1. RESISTANCE CIRCUITS

2. RESISTANCE CIRCUITS Series/Parallel Resistor Circuit Voltage Dividers
Circuit Current Dividers
Measurement of Voltage and Current
Wheatstone Bridge
Equal Circuit Delta-Wye (Pi-Tee)

3. Series Resistor

4. Equivalent Resistance
Req = R1 + R2 + ……….+ RN

5. Parallel Resistor

6. Equivalent Resistance

7. For two parallel resistor circuits

8. CIRCUITS VOLTAGE DIVIDER

9. By using Ohm’s law
Voltage on resistor R2

10. Circuit Current Dividers

11. From Ohm’s law (1)

12. From equation (1)

13. Measurement of Voltage and Current
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.

14. 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.

15. Ammeter and Voltmeter configuration

16. WHEATSTONE BRIDGE

17. Galvanometer, G was connected
between parallel path to detect
equilibrium.

18. We found,
I3 R3 = Ix Rx (1)
Balance condition, voltage at R1 and R2 also should be same,
I1 R1 = I2 R2 (2)

19. When no current go through Galvanometer, assume that,
I1 = I3 (3)
Change I3 with I1 and change IX with I2 .we have
I1 R3 = I2Rx (4)

20. Devide eq. (2) and eq. (4), we have (5)
We have, RX as

21. DELTA-WYE CIRCUITS(PI-TEE)
Galvanometer in Wheatstone bridge circuit replace by resistor Rm ,

22. Resistor R1, R2 and Rm (or R3, Rm and Rx) called delta connection (∆) and also called pi (π) .

23. Configuration of delta circuit

24. Resistor R1, Rm and R3 (or R2, Rm and Rx) known as wye (Y) connection
Resistor R1, Rm and R3 (or R2, Rm and Rx) known as wye (Y) connection. This configuration also known as tee (T) connection.

25. Configuration of wye circuit

26. ∆ - Y equivalent circuit

27. By using series-parallel theory, equivalent resistance in ∆ circuit for every terminal pair

28. From previous three equation, we have

29. For Y - ∆ circuits. Y circuits change to ∆ circuit and every path could be found like below.

30. EXAMPLE 1

31. From previous circuit, calculate.
v0 if RL not connected
v0 if RL = 150kΩ
Power absorbed by 25kΩ resistor if terminal load was close circuit.

32. Answer a) b)

33. c)

34. EXAMPLE 2
Calculate power that absorb by resistor
6Ω resistor

35. Answer
Equivalent resistor
find i0,

36. If current that flows through 1
If current that flows through 1.6Ω resistor is i0, current that flows through 4Ω and 6Ω resistor can be calculated

37. Power that obsorb by 6Ω resistor could be calculated as below,

38. Example 3
Calculate current and power that have been supplied by power supply 40V.

39. We can select to have above delta connection (100, 125, 25Ω) or below delta connection (40, 25, 37.5Ω) and change to Y connection. Here we select above delta connection.

40. Insert Y resistance in the circuit

42. Equivalent resistance,

43. Circuit

44. Equivalent circuit

45. Current I and power absorb by circuit

46. Example 3

47. Answer
Equivalent resistance
Current at 30Ω resistor

48. v0
Total drop voltage at resistor

49. vg

50. Example 4

51. Answer
Equivalent resistance

52. Then

53. thus

54. QUIZ 2

55. QUIZ 3