Electricity And Electronics Fundamentals

BTE1113

Chapter 7

Series-Parallel Circuits

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The Series-Parallel Network

• Branch– Part of a circuit that can be simplified into

two terminals

• Components between these two terminals – Resistors, voltage sources, or other

elements

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The Series-Parallel Network

• To analyze a circuit– Identify elements in series and elements in

parallel

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The Series-Parallel Network

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The Series-Parallel Network

• In this circuit– R2, R3, and R4 are in parallel

• This parallel combination – Series with R1 and R5

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The Series-Parallel Network

• In this circuit – R3 and R4 are in

parallel– Combination is in

series with R2

• Entire combination is in parallel with R1

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The Series-Parallel Network

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Analysis of Series-Parallel Circuits

• Rules for analyzing series and parallel circuits still apply

• Same current occurs through all series elements

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Analysis of Series-Parallel Circuits

• Same voltage occurs across all parallel elements

• KVL and KCL apply for all circuits– Whether they are series, parallel, or series-

parallel

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Analysis of Series-Parallel Circuits

• Redraw complicated circuits showing the source at the left-hand side

• Label all nodes

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Analysis of Series-Parallel Circuits

• Develop a strategy– Best to begin analysis with components most

distant from the source

• Simplify recognizable combinations of components

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Analysis of Series-Parallel Circuits

• Determine equivalent resistance RT

• Solve for the total current

• Label polarities of voltage drops on all components

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Analysis of Series-Parallel Circuits

• Calculate how currents and voltages split between elements in a circuit

• Verify your answer by taking a different approach (when feasible)

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Analysis of Series-Parallel Circuits

• Voltages– Use Ohm’s Law or Voltage Divider Rule

• Currents– Use Ohm’s Law or Current Divider Rule

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Analysis of Series-Parallel Circuits

Applications of Series-Parallel Circuits

• Example: bridge circuit– Calculate the current I and voltage Vab when:

a) Rx = 0 Ω

b) Rx = 15 kΩ

Applications of Series-Parallel Circuits (cont’d.)

• Solution

• Solution (cont’d.)

• Solution (cont’d.)

• Solution (cont’d.)

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Potentiometers

• Example of variable resistor used as potentiometer – Volume control on a receiver

• Moveable terminal is at uppermost position– Vbc = 60 V

• At the lowermost position– Vbc = 0 V

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Potentiometers

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Potentiometers

• Vbc changes– If load is connected

between b and c– At upper position

• Vbc = 40 V

• At the lower position– Vbc = 0 V

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ApplicationsBoosting a Car Battery

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ApplicationsBoosting a Car Battery

References

• Electricity and Electronics by Gerrish, Dugger and Roberts, 10th edition, 2009, GW Publisher

• Circuit Analysis: Theory and Practice by A. H. Robbins, W. C. Miller, 4th edition, 2006, Thomson Delmar Learning

• Introductory Circuit Analysis by R. L. Boylestad, 11th edition, 2007, Prentice Hall

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