Module 1 − Introduction to Matter, Energy, and Direct Current
To find the current through R2 and R3, refer to the original circuit, figure
3-54(A). You know ER2 and ER3 from previous calculation.
To find power used by R2 and R3, using values from previous
Now that you have solved for the unknown quantities in this circuit, you can
apply what you have learned to any series, parallel, or combination circuit. It
is important to remember to first look at the circuit and from observation make
your determination the type circuit, what is known, and what you are looking for.
A minute spent in this manner may save you many unnecessary calculations.
Having computed all the currents and voltages figure 3-54, a complete description
the operation the circuit can be made. The total current 3 amps leaves the negative
terminal the battery and flows through the 8-ohm resistor (R1). In so doing, a voltage
drop 24 volts occurs across resistor R1. At point A, this 3-ampere current divides
into two currents. the total current, 1.8 amps flows through the 20-ohm resistor.
The remaining current 1.2 amps flows from point A, down through the 30-ohm resistor
to point B. This current produces a voltage drop 36 volts across the 30-ohm resistor.
(Notice that the voltage drops across the 20- and 30-ohm resistors are the same.)
The two branch currents 1.8 and 1.2 amps combine at junction B and the total current
3 amps flows back to the source. The action the circuit has been completely described
with the exception power consumed, which could be described using the values previously
It should be pointed out that the combination circuit is not difficult to solve.
The key to its solution lies in knowing the order in which the steps the solution
must be accomplished.
Practice Circuit Problem
Figure 3-55 is a typical combination circuit. To make sure you understand the
techniques solving for the unknown quantities, solve for ER1.
Figure 3-55. - Combination practice circuit.
It is not necessary to solve for all the values in the circuit to compute the
voltage drop across resistor R1 (E R1). First look at the circuit and determine
that the values given do not provide enough information to solve for ER1 directly.
If the current through R1 (IR1) is known, then ER1 can be computed by applying
The following steps will be used to solve the problem.
1. The total resistance (RT) is calculated by the use equivalent resistance.
Redraw the circuit as shown in figure 3-55(B). Given:
Redraw the circuit as shown in figure 3-55(C). Given:
2. The total current (IT) is now computed. Given:
3. Solve for the voltage dropped across Req2. This represents the voltage dropped
across the network R1, R2, and R3 in the original circuit.
4. Solve for the current through Req1. (Req1 represents the network R1
and R2 in the original circuit.) Since the voltage across each branch a parallel
circuit is equal to the voltage across the equivalent resistor representing the
5. Solve for the voltage dropped across R1 (the quantity you were asked
to find). Since Reqi represents the series network R1 and R2 and total
current flows through each resistor in a series circuit, IR1 must equal IReq1.
Q42. Refer to figure 3-55(A). If the following resistors were replaced
with the values indicated: R1 = 900, R3 = 1k , what is the total
power in the circuit? What is ER2?
REDRAWING Circuits for CLARITY
You will notice that the schematic diagrams you have been working with have shown
parallel circuits drawn as neat square figures, with each branch easily identified.
In actual practice the wired circuits and more complex schematics are rarely
laid out in this simple form. For this reason, it is important for you to recognize
that circuits can be drawn in a variety ways, and to learn some the techniques for
redrawing them into their simplified form. When a circuit is redrawn for clarity
or to its simplest form, the following steps are used.
i. Trace the current paths in the circuit.
2. Label the junctions in the circuit.
3. Recognize points which are at the same potential.
4. Visualize a rearrangement, "stretching" or "shrinking," connecting
5. Redraw the circuit into simpler form (through stages if necessary).
To redraw any circuit, start at the source, and trace the path current flow through
the circuit. At points where the current divides, called JUNCTIONS, parallel branches
begin. These junctions are key points reference in any circuit and should be labeled
as you find them. The wires in circuit schematics are assumed to have NO Resistance
and there is NO Voltage drop along any wire. This means that any unbroken wire is
at the same voltage all along its length, until it is interrupted by a resistor,
battery, or some other circuit component. In redrawing a circuit, a wire can be
"stretched" or "shrunk" as much as you like without changing any electrical characteristic
Figure 3-56(A) is a schematic a circuit that is not drawn in the box-like fashion used in previous illustrations. To redraw this circuit, start at the voltage source
and trace the path for current to the junction marked (a). At this junction the
current divides into three paths. If you were to stretch the wire to show
three current paths, the circuit would appear as shown in figure 3-56(B).
Figure 3-56. - Redrawing a simple parallel circuit.
While these circuits may appear to be different, the two drawings actually
represent the same circuit. The drawing in figure 3-56(B) is the familiar box-like
structure and may be easier to work with. Figure 3-57(A) is a schematic a circuit
shown in a box-like structure, but may be misleading. This circuit in reality is
a series-parallel circuit that may be redrawn as shown in figure 3-57(B). The drawing
in part (B) the figure is a simpler representation the original circuit and could
be reduced to just two resistors in parallel.
Figure 3-57. - Redrawing a simple series-parallel circuit.
Redrawing a Complex Circuit
Figure 3-58(A) shows a complex circuit that may be redrawn for clarification
in the following steps.
Figure 3-58. - Redrawing a complex circuit.
Note: As you redraw the circuit, draw it in simple box-like form. Each time
you reach a junction, a new branch is created by stretching or shrinking the wires.
Start at the negative terminal the voltage source. Current flows through R1
to a junction and divides into three paths; label this junction (a). Follow one
the paths current through R2 and R3 to a junction where the current
divides into two more paths. This junction is labeled (b).
The current through one branch this junction goes through R5 and
back to the source. (The most direct path.) Now that you have completed a path for
current to the source, return to the last junction, (b). Follow current through
the other branch from this junction. Current flows from junction (b) through R4
to the source. All the paths from junction (b) have been traced. Only one path from
junction (a) has been completed. You must now return to junction (a) to complete
the other two paths. From junction (a) the current flows through R7 back to
the source. (There are no additional branches on this path.) Return to junction
(a) to trace the third path from this junction. Current flows through R6
and R8 and comes to a junction. Label this junction (c). From junction (c)
one path for current is through R9 to the source. The other path for
current from junction (c) is through R10 to the source. All the junctions
in this circuit have
now been labeled. The circuit and the junction can be redrawn as shown in figure
3-58(C). It is much easier to recognize the series and parallel paths in the redrawn
Q43. What is the total resistance the circuit shown in figure 3-59? (Hint:
Redraw the circuit to simplify and then use equivalent resistances to compute for
Figure 3-59. - Simplification circuit problem.
Q44. What is the total resistance the circuit shown in figure 3-60?
Figure 3-60. - Source resistance in a parallel circuit.
Q45. What effect does the internal resistance have on the rest the circuit
shown in figure 3-60?
EFFECTS OPEN and Short Circuits
Earlier in this chapter the terms open and short circuits were discussed. The
following discussion deals with the effects on a circuit when an open or a short
The major difference between an open in a parallel circuit and an open in a series
circuit is that in the parallel circuit the open would not necessarily disable the
circuit. If the open condition occurs in a series portion the circuit, there will
be no current because there is no complete path for current flow. If, on the other
hand, the open occurs in a parallel path, some current will still flow in the circuit.
The parallel branch where the open occurs will be effectively disabled, total resistance
the circuit will INCREASE, and total current will DECREASE.
To clarify these points, figure 3-61 illustrates a series parallel circuit. First
the effect an open in the series portion this circuit will be examined. Figure 3-61(A)
shows the normal circuit, RT = 40 ohms and IT = 3 amps. In figure 3-61(B)
an open is shown in the series portion the circuit, there is no complete path for
current and the resistance the circuit is considered to be infinite.
Figure 3-61. - Series-parallel circuit with opens.
In figure 3-61(C) an open is shown in the parallel branch R3. There
is no path for current through R3. In the circuit, current flows through R1
and R2 only. Since there is only one path for current flow, R1 and R2
are effectively in series.
Under these conditions RT = 120 and IT = 1 amp. As you
can see, when an open occurs in a parallel branch, total circuit resistance increases
and total circuit current decreases.
A short circuit in a parallel network has an effect similar to a short in a series
circuit. In general, the short will cause an increase in current and the possibility
component damage regardless the type
and Direct Current
||Alternating Current and Transformers
||Circuit Protection, Control, and Measurement
||Electrical Conductors, Wiring Techniques,
and Schematic Reading
||Generators and Motors
||Electronic Emission, Tubes, and Power Supplies
||Solid-State Devices and Power Supplies
||Wave-Generation and Wave-Shaping Circuits
||Wave Propagation, Transmission Lines, and
||Introduction to Number Systems and Logic Circuits
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||Principles of Synchros, Servos, and Gyros
||Introduction to Test Equipment
||Radio-Frequency Communications Principles
||The Technician's Handbook, Master Glossary
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||Introduction to Digital Computers
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