This document discusses series-parallel circuits and their analysis. It covers identifying components that are in series and parallel, and how to simplify circuits by recognizing series and parallel combinations. The key steps for analyzing series-parallel circuits are outlined, including redrawing the circuit, labeling nodes, determining the equivalent resistance, calculating currents and voltages. Examples are provided for calculating currents and voltages in a bridge circuit with different resistances, as well as the voltage produced by a potentiometer at different positions. Applications discussed include boosting a car battery.

1. Electricity And Electronics
Fundamentals
BTE1113

2. Chapter 7
Series-Parallel Circuits

3. 3
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

4. 4
The Series-Parallel Network
• To analyze a circuit
– Identify elements in series and elements in
parallel

5. 5
The Series-Parallel Network

6. 6
The Series-Parallel Network
• In this circuit
– R2, R3, and R4 are in parallel
• This parallel combination
– Series with R1 and R5

7. 7
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

8. 8
The Series-Parallel Network

9. 9
Analysis of Series-Parallel Circuits
• Rules for analyzing series and parallel
circuits still apply
• Same current occurs through all series
elements

10. 10
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

11. 11
Analysis of Series-Parallel Circuits
• Redraw complicated circuits showing the
source at the left-hand side
• Label all nodes

12. 12
Analysis of Series-Parallel Circuits
• Develop a strategy
– Best to begin analysis with components most
distant from the source
• Simplify recognizable combinations of
components

13. 13
Analysis of Series-Parallel Circuits
• Determine equivalent resistance RT
• Solve for the total current
• Label polarities of voltage drops on all
components

14. 14
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)

15. 15
Analysis of Series-Parallel Circuits
• Voltages
– Use Ohm’s Law or Voltage Divider Rule
• Currents
– Use Ohm’s Law or Current Divider Rule

16. 16
Analysis of Series-Parallel Circuits

17. Applications of Series-Parallel
Circuits
• Example: bridge circuit
– Calculate the current I and voltage Vab when:
a) Rx = 0 Ω
b) Rx = 15 kΩ

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

19. • Solution (cont’d.)

20. • Solution (cont’d.)

21. • Solution (cont’d.)

22. 22
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

23. 23
Potentiometers

24. 24
Potentiometers
• Vbc changes
– If load is connected
between b and c
– At upper position
• Vbc = 40 V
• At the lower position
– Vbc = 0 V

25. 25
Applications
Boosting a Car Battery

26. 26
Applications
Boosting a Car Battery

27. 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
27