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Chapter
6
Series-Parallel Circuits
Topics Covered in Chapter 6
6-1: Finding RT 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.
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 SeriesParallel Circuits
McGraw-Hill
© 2007 The McGraw-Hill Companies, Inc. All rights reserved.
6-1: Finding RT 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 RT for
Series-Parallel Resistances
 Overview of Series-Parallel Circuits
1
3
V
2
There are three branches in this
circuit; sections 1 and 2 are series strings.
6-1: Finding RT for
Series-Parallel Resistances
 Overview of Series-Parallel Circuits
1
3
V
2
There are three series sections in this
circuit; sections 1 and 2 are parallel banks.
6-1: Finding RT 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 RT:
1kΩ + 0.5kΩ = 1.5 kΩ
Prob. 6-2 & 3
Prob. 6-2 & 3
Prob. 6-2 & 3
Prob. 6-2 & 3
Prob. 6-6
RP
Prob. 6-6
Prob. 6-6
Prob. 6-6
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
V
I is the same
in this
section.
V is the same across each parallel branch.
Prob. 6-14
Prob. 6-14
Prob. 6-14
6-3: Resistance Banks in Series
Fig. 6-4a: Parallel bank of R2 and R3 in
series with R1 (Original circuit).
Copyright © The McGraw-Hill Companies, Inc. Permission required for reproduction or display.
Prob. 6-16
Prob. 6-16
Prob. 6-16
Prob. 6-16
Break
6-4: 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 R7.
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) R7 and R6 in series added for R13. (d) R13 and R5 in parallel combined for R18.
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 R18, R1, and R2 in series are added for the total resistance of 50Ω for RT.
Copyright © The McGraw-Hill Companies, Inc. Permission required for reproduction or display.
Prob. 6-25
Prob. 6-25
Prob. 6-25
Prob. 6-25
Prob. 6-25
Prob. 6-25
Prob. 6-25
I2 = I7 = IT – I1
Prob. 6-25
Prob. 6-25
Prob. 6-25
Prob. 6-25
Prob. 6-25
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 (RX) is in the same branch as the
standard resistor (RS).
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
 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.
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:
R1
RX
=
RS
R2
RX
R1
= RS ×
R2
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.