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1. Elektronika AgusSetyo Budi, Dr. M.Sc Sesion #05 JurusanFisika FakultasMatematikadanIlmuPengetahuanAlam

2. Analyzing Series-Parallel Circuits with Random Unknowns The Wheatstone Bridge Troubleshooting: Opens and Shorts in Series-Parallel Circuits 07/01/2011 © 2010 Universitas Negeri Jakarta | www.unj.ac.id | 2

3. 07/01/2011 © 2010 Universitas Negeri Jakarta | www.unj.ac.id | 3 Series - Parallel Circuits

4. Finding RT for Series-Parallel Resistances Overview of Series-Parallel Circuits A series-parallel circuit, or combination circuit, combines both series and parallel connections. Most electronic circuits fall into this category.Series-parallel circuits are typically used when different voltage and current values are required from the same voltage source. Series components form a seriesstring. Parallel components form a parallelbank. 07/01/2011 © 2010 Universitas Negeri Jakarta | www.unj.ac.id | 4

5. 1 3 2 V There are three branches in this circuit; sections 1 and 2 are series strings. Finding RT for Series-Parallel Resistances Overview of Series-Parallel Circuits 07/01/2011 © 2010 Universitas Negeri Jakarta | www.unj.ac.id | 5

6. 1 3 V 2 Finding RT for Series-Parallel Resistances Overview of Series-Parallel Circuits There are three series sections in this circuit; sections 1 and 2 are parallel banks. 07/01/2011 © 2010 Universitas Negeri Jakarta | www.unj.ac.id | 6

7. Finding RT for Series-Parallel Resistances To find RTfor a series-parallel circuit, add the series resistances and combine the parallel resistances. In this diagram, R1 and R2 are in series, and R3and R4 are in parallel. However, R2is not in series with the parallel resistances: Resistances in series have the same current, but the current in R2 is equal to the sum of the branch currents I3and I4. Fig. 6-1b: Schematic diagram of a series-parallel circuit. 07/01/2011 © 2010 Universitas Negeri Jakarta | www.unj.ac.id | 7

8. Finding RT for Series-Parallel Resistances For Fig. 6-1b, The series resistances are: 0.5kΩ + 0.5kΩ = 1kΩ The parallel resistances are: 1kΩ / 2 = 0.5kΩ The series and parallel values are then added for the value of RT: 1kΩ + 0.5kΩ = 1.5 kΩ 07/01/2011 © 2010 Universitas Negeri Jakarta | www.unj.ac.id | 8

9. Resistance Strings in Parallel In this figure, branch 1 has two resistances in series; branch 2 has only one resistance. Ohm’s Law can be applied to each branch, using the same rules for the series and parallel components that were discussed in Chapters 4 and 5. Fig. 6-3a: Series string in parallel with another branch (schematic diagram). 07/01/2011 © 2010 Universitas Negeri Jakarta | www.unj.ac.id | 9

10. Resistance Strings in Parallel Series Circuit Current is the same in all components. V across each series R is I × R. VT = V1 + V2 + V3 +...+ etc. Parallel Circuit Voltage is the same across all branches. I in each branch R is V/R. IT = I1 + I2 + I3 +...+ etc. 07/01/2011 © 2010 Universitas Negeri Jakarta | www.unj.ac.id | 10

11. I is the same in this section. Resistance Strings in Parallel V V is the same across each parallel branch. 07/01/2011 © 2010 Universitas Negeri Jakarta | www.unj.ac.id | 11

12. Resistance Strings in Parallel The current in each branch equals the voltage applied across the branch divided by the branch RT. The total line current equals the sum of the branch currents for all parallel strings. The RT for the entire circuit equals the applied voltage divided by the total line current. For any resistance in a series string, the IR voltage drop across that resistance equals the string’s current multiplied by the resistance. The sum of the voltage drops in the series string equals the voltage across the entire string. 07/01/2011 © 2010 Universitas Negeri Jakarta | www.unj.ac.id | 12

13. Resistance Banks in Series In this figure, R2 and R3 are parallel resistances in a bank. The parallel bank is in series with R1. There may be more than two parallel resistances in a bank, and any number of banks in series. Ohm’s Law is applied to the series and parallel components as seen previously. Fig. 6-4a: Parallel bank of R2 and R3 in series with R1 (Original circuit). 07/01/2011 © 2010 Universitas Negeri Jakarta | www.unj.ac.id | 13

14. V R = 10 Ω (of R2 + R3) I 6Ω = 24V + 1Ω (R1) 2 branches R = 4A 24V 6Ω = 5Ω + 1Ω 6Ω = 4A Resistance Banks in Series To find the total resistance of this type of circuit, combine the parallel resistances in each bank and add the series resistances. 07/01/2011 © 2010 Universitas Negeri Jakarta | www.unj.ac.id | 14

15. Resistance Banks and Strings in Series-Parallel To solve series-parallel (combination) circuits, it is important to know which components are in series with one another and which components are in parallel. Series components must be in one current path without any branch points. To find particular values for this type of circuit, Reduce and combine the components using the rules for individual series and parallel circuits. Reduce the circuit to its simplest possible form. Then solve for the needed values using Ohm’s Law. 07/01/2011 © 2010 Universitas Negeri Jakarta | www.unj.ac.id | 15

16. Resistance Banks and Strings in Series-Parallel Example: Find all currents and voltages in Fig. 6-5. Step 1: Find RT. Step 2: Calculate main line current as IT = VT / RT Fig. 6-5: Reducing a series-parallel circuit to an equivalent series circuit to find the RT. (a) Actual circuit. (b) R3 and R4 in parallel combined for the equivalent RT. 07/01/2011 © 2010 Universitas Negeri Jakarta | www.unj.ac.id | 16

17. Resistance Banks and Strings in Series-Parallel Fig. 6-5, cont. (c) RT and R6 in series added for R13. (d) R13 and R5in parallel combined for R18. 07/01/2011 © 2010 Universitas Negeri Jakarta | www.unj.ac.id | 17

18. Resistance Banks and Strings in Series-Parallel Fig. 6-5e: The R18, R1, and R2in series are added for the total resistance of 50Ω for RT. 07/01/2011 © 2010 Universitas Negeri Jakarta | www.unj.ac.id | 18

19. Analyzing Series-Parallel Circuits with Random Unknowns In solving such circuits, apply the same principles as before: Reduce the circuit to its simplest possible form. Apply Ohm’s Law. 07/01/2011 © 2010 Universitas Negeri Jakarta | www.unj.ac.id | 19

20. Analyzing Series-Parallel Circuits with Random Unknowns Example: In Fig. 6-6, we can find branch currents I1 and I2-3, and IT, and voltage drops V1, V2, and V3, without knowing the value of RT. Fig. 6-6: Finding all the currents and voltages by calculating the branch currents first. 07/01/2011 © 2010 Universitas Negeri Jakarta | www.unj.ac.id | 20

21. V I1 = R (parallel branches have the same voltage) 90V I1 = 30Ω Analyzing Series-Parallel Circuits with Random Unknowns Find I1, I2-3, and IT. I1= 3A 07/01/2011 © 2010 Universitas Negeri Jakarta | www.unj.ac.id | 21

22. V I2-3 = R IT = I1 + I2-3 90V I2-3 = 20Ω + 25Ω IT = 3A + 2A 90V IT = 5A = I2-3 45Ω I2-3 = 2A Analyzing Series-Parallel Circuits with Random Unknowns 07/01/2011 © 2010 Universitas Negeri Jakarta | www.unj.ac.id | 22

23. Analyzing Series-Parallel Circuits with Random Unknowns Find voltage drops V1, V2, and V3: Copyright © The McGraw-Hill Companies, Inc. Permission required for reproduction or display. 07/01/2011 © 2010 Universitas Negeri Jakarta | www.unj.ac.id | 23

24. Analyzing Series-Parallel Circuits with Random Unknowns V1 = VA (parallel branches have the same voltage) V1 = 90V or V1 = I1R1 V2 = I2-3R2 V3 = I2-3R3 V1= 3A × 30ΩV2 = 2A(20 Ω) V3 = 2A(25 Ω) V1 = 90V V2 = 40V V3 = 50V Note: V2 + V3 = VA 40V + 50V = 90V 07/01/2011 © 2010 Universitas Negeri Jakarta | www.unj.ac.id | 24

25. RT 18Ω = VA 90A RT RT = = IT 5A Analyzing Series-Parallel Circuits with Random Unknowns 07/01/2011 © 2010 Universitas Negeri Jakarta | www.unj.ac.id | 25

26. The Wheatstone Bridge A Wheatstone bridge is a circuit that is used to determine the value of an unknown resistance. The unknown resistor (RX) is in the same branch as the standard resistor (RS). Fig. 6-10: Wheatstone bridge. 07/01/2011 © 2010 Universitas Negeri Jakarta | www.unj.ac.id | 26

27. The Wheatstone Bridge Resistors R1 and R2form the ratio arm; they have very tight resistance tolerances. The galvanometer (M1), a sensitive current meter, is connected between the output terminals C and D. When R1 / R2 = R3 / R4, the bridge is balanced. When the bridge is balanced, the current in M1 is zero. 07/01/2011 © 2010 Universitas Negeri Jakarta | www.unj.ac.id | 27

28. The Wheatstone Bridge Using a Wheatstone Bridge to Measure an Unknown Resistance RS is adjusted for zero current in M1.. When the current in M1 = 0A, the voltage division between RX and RS is equal to that between R1 and R2. 07/01/2011 © 2010 Universitas Negeri Jakarta | www.unj.ac.id | 28

29. R1 RX = RS R2 R1 RX RS × = R2 The Wheatstone Bridge Note: When the Wheatstone bridge is balanced, it can be analyzed as two series strings in parallel. Note the following relationship: 07/01/2011 © 2010 Universitas Negeri Jakarta | www.unj.ac.id | 29

30. Troubleshooting: Opens and Shorts in Series-Parallel Circuits In series-parallel circuits, an open or short in one part of the circuit changes the values in the entire circuit. When troubleshooting series-parallel circuits, combine the techniques used when troubleshooting individual series and parallel circuits. 07/01/2011 © 2010 Universitas Negeri Jakarta | www.unj.ac.id | 30

31. Troubleshooting: Opens and Shorts in Series-Parallel Circuits Effect of a Short in a Series-Parallel Circuit The total current and total power increase. . Fig. 6-13: Effect of a short circuit with series-parallel connections. (a) Normal circuit with S1 open. (b) Circuit with short between points A and B when S1 is closed; now R2and R3 are short-circuited. 07/01/2011 © 2010 Universitas Negeri Jakarta | www.unj.ac.id | 31

32. The total current increases from 2A with S1 open to 10A with S1closed. With S1 closed, R2 and R3 are shorted out. Troubleshooting: Opens and Shorts in Series-Parallel Circuits Effect of a Short in a Series-Parallel Circuit 07/01/2011 © 2010 Universitas Negeri Jakarta | www.unj.ac.id | 32

33. With S2 open, R3 is effectively removed from the circuit. Troubleshooting: Opens and Shorts in Series-Parallel Circuits Effect of an Open in a Series-Parallel Circuit Fig. 6-14: Effect of an open path in a series-parallel circuit. (a) Normal circuit with S2closed. (b) Series circuit with R1 and R2 when S2 is open. Now R3 in the open path has no current and zero IR voltage drop. 07/01/2011 © 2010 Universitas Negeri Jakarta | www.unj.ac.id | 33

34. With S2 open the voltage across points C and D equals the voltage across R2,which is 89V. The voltage across R3 is zero. Troubleshooting: Opens and Shorts in Series-Parallel Circuits Effect of an Open in a Series-Parallel Circuit 07/01/2011 © 2010 Universitas Negeri Jakarta | www.unj.ac.id | 34

35. 07/01/2011 © 2010 Universitas Negeri Jakarta | www.unj.ac.id | 35 TerimaKasih