1. RESISTIVE CIRCUIT
Topic 2

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

3. SERIES/PARALLEL RESISTOR
Resistors that are arranged in series:
Resistance equivalent
Req = R1 + R2 + ……….+ RN

4. CURRENT IN SERIES CIRCUIT
Current in series circuit is same at all circuit elements
VOLTAGE IN SERIES CIRCUIT
Voltage (VT) in series circuit is the total of voltage for each elements.

5. Resistors that are arranged in parallel:

6. Resistance equivalent:

7. For circuits with two resistors in parallel:

8. CURRENT IN PARALLEL CIRCUIT
Current in parallel circuits is the total current for each of the circuit elements.
VOLTAGE IN PARALLEL CIRCUIT
Voltage (VT) for parallel circuits is the same for all circuits elements

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

10. VOLTAGE DIVIDER 1 R 2 V _ + I -

11. Using Ohm law, we will get:
Voltage at resistor R2:

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

13. CURRENT DIVIDER

14. Using Ohm law, (1)

15. From equation (1):

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

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

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

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. The Wheatstone bridge circuit:

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

24. Solving these equation, yields

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

26. DELTA-WYE (PI-TEE) CIRCUIT
If the galvanometer in Wheatstone bridge is replace with its equivalent resistance Rm,

27. The resistor R1, R2 and Rm (or R3, Rm dan Rx) are referred as a delta (∆) interconnection. It also is referred as a pi (π) interconnection because the ∆ can be shaped into a π without disturbing the electrical equivalance of the two confiurations.

28. Delta configuration

29. The resistors R1, Rm and R3 (or R2, Rm and Rx) 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. Wye configuration

31. The ∆ - Y transformation

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

33. Using straightforward algebraic manipulation gives,

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

35. EXAMPLE 1
Find the current and power supplied by the 40V sources in the circuit shown below.

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

38. Substituting the Y-resistor into the circuit,

39. The equivalent circuit,

40. Calculate the equivalent resistance,

41. Simplification of the circuit,

42. Then, the current and power values are,

43. Example 2

44. Find no load value of vo.
Find vo when RL = 150kΩ
How much power is dissipated in the 25kΩ resistor if the load terminals are accidentl short-circuited?

45. Answer: a) b)

46. c)

47. EXAMPLE 3
Find the power dissipated in the
6Ω resistor.

48. Equivalent resistance
Asnwer
Equivalent resistance
current io,

49. Note that io is the current in the 1.6Ω resistor.
Use current divider to get current in the 6Ω resistor,

50. Then the power dissipated by the resistor is

51. EXAMPLE 4
Find the voltage of vo and vg.

52. Asnwer
Equivalent resistance
Current in resistor 30Ω

53. Voltage v0
Total voltage at the resistor

54. Voltage vg

55. EXAMPLE 5
Find the current of ig and.io

56. Equivalent resistance:
Answer
Equivalent resistance:

57. Current values,

58. Thus,

59. EXAMPLE 6
Determine the value of io