Download Parallel Circuits

Chapter 7 – Serial-Parallel Circuits
Introductory Circuit Analysis
Robert L. Boylestad
7.1 – Introduction
A series-parallel configuration is one that is
formed by a combination of series and parallel
elements.
A complex configuration is one in which none of
the elements are in series or parallel.
7.2 - Series-Parallel Networks
 General approach to circuit analysis:
 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
7.3 – Reduce and Return Approach
 Reduce:
Reduce the circuit to its simplest form across the
source and then determine the source current (Is).
Return:
 Using the resulting source current (Is) to work back
to the desired unknown.
7.4 – 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 with practice.
 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.
7.5 – Descriptive Examples
 Example 7.5 – Find the current I4 and the voltage V2 for
the network in Fig 7.14.
Descriptive Examples
 Example 7.6 – Find the indicated currents and voltages
for the network in Fig. 7.17.
Descriptive Examples
 Example 7.7
a. Find the voltages V1, V2 and Vab for the network in Fig. 7.20.
b. Calculate the source current Is .
Descriptive Examples
Example 7.8 – For the network in Fig. 7.22, determine
the voltages V1 and V2 and the current I.
Descriptive Examples
 Example 7.10 – Calculate the indicated currents and
voltage in Fig. 7.26.
Insert Fig. 7.22
7.6 – 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.
7.7 – Voltage Divider Supply
(Unloaded and Loaded)
 Loading
is the process of introducing elements that
will draw current from the system. The heavier the
current, the greater the loading effect.
 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.
7.8 – Potentiometer Loading
Unloaded potentiometer – the output voltage is determined
by the voltage divider rule, with RT representing the total
resistance of the potentiometer.

Potentiometer 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.
7.9 – 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.
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 shunt resistance
( Rshunt ) to be used for the maximum current indicated
on the face of the meter.
The Voltmeter
 The voltmeter
 Additional circuitry allows the d’Arsonval movement to be
used as 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.
The Ohmmeter
 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.
7.10 – 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.
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.