Biomedical Engineering Reference
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I A
I A
=
+
+
Circuit
A
V S
V S
R EQ
FIGURE 9.15
Equivalent circuits.
by a DC voltage
V s . These two circuits are equivalent if
I A ¼ I B :
We represent the resistance
of either circuit using Ohm's law as
R EQ ¼ V s
I A ¼ V s
ð
9
:
12
Þ
I B
Thus, it follows that any circuit consisting of resistances can be replaced by an equivalent
circuit, as shown in Figure 9.15. When we discuss a Th´venin equivalent circuit later in this
chapter, we will expand this remark to include any combination of sources and resistances.
9.4.4 Series and Parallel Combinations of Resistance
Resistors in Series
If the same current flows from one resistor to another, the two are said to be in series. If
these two resistors are connected to a third and the same current flows through all of them,
then the three resistors are in series. In general, if the same current flows through
N
resis-
tors, then the
resistors are in series. Consider Figure 9.16 with three resistors in series.
An equivalent circuit can be derived through KVL as
N
V s þ IR
þ IR
þ IR
¼
0
1
2
3
I
R 1
+
V S
R 2
R 3
FIGURE 9.16
A series circuit.
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