIRD EDITION G I O R G I O R I Z Z O N I

16. © The McGraw-Hill Companies, Inc. 2000 McGraw-Hill 16 PRINCIPLES AND APPLICATIONS OF ELECTRICAL ENGINEERING THIRD EDITION G I O R G I O R I Z Z O N I

17. © The McGraw-Hill Companies, Inc. 2000 McGraw-Hill 17 PRINCIPLES AND APPLICATIONS OF ELECTRICAL ENGINEERING THIRD EDITION G I O R G I O R I Z Z O N I

18. © The McGraw-Hill Companies, Inc. 2000 McGraw-Hill 18 PRINCIPLES AND APPLICATIONS OF ELECTRICAL ENGINEERING THIRD EDITION G I O R G I O R I Z Z O N I Ideal and practical sources An ideal voltage source has a fixed voltage independent of its current( its internal series resistance is zero) The voltage of a practical voltage source depends on its current( its internal series resistance is not zero). The ideal current source has infinite parallel resistance while practical current source has finite parallel resistance.

19. © The McGraw-Hill Companies, Inc. 2000 McGraw-Hill 19 PRINCIPLES AND APPLICATIONS OF ELECTRICAL ENGINEERING THIRD EDITION G I O R G I O R I Z Z O N I Kirchhoff’s voltage/current law, Ohm’s law Kirchhoff’s current law: The sum of the currents entering a node is zero. Kirchhoff’s voltage law: The sum of the voltages around a loop is zero. Ohm’s law: V =I * R With this basic laws we can solve resistive circuits and find current and voltage of each branch. More sophisticated techniques will be presented in the next chapter.

20. © The McGraw-Hill Companies, Inc. 2000 McGraw-Hill 20 PRINCIPLES AND APPLICATIONS OF ELECTRICAL ENGINEERING THIRD EDITION G I O R G I O R I Z Z O N I Figure 2.47 Definition of a node Examples of nodes in practical circuits Node a Node b v S i S Node cNode a Node b Node

21. © The McGraw-Hill Companies, Inc. 2000 McGraw-Hill 21 PRINCIPLES AND APPLICATIONS OF ELECTRICAL ENGINEERING THIRD EDITION G I O R G I O R I Z Z O N I Figure 2.49 Definition of a mesh

22. © The McGraw-Hill Companies, Inc. 2000 McGraw-Hill 22 PRINCIPLES AND APPLICATIONS OF ELECTRICAL ENGINEERING THIRD EDITION G I O R G I O R I Z Z O N I Dependent Sources These are also current and voltage sources but their value depends on a specified voltage or current in circuit. There are 4 types of dependent sources: Voltage controlled voltage source. Voltage controlled current source. Current controlled voltage source. Current controlled current source.

23. © The McGraw-Hill Companies, Inc. 2000 McGraw-Hill 23 PRINCIPLES AND APPLICATIONS OF ELECTRICAL ENGINEERING THIRD EDITION G I O R G I O R I Z Z O N I Figure 2.4 (a) Automotive circuits

24. © The McGraw-Hill Companies, Inc. 2000 McGraw-Hill 24 PRINCIPLES AND APPLICATIONS OF ELECTRICAL ENGINEERING THIRD EDITION G I O R G I O R I Z Z O N I Figure 2.4 (b) Equivalent electrical circuit

25. © The McGraw-Hill Companies, Inc. 2000 McGraw-Hill 25 PRINCIPLES AND APPLICATIONS OF ELECTRICAL ENGINEERING THIRD EDITION G I O R G I O R I Z Z O N I Figure 2.8 (a) Electrical vehicle battery pack

26. © The McGraw-Hill Companies, Inc. 2000 McGraw-Hill 26 PRINCIPLES AND APPLICATIONS OF ELECTRICAL ENGINEERING THIRD EDITION G I O R G I O R I Z Z O N I Figure 2.8 (b) Illustration of KVL (b) Power converter and motor v batt1 + – v drive + – v batt2 +– v batt3 +– v batt31 +–

27. © The McGraw-Hill Companies, Inc. 2000 McGraw-Hill 27 PRINCIPLES AND APPLICATIONS OF ELECTRICAL ENGINEERING THIRD EDITION G I O R G I O R I Z Z O N I Figure 2.10 Various representations of an electrical system Headlight Car battery +– R i i + – v Source Load (a) Conceptual representation Power flow (b) Symbolic (circuit) representation (c) Physical representation + _ i + – v V S

28. © The McGraw-Hill Companies, Inc. 2000 McGraw-Hill 28 PRINCIPLES AND APPLICATIONS OF ELECTRICAL ENGINEERING THIRD EDITION G I O R G I O R I Z Z O N I Figure 2.20 The resistance element

29. © The McGraw-Hill Companies, Inc. 2000 McGraw-Hill 29 PRINCIPLES AND APPLICATIONS OF ELECTRICAL ENGINEERING THIRD EDITION G I O R G I O R I Z Z O N I Figure 2.22 Resistor color code b 4 b 3 b 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

30. © The McGraw-Hill Companies, Inc. 2000 McGraw-Hill 30 PRINCIPLES AND APPLICATIONS OF ELECTRICAL ENGINEERING THIRD EDITION G I O R G I O R I Z Z O N I

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33. © The McGraw-Hill Companies, Inc. 2000 McGraw-Hill 33 PRINCIPLES AND APPLICATIONS OF ELECTRICAL ENGINEERING THIRD EDITION G I O R G I O R I Z Z O N I

34. © The McGraw-Hill Companies, Inc. 2000 McGraw-Hill 34 PRINCIPLES AND APPLICATIONS OF ELECTRICAL ENGINEERING THIRD EDITION G I O R G I O R I Z Z O N I Figure 2.18 Volt-ampere characteristic of a tungsten light bulb

35. © The McGraw-Hill Companies, Inc. 2000 McGraw-Hill 35 PRINCIPLES AND APPLICATIONS OF ELECTRICAL ENGINEERING THIRD EDITION G I O R G I O R I Z Z O N I

36. © The McGraw-Hill Companies, Inc. 2000 McGraw-Hill 36 PRINCIPLES AND APPLICATIONS OF ELECTRICAL ENGINEERING THIRD EDITION G I O R G I O R I Z Z O N I

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38. © The McGraw-Hill Companies, Inc. 2000 McGraw-Hill 38 PRINCIPLES AND APPLICATIONS OF ELECTRICAL ENGINEERING THIRD EDITION G I O R G I O R I Z Z O N I

39. © The McGraw-Hill Companies, Inc. 2000 McGraw-Hill 39 PRINCIPLES AND APPLICATIONS OF ELECTRICAL ENGINEERING THIRD EDITION G I O R G I O R I Z Z O N I Figure 2.30 The current 1.5 V + _ R v+– v–+ + – v i R i flows through each of the four series elements. Thus, by KVL, 1.5 =v 1 + v 2 + v 3 R 1 R 2 R 3 R n R N R EQ N series resistors are equivalent to a single resistor equal to the sum of the individual resistances.

40. © The McGraw-Hill Companies, Inc. 2000 McGraw-Hill 40 PRINCIPLES AND APPLICATIONS OF ELECTRICAL ENGINEERING THIRD EDITION G I O R G I O R I Z Z O N I Figure 2.32 Parallel circuits

41. © The McGraw-Hill Companies, Inc. 2000 McGraw-Hill 41 PRINCIPLES AND APPLICATIONS OF ELECTRICAL ENGINEERING THIRD EDITION G I O R G I O R I Z Z O N I Figure 2.36 Wheatstone bridge circuits

42. © The McGraw-Hill Companies, Inc. 2000 McGraw-Hill 42 PRINCIPLES AND APPLICATIONS OF ELECTRICAL ENGINEERING THIRD EDITION G I O R G I O R I Z Z O N I Figure 2.37 A force-measuring instrument

43. © The McGraw-Hill Companies, Inc. 2000 McGraw-Hill 43 PRINCIPLES AND APPLICATIONS OF ELECTRICAL ENGINEERING THIRD EDITION G I O R G I O R I Z Z O N I Figure 2.38 Practical voltage source

44. © The McGraw-Hill Companies, Inc. 2000 McGraw-Hill 44 PRINCIPLES AND APPLICATIONS OF ELECTRICAL ENGINEERING THIRD EDITION G I O R G I O R I Z Z O N I Figure 2.39 Practical current source

45. © The McGraw-Hill Companies, Inc. 2000 McGraw-Hill 45 PRINCIPLES AND APPLICATIONS OF ELECTRICAL ENGINEERING THIRD EDITION G I O R G I O R I Z Z O N I Figure 2.41 Measurement of current

46. © The McGraw-Hill Companies, Inc. 2000 McGraw-Hill 46 PRINCIPLES AND APPLICATIONS OF ELECTRICAL ENGINEERING THIRD EDITION G I O R G I O R I Z Z O N I Figure 2.42 Measurement of voltage

47. © The McGraw-Hill Companies, Inc. 2000 McGraw-Hill 47 PRINCIPLES AND APPLICATIONS OF ELECTRICAL ENGINEERING THIRD EDITION G I O R G I O R I Z Z O N I Figure 2.43 Models for practical ammeter and voltmeter r m A Practical ammeter V Practical voltmeter r m

48. © The McGraw-Hill Companies, Inc. 2000 McGraw-Hill 48 PRINCIPLES AND APPLICATIONS OF ELECTRICAL ENGINEERING THIRD EDITION G I O R G I O R I Z Z O N I Figure 2.44 Measurement of power i

49. © The McGraw-Hill Companies, Inc. 2000 McGraw-Hill 49 PRINCIPLES AND APPLICATIONS OF ELECTRICAL ENGINEERING THIRD EDITION G I O R G I O R I Z Z O N I Figure 2.45 Definition of a branch a

50. © The McGraw-Hill Companies, Inc. 2000 McGraw-Hill 50 PRINCIPLES AND APPLICATIONS OF ELECTRICAL ENGINEERING THIRD EDITION G I O R G I O R I Z Z O N I Figure 2.47 Definition of a node Examples of nodes in practical circuits Node a Node b v S i S Node cNode a Node b Node

51. © The McGraw-Hill Companies, Inc. 2000 McGraw-Hill 51 PRINCIPLES AND APPLICATIONS OF ELECTRICAL ENGINEERING THIRD EDITION G I O R G I O R I Z Z O N I Figure 2.48 Definition of a loop

52. © The McGraw-Hill Companies, Inc. 2000 McGraw-Hill 52 PRINCIPLES AND APPLICATIONS OF ELECTRICAL ENGINEERING THIRD EDITION G I O R G I O R I Z Z O N I Figure 2.49 Definition of a mesh

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