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 Chapter 6 6 © 2007 The McGraw-Hill Companies, Inc. All rights reserved.

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.

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.

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

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

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

Prob. 6-2 & 3

Prob. 6-6 RPRP

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.

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

Prob. 6-14

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.

Prob. 6-16

Break

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.

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.

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.

Prob. 6-25

I2 = I7 = I T – I1

Prob. 6-25

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.

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.

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: = RSRS RXRX R1R1 R2R2 = RXRX R S × R1R1 R2R2

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.