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**Unformatted text preview: **SERIES RESISTORS
MY
136 141 SERIES de CIRCUITS
The current is limited only by the resistor R. The higher the rey
EXAMPLE 5.1 Determine the total resistance of the series conne
the less is the current, and conversely, as determined by Ohm's lay
In Pig. 5.6. Note that all the resistors appearing in this network are stas
For all one voltage
By convention (as discussed in Chapter 2), the direction of conven
source do circuits
current flow (conventional) as shown in Fig. 5.1 is opposite to
dard values.
Solution: Note in Fig. 5.6 that even though resistor Ry is on the ver
FIG. 5.2
electron flow (alston). Also, the uniform flow of charge dictates
Beal and resistor R, returns at the bottom to terminal b, all the resis-
Defining the direction of conventional flow for
direct current / be the same everywhere in the circuit. By following
tor are in series since there are only two resistor leads at each
rection of conventional flow, we notice that there is a rise in po
FIG. 5.6
single-source de circuits.
across the battery (- to + ) and a drop in potential across the resistor
connection point.
Series connection of resistors for Example $ 1
-). For single-voltage-source de circuits, conventional flow always
Applying Eq. (5.1) gives
V -
from a low potential to a high potential when pa
Ry - 20 02 + 220 0 + 1.210 + 3610
source, as shown in Fig. 5.2. However, conventional flow always
Ry = 7040 0 - 7.04 kf)
R
from a high to a low potential when passing through a resistor for
For any combination of voltage
sources in the same de circuit
number of voltage sources in the same
The circuit in Fig. 5.1
as shown in Fig. 5.3.
and
FIG. 5.3
For the special case where resistors are the same value, Eq. (5.1) can
Defining the polarity resulting from a conventional
chapter and the following chapters add elements to the system in
specific manner to introduce a range of concepts that will form a
current I through a resistive element.
part of the foundation required to analyze the most complex system
be modified as follows:
RT - NR
(5.2)
aware that the laws, rules, and so on introduced in Chapters 5 and
be used throughout your studies of electrical, electronic, or comp
systems. They are not replaced by a more advanced set as you pro
where / is the number of resistors in series of value R.
to more sophisticated material. It is therefore critical that you und
the concepts thoroughly and are able to apply the various procedural
methods with confidence.
EXAMPLE 5.2 Find the total resistance of the series resistors in
15.2 SERIES RESISTORS
Fig. 5.7. Again, recognize 3.3 kf) as a standard value.
2 3
10 0
30 0
100 0
Solution: Again, don't be concerned about the change in configura-
33kn
Before the series connection is described, first recognize that every
tion. Neighboring resistors are connected only at one point, satisfying
resistor has only two terminals to connect in a configuration-it is the
FIG. 5.7
fore referred to as a two-terminal device. In Fig. 5.4, one terminal of
the definition of series elements.
FIG. 5.4
sistor R2 is connected to resistor R, on one side, and the remain
Eq. (5.2):
RT = NR
in of four resistors of the so
(4)(3.3 kf2) = 13.2 k!?
(Example 5.21
Series connection of resistors
terminal is connected to resistor Ry on the other side, resulting in a
and only one, connection between adjoining resistors. When conne
in this manner, the resistors have establis
elements were con
ed a series connection. If de
cted to the same point, as shown in Fig. 5.5, the
It is important to realize that since the parameters of Eq. (5.1) can be
would not be a series connection between resistors R, and R2.
put in any order,
100
30 0
For resistors in series,
the total resistance of resistors in series is unaffected by the order in
Re $ 220 0
the total resistance of a series configuration is the sum of the
which they are connected.
resistance levels.
The result is that the total resistance in Fig. 5.8(a) is the same as in Fig
In equation form for any number (N) of resistors,
5.8(b). Again, note that all the resistors are standard values.
FIG. 5.5
n which none of the resistors
RT = R1 + R2 + R3 + Rx + ...+ RN
are in series.
A result of Eq. (5.1) is that
NYY
Wr
the more resistors we add in series, the greater is the resistance, no
20 0
matter what their vaine.
3 2 10 0
Further,
the largest resistor in a series combination will have the most impact
on the total resistance.
For the configuration in Fig. 5.4, the total resistance is
RT = RI + RX + R ,
FIG. 5.8
= 100 + 30 0 + 100 0
Two series combinations of the some elements with the sum
and...

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- Fall '19
- SK Abid