1. Chapter 7 – Serial-Parallel Networks
Introductory Circuit Analysis
Robert L. Boylestad 1

2. 7.1 - Series-Parallel Networks
Series and parallel circuits are networks that contain both series and parallel circuit configurations
One can become proficient in the analysis of series-parallel networks only through exposure, practice and experience 2

3. Series-Parallel Networks
General approach
Study the problem in total and make a brief mental sketch of the overall approach you plan to use
Examine each region of the network independently before tying them together in series-parallel combinations
Redraw the network as often as possible with reduced branches and undisturbed unknown quantities to maintain clarity
When you have a solution, check to see that it is reasonable by considering the magnitudes of the energy source and the elements in the network. If it does not seem reasonable, either solve using another approach or check over your work very carefully 3

4. Series-Parallel Networks
Reduce and return approach
This analysis is one that works back to the source, determines the source current and then finds its way to the desired unknown
Work back for Is and then follow the return path for the specific unknown 4

5. Series-Parallel Networks
Block diagram approach
Network is broken down into combinations of elements
Initially, there will be some concern about identifying series and parallel elements, but that will come by working through some examples
In reverse, the block diagram approach can be used effectively to reduce the apparent complexity of a system by identifying the major series and parallel components of the network 5

6. 7.2 - Descriptive Examples
Example 7.4 – Find the current of I4 and the voltage of V2 for the network of Fig 7.10 6

7. Descriptive Examples
Example 7.5 – Find the indicated currents and voltages for the network of Fig. 7.13 7

8. Descriptive Examples Example 7.6
a. Find the voltages V1, V2 and Vab for the network of Fig. 7.16
b. Calculate the source current Is 8

9. Descriptive Examples
Example 7.7 – For the network of Fig. 7.18, determine the voltages V1 and V2 and the current I 9

10. Descriptive Examples
Example 7.9 – Calculate the indicated currents and voltages of Fig
Insert Fig. 7.22 10

11. 7.3 - Ladder Networks Repetitive structure that looks like a ladder
Method 1 – Calculate the total resistance and resulting source current, and then work back through the ladder until the desired current or voltage is obtained
Method 2 – Assign a letter symbol to the last branch current, and work back through the network to the source, maintaining this assigned current or other current of interest. 11

12. 7.4 - Voltage Divider Supply (Unloaded and Loaded)
Loaded refers to the application of an element, network, or system to a supply that will draw current from the supply
The larger the resistance level of the applied loads compared to the resistance of the voltage divider network, the closer the resulting terminal voltage to the no-load levels. In other words, the lower the current demand from a supply, the closer the terminal characteristics are to the no-load levels. 12

13. 7.5 - Potential Loading
Unloaded potentiometer – the output voltage is determined by the voltage divider rule, with RT representing the total resistance of the potentiometer
Insert Fig 7.37 13

14. Potential Loading
When a load is applied as shown, the output voltage VL is now a function of the magnitude of the load applied since R1 is not as shown in the previous slide but is instead the parallel combination of R1 and RL.
Insert Fig 7.38 14

15. 7.6 - Ammeter, Voltmeter, and Ohmmeter Design
Fundamental design of an ammeter, voltmeter, and ohmmeter.
d’Arsonval analog movement: an iron-core coil mounted on bearings between a permanent magnet. The helical springs limit the tuning motion of the coil and provide a path for the current to reach the coil.
When current is passed through the movable coil, the fluxes of the coil and permanent magnet will interact to develop a torque on the coil that will cause it to rotate on its bearings
The movement is adjusted to indicate zero deflection on a meter scale when the current through the coil is zero
The direction of the current through the coil will determine whether the pointer will display an up-scale or below-zero indication 15

16. Ammeter, Voltmeter, and Ohmmeter Design
The ammeter
The maximum current that the d’Arsonval movement can read is equal to the current sensitivity of the movement. Higher current can be measured if additional circuitry is introduced.
Multirange ammeters can be constructed using a rotary switch that determines the Rshunt to be used for the maximum current indicated on the face of the meter 16

17. Ammeter, Voltmeter, and Ohmmeter Design
The voltmeter
Additional circuitry in the d’Arsonval movement is introduced to create a voltmeter
The millivolt rating is sometimes referred to as the voltage sensitivity (VS)
The Rseries is adjusted to limit the current through the movement when maximum voltage is applied 17

18. Ammeter, Voltmeter, and Ohmmeter Design
The ohmmeter
Ohmmeters are designed to measure resistance in the low, mid-, or high range
The most common is the series ohmmeter, designed to read resistance levels in the midrange
The design is different from that of the ammeter and voltmeter because it will show a full-scale deflection for zero ohms and no deflection for infinite resistance
The megohmmeter (megger) is an instrument for measuring very high resistance. Its primary function is to test the insulation found in power transmission systems, electrical machinery, transformers and so on. 18

19. 7.7 - Grounding
Grounding and the measure of safety it provides to a design is very important
Ground potential is 0 V at every point in the network that has a ground symbol
All ground potentials are the same and so they can all be connected together, but for clarity most are left isolated on a large schematic
On a schematic, the voltage levels provided are always with respect to ground
To check a system, connect the black lead of a meter to ground and the red lead at the various points where the typical operating voltage is provided. A close match to the expected voltage normally implies that that portion of the network is operating properly. 19

20. Grounding
Earth ground: ground directly connected to the earth by a low impedance connection
The entire surface of the earth is defined to have a potential of 0 V.
Every home has an earth ground, usually established by a long conductor rod driven into the ground and connected to the power panel
The electrical code requires a direct connection from earth ground to the cold-water pipes of a home for safety reasons 20

21. Grounding
Chassis ground: may be floating or connected directly to an earth ground
A chassis ground simply states that the chassis has a reference potential for all points of the network
If the chassis is not connected to earth potential (0 V), it is considered to be floating and can have any other reference voltage for other voltages to be compared to 21

22. Grounding
Grounding can be particularly important when working with numerous pieces of measuring equipment in the laboratory
Oscilloscope
The National Electrical Code requires that the “hot” (or feeder) line that carries the current load to a load be black, and the line (called the neutral) that carries the current back to the supply be white. Three-wire conductors have a ground wire that must be green or bare 22

23. 7.8 - Applications Boosting a car battery
Cables should have sufficient length (16-ft) with #6 gage stranded wire and well-designed clips
Proper sequence of events in connecting the cable to a car with a discharged battery
Protective eye equipment is recommended
Identify which terminals are positive and which terminals are negative
Connect the red wire to the positive terminal of the discharged battery making sure that the black lead is not touching the negative terminal or the car.
Connect the red wire to the positive terminal of the fully charged battery again making sure that the black lead is not touching the negative terminal of the battery or the car.
Connect the black terminal to the negative terminal of the fully charged battery and the black lead of the discharged battery to the block of the car and have someone maintain a constant idle speed on the car with the good battery 23

24. Applications
It is advised to let the charging action of the running car occur for 10 to 15 minutes before starting the car with the discharged battery
This is to protect the battery of the car with the good battery
Disconnecting the cables from a jumped car
Remove the cables in the reverse order as they were connected, making sure that the clamps don’t accidentally come in contact with the battery or the chassis of the car 24

25. Applications Electronic Circuits
The operation of most electronic systems requires a distribution of dc voltages throughout the design 25