1. 1 CHAPTER 2 EET 101 [Electric Circuit I]: V2009 School of Computer and Communication Engineering, UniMAP Prepared By: Prepared By: Wan Nur Suryani Firuz bt Wan Ariffin Amir Razif A. b. Jamil Abdullah Resistive Circuit

2. 2 RESISTIVE CIRCUIT  Series/parallel resistor  Voltage divider circuit  Current divider circuit  Voltage and current measurement  Wheatstone bridge  Delta-wye (Pi-Tee) equivalent circuit

3. 3 SERIES/PARALLEL RESISTOR  Resistors in series: Resistance equivalent R eq = R 1 + R 2 + ……….+ R N

4. 4 Current in Series Circuit  Current in series circuit is same at all circuit elements VOLTAGE IN SERIES CIRCUIT  Voltage (V T ) in series circuit is the total of voltage for each elements.

5. 5 Resistors in Parallel

6. 6 Equivalent Resistors in Parallel:

7. 7  Two resistors in parallel:

8. 8 Current in Parallel Circuit  Currents in parallel circuit is the total of current for each elements. VOLTAGE IN PARALLEL CIRCUIT  Voltage (V T ) in parallel circuit is same at all circuit elements.

9. 9 Example #1  Find the equivalent resistor (R eq ) in the circuit.

10. 10 RESISTIVE CIRCUIT  Series/parallel resistor  Voltage divider circuit  Current divider circuit  Voltage and current measurement  Wheatstone bridge  Delta-wye (Pi-Tee) equivalent circuit

11. 11 Voltage Divider 2 2 2

12. 12  Using Ohm law, we will get:  Voltage at resistor R 2 :

13. 13 RESISTIVE CIRCUIT Series/parallel resistorSeries/parallel resistor Voltage divider circuitVoltage divider circuit Current divider circuitCurrent divider circuit Voltage and current measurementVoltage and current measurement Wheatstone bridgeWheatstone bridge Delta-wye (Pi-Tee) equivalent circuitDelta-wye (Pi-Tee) equivalent circuit

14. 14 Current Divider

15. 15  From the Ohm’s law, (1)

16. 16  Series/parallel resistor  Voltage divider circuit  Current divider circuit  Voltage and current measurement  Wheatstone bridge  Delta-wye (Pi-Tee) equivalent circuit RESISTIVE CIRCUIT

17. 17 Voltage and Current Measurement  An ammeter is an instrument designed to measure current.  It is placed in series with the circuit element whose current is being measured.  An ideal ammeter has an equivalent resistance of 0Ω and functions as a short circuit in series with the element whose current is being measured.

18. 18  A voltmeter is an instrument designed to measure voltage.  It is placed in parallel with the element whose voltage is being measured.  An ideal voltmeter has an infinite equivalent resistance and thus functions as an open circuit in parallel with the element whose voltage is being measured.

19. 19  The configurations for an ammeter and voltmeter to measure current and voltage

20. 20 RESISTIVE CIRCUIT  Series/parallel resistor  Voltage divider circuit  Current divider circuit  Voltage and current measurement  Wheatstone bridge  Delta-wye (Pi-Tee) equivalent circuit

21. 21 Wheatstone Bridge  The Wheatstone bridge circuit is used to precisely measure resistance of medium values, that is in the range of 1Ω to 1MΩ.  The bridge circuit consists of four resistors, a dc voltage source and a detector.

22. 22  The Wheatstone bridge circuit: Wheatstone Bridge

23. 23  When the bridge is balanced:  Combining these equation, gives Wheatstone Bridge

24. 24  Solving these equation, yields Wheatstone Bridge

25. 25  Series/parallel resistor  Voltage divider circuit  Current divider circuit  Voltage and current measurement  Wheatstone bridge  Delta-wye (Pi-Tee) equivalent circuit RESISTIVE CIRCUIT

26. 26 Delta-Wye (PI-TEE) Circuit  If the galvanometer in Wheatstone bridge is replace with its equivalent resistance R m,

27. 27  The resistor R 1, R 2 and R m (or R 3, R m and R x ) are referred as a delta (∆) interconnection.  It is also referred as a pi (π) interconnection because the ∆ can be shaped into a π without disturbing the electrical equivalent of the two configurations.

28. 28  Delta configuration

29. 29  The resistors R 1, R m dan R 3 (or R 2, R m and R x ) are referred as a wye (Y) interconnection because it can be shaped to look like the letter Y.  The Y configuration also referred as a tee (T) interconnection.

30. 30  Wye configuration

31. 31 The ∆ - Y Transformation

32. 32  Using series and parallel simplifications in Δ-connected, yield

33. 33  Using straightforward algebraic manipulation gives,

34. 34  The expression for the three Δ- connected resistors as functions of three Y-connected resistors are

35. 35 Example #2  Find the current and power supplied by the 40 V sources in the circuit shown below.

36. 36 Solution:  We can find this equivalent resistance easily after replacing either the upper Δ (100Ω, 125Ω, 25Ω) or the lower Δ (40Ω, 25Ω, 37.5Ω) with its equivalent Y.  We choose to replace the upper Δ. Thus, Example #2

37. 37 Example #2

38. 38  Substituting the Y-resistor into the circuit,

39. 39  The equivalent circuit,

40. 40  Calculate the equivalent resistance,  Simplify the circuit,

41. 41  Then, the current and power values are,

42. 42 Example #3 Find no load value of v o. Find vo when RL = 150 kΩ How much power is dissipated in the 25 kΩ resistor if the load terminals are short- circuited ?

43. 43 a) b) Example #3

44. 44 c) Example #3

45. 45 Example #4  Find the power dissipated in the 6 Ω resistor.

46. 46 Solution:  Equivalent resistance  current i o, Example #4

47. 47  Note that i o is the current in the 1.6Ω resistor.  Use current divider to get current in the 6Ω resistor,  Then the power dissipated by the resistor is Example #4

48. 48 Example #5  Find the voltage of v o and v g.

49. 49 Solution:  Equivalent resistance  Current in resistor 30Ω Example #5

50. 50  Voltage v 0  Total voltage at the resistor

51. 51  Voltage v g

52. 52 Example #6  Find the current of i g and io in the circuit. Solution:  Equivalent resistance:

53. 53  The current values,  Thus, Example #6

54. 54 Example #7  Determine the value of i o

55. 55 Example #8  Find i and V o

56. 56 Example #9  Calculate the value of current; I.