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Chapter 7
Principles of Electric Circuits, Conventional Flow, 9th ed.
Floyd
© 2010 Pearson Higher Education,
Upper Saddle River, NJ 07458. • All Rights Reserved
Chapter 7
Summary
Combination circuits
Most practical circuits have combinations of series
and parallel components. You can frequently
simplify analysis by combining series and parallel
components.
An important analysis method is to form an equivalent
circuit. An equivalent circuit is one that has
characteristics that are electrically the same as
another circuit but is generally simpler.
Principles of Electric Circuits, Conventional Flow, 9th ed.
Floyd
© 2010 Pearson Higher Education,
Upper Saddle River, NJ 07458. • All Rights Reserved
Chapter 7
Summary
Combination circuits
For example:
R1
1.0 k
R2
is equivalent to
R1
2.0 k
1.0 k
There are no electrical measurements that can
distinguish the boxes.
Principles of Electric Circuits, Conventional Flow, 9th ed.
Floyd
© 2010 Pearson Higher Education,
Upper Saddle River, NJ 07458. • All Rights Reserved
Chapter 7
Summary
Combination circuits
Another example:
is equivalent to
R1
R2
1.0 k 1.0 k
R1,2
500 
There are no electrical measurements that can
distinguish the boxes.
Principles of Electric Circuits, Conventional Flow, 9th ed.
Floyd
© 2010 Pearson Higher Education,
Upper Saddle River, NJ 07458. • All Rights Reserved
Chapter 7
Summary
is equivalent to
R1
1.0 k
R3
R 1,2
R3
R2
4.7 k
3.7 k
4.7 k
2.7 k
is equivalent to
R1,2,3
2.07 k
Principles of Electric Circuits, Conventional Flow, 9th ed.
Floyd
There are no electrical
measurements that can
distinguish between the
three boxes.
© 2010 Pearson Higher Education,
Upper Saddle River, NJ 07458. • All Rights Reserved
Chapter 7
Summary
Combination circuits
Kirchhoff’s voltage law and Kirchhoff’s current law
can be applied to any circuit, including combination
circuits.
So will
For example,
this path!
R2
applying KVL, the
2
path shown will
have a sum of 0 V.
470 
VS
5.0 V
R11
270 
R4
100 
R3
330 
R6
Start/Finish
Principles of Electric Circuits, Conventional Flow, 9th ed.
Floyd
Start/Finish
R5
100 
100 
© 2010 Pearson Higher Education,
Upper Saddle River, NJ 07458. • All Rights Reserved
Chapter 7
Summary
Kirchoff’s current law can also be applied to the same
circuit. What are the readings for node A?
I
+
I
-
26.5 mA
+
A
I
VS
5.0 V
+
+
8.0 mA
R2
470 
R4
-
18.5 mA
100 
R1
270 
R3
330 
R6
R5
100 
100 
Principles of Electric Circuits, Conventional Flow, 9th ed.
Floyd
© 2010 Pearson Higher Education,
Upper Saddle River, NJ 07458. • All Rights Reserved
Chapter 7
Summary
Combination
circuit
VS +
10 V
R1
270 
R2
330 
R3
470 
Tabulating current, resistance, voltage and power is a
useful way to summarize parameters. Solve for the
unknown quantities in the circuit shown.
I1= 21.6 mA
I2= 12.7 mA
I3= 8.9 mA
IT= 21.6 mA
R1= 270 
R2= 330 
R3= 470 
RT= 464 
Principles of Electric Circuits, Conventional Flow, 9th ed.
Floyd
V1= 5.82 V P1= 126 mW
V2= 4.18 V P2= 53.1 mW
V3= 4.18 V P3= 37.2 mW
VS= 10 V PT= 216 mW
© 2010 Pearson Higher Education,
Upper Saddle River, NJ 07458. • All Rights Reserved
Chapter 7
Summary
Kirchhoff’s laws can be applied
as a check on the answer.
R1
270 
VS +
10 V
R2
330 
R3
470 
Notice that the current in R1 is
equal to the sum of the branch currents in R2 and R3.
The sum of the voltages around the outside loop is zero.
I1= 21.6 mA
I2= 12.7 mA
I3= 8.9 mA
IT= 21.6 mA
R1= 270 
R2= 330 
R3= 470 
RT= 464 
Principles of Electric Circuits, Conventional Flow, 9th ed.
Floyd
V1= 5.82 V P1= 126 mW
V2= 4.18 V P2= 53.1 mW
V3= 4.18 V P3= 37.2 mW
VS= 10 V PT= 216 mW
© 2010 Pearson Higher Education,
Upper Saddle River, NJ 07458. • All Rights Reserved
Chapter 7
Loading effect of
a voltmeter
Summary
VS +
10 V
R1
470 k
+
4.04
10 VV
R2
Assume VS = 10 V, but the
+
4.04 V
47
0
k

meter reads only 4.04 V
when it is across either R1
or R2.
Can you explain what is happening?
All measurements affect the quantity being measured. A
voltmeter has internal resistance, which can change the
resistance of the circuit under test. In this case, a 1 M
internal resistance of the meter accounts for the readings.
Principles of Electric Circuits, Conventional Flow, 9th ed.
Floyd
© 2010 Pearson Higher Education,
Upper Saddle River, NJ 07458. • All Rights Reserved
Chapter 7
Summary
Wheatstone bridge
The Wheatstone bridge consists
R3
R1
VS
of four resistive arms forming
Output
two voltage dividers and a dc
voltage source. The output is
R2
R4
taken between the dividers.
Frequently, one of the bridge
resistors is adjustable.
When the bridge is balanced, the output voltage is zero,
and the products of resistances in the opposite diagonal
arms are equal.
+
-
Principles of Electric Circuits, Conventional Flow, 9th ed.
Floyd
© 2010 Pearson Higher Education,
Upper Saddle River, NJ 07458. • All Rights Reserved
Chapter 7
Summary
Wheatstone bridge
The Wheatstone bridge consists
R3
R1
VS
of four resistive arms forming
Output
two voltage dividers and a dc
voltage source. The output is
R2
R4
taken between the dividers.
Frequently, one of the bridge
resistors is adjustable.
When the bridge is balanced, the output voltage is zero,
and the products of resistances in the opposite diagonal
arms are equal.
+
-
Principles of Electric Circuits, Conventional Flow, 9th ed.
Floyd
© 2010 Pearson Higher Education,
Upper Saddle River, NJ 07458. • All Rights Reserved
Chapter 7
Summary
Application of the Wheatstone bridge
Wheatstone bridges are used in load cells, which are widely
used in scales. The bridge arms are constructed from four
strain gauges - two are in tension and two in compression.
Principles of Electric Circuits, Conventional Flow, 9th ed.
Floyd
© 2010 Pearson Higher Education,
Upper Saddle River, NJ 07458. • All Rights Reserved
Chapter 7
Key Terms
Balanced bridge A bridge circuit that is in the balanced state is
indicated by 0 V across the output.
Bleeder current The current left after the load current is
subtracted from the total current into the
circuit.
Load An element (resistor or other component)
connected across the output terminals of a
circuit that draws current from the circuit.
Principles of Electric Circuits, Conventional Flow, 9th ed.
Floyd
© 2010 Pearson Higher Education,
Upper Saddle River, NJ 07458. • All Rights Reserved
Chapter 7
Key Terms
Unbalanced A bridge circuit that is in the unbalanced state
bridge is indicated by a voltage across the output that
is proportional to the amount of deviation
from the balanced state.
Wheatstone A 4-legged type of bridge circuit with which
bridge an unknown resistance can be accurately
measured using the balanced state. Deviations
in resistance can be measured using the
unbalanced state.
Principles of Electric Circuits, Conventional Flow, 9th ed.
Floyd
© 2010 Pearson Higher Education,
Upper Saddle River, NJ 07458. • All Rights Reserved
Chapter 7
Quiz
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
Principles of Electric Circuits, Conventional Flow, 9th ed.
Floyd
© 2010 Pearson Higher Education,
Upper Saddle River, NJ 07458. • All Rights Reserved
Chapter 7
Quiz
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. Kirchhoff’s voltage law
c. both of the above
d. none of the above
Principles of Electric Circuits, Conventional Flow, 9th ed.
Floyd
© 2010 Pearson Higher Education,
Upper Saddle River, NJ 07458. • All Rights Reserved
Chapter 7
Quiz
3. For the circuit shown,
a. R1 is in series with R2
-
c. R2 is in series with R3
VS
+
b. R1 is in parallel with R2
R1
R2
R3
d. R2 is in parallel with R3
Principles of Electric Circuits, Conventional Flow, 9th ed.
Floyd
© 2010 Pearson Higher Education,
Upper Saddle River, NJ 07458. • All Rights Reserved
Chapter 7
Quiz
4. For the circuit shown,
R4
a. R1 is in series with R2
R1
b. R4 is in parallel with R1
Principles of Electric Circuits, Conventional Flow, 9th ed.
Floyd
-
d. none of the above
+
c. R2 is in parallel with R3
VS
R2
R3
© 2010 Pearson Higher Education,
Upper Saddle River, NJ 07458. • All Rights Reserved
Chapter 7
Quiz
5. The total resistance, RT, of the group of resistors is
a. 1.0 k
R1
b. 2.0 k
c. 3.0 k
d. 4.0 k
500 
1.0 k 
R3
2.0 k 
RT
R5
500 
Principles of Electric Circuits, Conventional Flow, 9th ed.
Floyd
R2
R4
1.0 k 
© 2010 Pearson Higher Education,
Upper Saddle River, NJ 07458. • All Rights Reserved
Chapter 7
Quiz
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.
VS +
10 V
R1
270 
A
R2
330 
Principles of Electric Circuits, Conventional Flow, 9th ed.
Floyd
R3
470 
© 2010 Pearson Higher Education,
Upper Saddle River, NJ 07458. • All Rights Reserved
Chapter 7
Quiz
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
Principles of Electric Circuits, Conventional Flow, 9th ed.
Floyd
© 2010 Pearson Higher Education,
Upper Saddle River, NJ 07458. • All Rights Reserved
Chapter 7
Quiz
8. An unbalanced Wheatstone bridge has the voltages
shown. The voltage across R4 is
a. 4.0 V
d. 7.0 V
Principles of Electric Circuits, Conventional Flow, 9th ed.
Floyd
-
c. 6.0 V
VS
12 V
+
b. 5.0 V
R1
7.0 V
R2
R3
+ RL 1.0 V
R4
© 2010 Pearson Higher Education,
Upper Saddle River, NJ 07458. • All Rights Reserved
Chapter 7
Quiz
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
d. 7.0 V
Principles of Electric Circuits, Conventional Flow, 9th ed.
Floyd
+ RL -
-
c. 6.0 V
VS
12 V
+
b. 5.0 V
R3
R1
R2
R4
5.0 V
© 2010 Pearson Higher Education,
Upper Saddle River, NJ 07458. • All Rights Reserved
Chapter 7
Quiz
10. For the circuit shown, if R3 opens, the voltage at point
A will
R1
270 
a. decrease
b. stay the same.
c. increase.
Principles of Electric Circuits, Conventional Flow, 9th ed.
Floyd
VS +
10 V
A
R2
330 
R3
470 
© 2010 Pearson Higher Education,
Upper Saddle River, NJ 07458. • All Rights Reserved
Chapter 7
Quiz
Answers:
Principles of Electric Circuits, Conventional Flow, 9th ed.
Floyd
1. b
6. c
2. c
7. a
3. d
8. a
4. d
9. d
5. b
10. c
© 2010 Pearson Higher Education,
Upper Saddle River, NJ 07458. • All Rights Reserved