Chapter 6

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electronics fundamentals
circuits, devices, and applications
THOMAS L. FLOYD DAVID M. BUCHLA
Chapter 6 Series and Parallel Combination
Circuits
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Most practical circuits have combinations of
series and parallel components.
From Chapters 4 and 5
Components that are connected in series will
share a common path.
Components that are connected in parallel will be
connected across the same two nodes.
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Combination circuits
Circuits containing both series and parallel
circuits are called COMBINATION circuits
You can frequently simplify analysis by combining
series and parallel components.
Solve by forming the simplest equivalent circuit
possible.
An equivalent circuit is one that has
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is equivalent to
There are no electrical measurements that can
distinguish the boxes.
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Another example
There are no electrical measurements that can
distinguish the boxes.
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• What Do We Know
• For Series Circuits
• Current at all points is the
• IT IR1 IR2
• Voltage across each resistor
• VT V1 V2
• For Parallel Circuit
• Current
• IT IR1 IR2
• Voltage at all nodes is the
• VT V1 V2

same
drops
divides across each resistor in the branch
same
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Seven Step Process for Solving a Combination
Circuit

1. Simplify the circuit to a series circuit by
   finding the effective equivalent resistance (REQ)
   of each parallel section in the circuit. Redraw
   the simplified circuit.
2. Calculate the total resistance (RT) of the
   circuit by adding all REQs to the other series
   resistances.
3. Calculate the total current (IT) using RT in
   Ohms law.
4. Calculate the voltage drop across any series
   resistances or REQs using Ohms law.
5. Calculate the branch currents in all parallel
   sections of the circuit using the voltage drop
   across REQ and Ohms law.
6. Use the branch currents and resistance values to
   calculate the voltage of the parallel
   resistances.
7. Make a summary of the voltage drops and currents
   for each resistance to make sure they total
   correctly.

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A simple series-parallel resistive circuit.
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R4 is added to the circuit in series with R1.
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R5 is added to the circuit in series with R2.
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R6 is added to the circuit in parallel with the
series combination of R1 and R4.
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FIGURE 65
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FIGURE 66
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FIGURE 67
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Sketch the circuits for nodesA to BA to CB to C
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Sketch the circuits for nodesA to B
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Sketch the circuits for nodesA to C
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Sketch the circuits for nodesB to C
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FIGURE 69
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FIGURE 610
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Reduce the following circuit to REQ
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6 O
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10 O
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5 O
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IT
50 O
IT
2 amps
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FIGURE 613
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FIGURE 614
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FIGURE 615
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FIGURE 616
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FIGURE 617
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FIGURE 618
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FIGURE 619
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Review of voltage relationships.
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Kirchoffs current law What are the readings for
node A?
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FIGURE 621
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Loaded voltage divider
The voltage-divider equation was developed for a
series circuit. Recall that the output voltage is
given by

A

1. A voltage-divider with a resistive load forms a
   combination (parallel) circuit.

1. The voltage divider is said to be LOADED.

1. The loading reduces the total resistance from
   node A to ground.

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Loaded voltage divider
What is the voltage across R3?
A
Form an equivalent series circuit by combining R2
and R3 then apply the voltage-divider formula to
the equivalent circuit
8.10 V
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FIGURE 622
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FIGURE 623
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FIGURE 624
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FIGURE 625
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FIGURE 626 A voltage divider with both unloaded
and loaded outputs.
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FIGURE 628
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FIGURE 629
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FIGURE 631
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FIGURE 632
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The loading effect of a voltmeter.
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Loading effect of a voltmeter
Given VS 10 V and R1 and R2 are not defective
but the meter reads only 4.04 V when it is across
either R1 or R2.
What is a possible explanation of the meter not
displaying 10 volts?

1. A voltmeter has internal resistance
2. This RINT can change the resistance of the
   circuit under test.
3. A 1 MW internal resistance of the meter accounts
   for the readings.

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FIGURE 634
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Wheatstone bridge

• The Wheatstone bridge consists of
• a dc voltage source and
• four resistive arms forming two voltage dividers.
  
• The output is taken between the dividers.
• Frequently, one of the bridge resistors is
  adjustable. (R2)

.
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Balanced Wheatstone bridge
When the bridge is balanced, the output voltage
is
zero
The products of resistances in the opposite
diagonal arms are
equal.
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Wheatstone bridge.
Voltage Divider 1
Voltage Divider 2
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Wheatstone bridge.
V1V2 I1I3
V3V4 I2I4
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Wheatstone bridge
What is the value of R2 if the bridge is balanced?
330 W
470 W
12 V
384 W
270 W
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Finding an Unknown Resistance
Scale Factor
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Measuring a physical parameter using a transducer.
Unbalanced Wheatstone Bridge

• Unbalance occurs when VOUT ? 0
• Used to measure
• Mechanical Strain
• Temperature
• Pressure
• VOUT is converted to a digital output indicating
  the value of the reading.

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VOUT VA-VB 0
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10
10
10
10
10
Using the Thermistor chart, what is VOUT when the
temperature is 50o C
VA8.8v
VB6.0v
VA-B2.8v
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Example of a load cell.
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Wheatstone Bridge

1. Remove RL to make an open circuit between A B
2. Calculate R1R3
3. Calculate R2R4
4. Calculate the voltage from A to ground
5. Calculate the voltage from B to ground

165 W
179 W
7.5 V
6.87 V
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FIGURE 643
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FIGURE 644
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FIGURE 647
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FIGURE 648
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FIGURE 649 A Wheatstone bridge with a load
resistor connected between the output terminals
is not a straightforward series-parallel circuit.
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FIGURE 651
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FIGURE 652
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FIGURE 653
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FIGURE 654 Maximum power is transferred to the
load when RL RS.
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Maximum power transfer Theorem
The maximum power is transferred from a source to
a load when RL RS(resistance of the voltage
source)
The maximum power transfer theorem assumes the
source voltage and resistance are fixed.
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Maximum power transfer Theorem
What is the power delivered to the load?
The voltage to the load is
5.0 V
The power delivered is
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FIGURE 655
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FIGURE 656 Curve showing that the load power is
maximum when RL RS.
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Superposition theorem

• A way to determine currents and voltages in a
  linear circuit that has multiple sources
• Take one source at a time and
• Algebraically summing the results.

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Superposition theorem

• Four Step Process
• Leave one voltage or current source at a time in
  the circuit (circuit 1) and replace the other
  (circuit 2) with a short.
• Calculate REQ/Total and then calculate the
  voltage or current for the resistor(s).
• Repeat steps 1 and 2 for the other circuit
  (circuit 2).
• Algebraically add the results for all sources.

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Summary
Summary
What does the ammeter read for I2?
1.56 mA
6.10 kW
1.97 mA
0.98 mA
8.73 kW
2.06 mA
0.58 mA
1.56 mA
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Thevenins theorem and Wheatstone Bridge
Putting the load on the Thevenin circuits and
applying the superposition theorem allows you to
calculate the load current. The load current is
1.27 mA
.0152-.0191
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Troubleshooting
The effective troubleshooter must think logically
about circuit operation.
Understand normal circuit operation and find out
the symptoms of the failure.
Analysis
Decide on a logical set of steps to find the
fault.
Planning
Following the steps in the plan, make
measurements to isolate the problem. Modify the
plan if necessary.
Measurement
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Troubleshooting
The output of the voltage-divider is 6.0 V.
Describe how you would use analysis and planning
in finding the fault.
A
From an earlier calculation, V3 should equal 8.10
V. A low voltage is most likely caused by a low
source voltage or incorrect resistors (possibly
R1 and R2 reversed). If the circuit is new,
incorrect components are possible.
Decide on a logical set of steps to locate the
fault. You could decide to 1) check the source
voltage, 2) disconnect the load and check the
output voltage, and if it is correct, 3) check
the load resistance. If R3 is correct, check
other resistors.
Planning
Analysis
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FIGURE 658
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FIGURE 659
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FIGURE 660
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FIGURE 661
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FIGURE 662
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FIGURE 663
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FIGURE 664
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FIGURE 665
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FIGURE 666
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FIGURE 667
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FIGURE 668
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FIGURE 669
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FIGURE 673
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FIGURE 674 The meters indicate the correct
readings for this circuit.
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FIGURE 675
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FIGURE 676
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FIGURE 677
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FIGURE 678
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FIGURE 679
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FIGURE 680
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FIGURE 681
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FIGURE 682
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FIGURE 683
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FIGURE 684
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FIGURE 685
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FIGURE 686
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FIGURE 687
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FIGURE 688
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FIGURE 689
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FIGURE 690
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FIGURE 691
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FIGURE 692
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FIGURE 693
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FIGURE 694
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FIGURE 695
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FIGURE 696
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FIGURE 697
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FIGURE 698
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FIGURE 699
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FIGURE 6100
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FIGURE 6101
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FIGURE 6103
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FIGURE 6104
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FIGURE 6105
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FIGURE 6106
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FIGURE 6107
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FIGURE 6108
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FIGURE 6109
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FIGURE 6110
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Selected Key Terms
The effect on a circuit when an element that
draws current from the circuit is connected
across the output terminals.
Loading Load current Bleeder
current Wheatstone bridge

The output current supplied to a load.
The current left after the load current is
subtracted from the total current into the
circuit.
A 4-legged type of bridge circuit with which an
unknown resistance can be accurately measured
using the balanced state. Deviations in
resistance can be measured using the unbalanced
state.
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Selected Key Terms
A circuit theorem that provides for reducing any
two-terminal resistive circuit to a single
equivalent voltage source in series with an
equivalent resistance.
Thevenins theorem Maximum power
transfer Superposition

The condition, when the load resistance equals
the source resistance, under which maximum power
is transferred to the load.
A method for analyzing circuits with two or more
sources by examining the effects of each source
by itself and then combining the effects.
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1. Two circuits that are equivalent have the
same a. number of components b. response to an
electrical stimulus c. internal power
dissipation d. all of the above
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2. If a series equivalent circuit is drawn for a
complex circuit, the equivalent circuit can be
analyzed with a. the voltage divider
theorem b. Kirchhoffs voltage law c. both of
the above d. none of the above
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3. For the circuit shown, a. R1 is in series
with R2 b. R1 is in parallel with R2 c. R2 is
in series with R3 d. R2 is in parallel with R3
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4. For the circuit shown, a. R1 is in series
with R2 b. R4 is in parallel with R1 c. R2 is
in parallel with R3 d. none of the above
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5. A signal generator has an output voltage of
2.0 V with no load. When a 600 W load is
connected to it, the output drops to 1.0 V. The
Thevenin resistance of the generator is a. 300
W b. 600 W c. 900 W d. 1200 W.
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6. For the circuit shown, Kirchhoff's voltage law
a. applies only to the outside loop b. applies
only to the A junction. c. can be applied to any
closed path. d. does not apply.
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7. The effect of changing a measured quantity due
to connecting an instrument to a circuit is
called a. loading b. clipping c.
distortion d. loss of precision
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8. An unbalanced Wheatstone bridge has the
voltages shown. The voltage across R4 is a. 4.0
V b. 5.0 V c. 6.0 V d. 7.0 V
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9. Assume R2 is adjusted until the Wheatstone
bridge is balanced. At this point, the voltage
across R4 is measured and found to be 5.0 V. The
voltage across R1 will be a. 4.0 V b. 5.0 V c.
6.0 V d. 7.0 V
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10. Maximum power is transferred from a fixed
source when a. the load resistor is ½ the
source resistance b. the load resistor is equal
to the source resistance c. the load resistor is
twice the source resistance d. none of the above
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Quiz
Answers 1. b 2. c 3. d 4. d 5. b
6. c 7. a 8. a 9. d 10. b