Series-Parallel Circuits

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1 Chapter 6 Series-Parallel Circuits Topics Covered in Chapter 6 6-1: Finding R T for Series-Parallel Resistances 6-2: Resistance Strings in Parallel 6-3: Resistance Banks in Series 6-4: Resistance Banks and Strings in Series-Parallel 2007 The McGraw-Hill Companies, Inc. All rights reserved.

2 Topics Covered in Chapter 6 6-5: Analyzing Series-Parallel Circuits with Random Unknowns 6-6: The Wheatstone Bridge 6-7: Troubleshooting: Opens and Shorts in Series- Parallel Circuits McGraw-Hill 2007 The McGraw-Hill Companies, Inc. All rights reserved.

3 6-1: Finding R T for Series-Parallel Resistances Overview of Series-Parallel Circuits A series-parallel circuit, or combination circuit, combines both series and parallel connections. Series components form a series string. Parallel components form a parallel bank.

4 6-1: Finding R T for Series-Parallel Resistances Overview of Series-Parallel Circuits V There are three branches in this circuit; sections 1 and 2 are series strings.

5 6-1: Finding R T for Series-Parallel Resistances Overview of Series-Parallel Circuits 1 V 3 2 There are three series sections in this circuit; sections 1 and 2 are parallel banks.

6 6-1: Finding R T for Series-Parallel Resistances The series resistances are: 0.5kΩ + 0.5kΩ = 1kΩ The equivalent resistance of the parallel resistances is: 1kΩ / 2 = 0.5kΩ The series and parallel values are then added for the value of R T : 1kΩ + 0.5kΩ = 1.5 kω

7 Prob. 6-2 & 3

8 Prob. 6-2 & 3

9 Prob. 6-2 & 3

10 Prob. 6-2 & 3

11 Prob. 6-6 R P

12 Prob. 6-6

13 Prob. 6-6

14 Prob. 6-6

15 6-2: Resistance Strings in Parallel Fig. 6-3a: Series string in parallel with another branch (schematic diagram). Copyright The McGraw-Hill Companies, Inc. Permission required for reproduction or display.

16 6-2: Resistance Strings in Parallel V I is the same in this section. V is the same across each parallel branch.

17 Prob. 6-14

18 Prob. 6-14

19 Prob. 6-14

20 6-3: Resistance Banks in Series Fig. 6-4a: Parallel bank of R 2 and R 3 in series with R 1 (Original circuit). Copyright The McGraw-Hill Companies, Inc. Permission required for reproduction or display.

21 Prob. 6-16

22 Prob. 6-16

23 Prob. 6-16

24 Prob. 6-16

25 Break

26 6-4: Resistance Banks and Strings in Series-Parallel Example: Find all currents and voltages in Fig Step 1: Find R T. Step 2: Calculate main line current as I T = V T / R T Fig. 6-5: Reducing a series-parallel circuit to an equivalent series circuit to find the R T. (a) Actual circuit. (b) R 3 and R 4 in parallel combined for the equivalent R 7. Copyright The McGraw-Hill Companies, Inc. Permission required for reproduction or display.

27 6-4: Resistance Banks and Strings in Series-Parallel Fig. 6-5, cont. (c) R 7 and R 6 in series added for R 13. (d) R 13 and R 5 in parallel combined for R 18. Copyright The McGraw-Hill Companies, Inc. Permission required for reproduction or display.

28 6-4: Resistance Banks and Strings in Series-Parallel Fig. 6-5 (e): The R 18, R 1, and R 2 in series are added for the total resistance of 50Ω for R T. Copyright The McGraw-Hill Companies, Inc. Permission required for reproduction or display.

29 Prob. 6-25

30 Prob. 6-25

31 Prob. 6-25

32 Prob. 6-25

33 Prob. 6-25

34 Prob. 6-25

35 I2 = I7 = I T I1 Prob. 6-25

36 Prob. 6-25

37 Prob. 6-25

38 Prob. 6-25

39 Prob. 6-25

40 Prob. 6-25

41 Prob. 6-25

42 6-6: The Wheatstone Bridge A Wheatstone bridge is a circuit that is used to determine the value of an unknown resistance. The unknown resistor (R X ) is in the same branch as the standard resistor (R S ). Fig. 6-10: Wheatstone bridge. Copyright The McGraw-Hill Companies, Inc. Permission required for reproduction or display.

43 6-6: The Wheatstone Bridge Using a Wheatstone Bridge to Measure an Unknown Resistance R S is adjusted for zero current in M 1.. When the current in M 1 = 0A, the voltage division between R X and R S is equal to that between R 1 and R 2. Copyright The McGraw-Hill Companies, Inc. Permission required for reproduction or display.

44 6-6: The Wheatstone Bridge Note: When the Wheatstone bridge is balanced, it can be analyzed as two series strings in parallel. Note the following relationship: R X = R 1 R S R 2 R X = R S R 1 R 2

45 6-7: 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. The voltage across a short is zero and the current usually increases. The current through an open is zero and the voltage usually increases. When troubleshooting series-parallel circuits, combine the techniques used when troubleshooting individual series and parallel circuits.

Chapter 26 DC Circuits

Chapter 26 DC Circuits Electric circuit needs battery or generator to produce current these are called sources of emf. Battery is a nearly constant voltage source, but does have a small internal resistance,