Figure 25. A series circuit
−V
s
+ I R
1
+ I R
2
+ I R
3
=0
Above equation can be also rewritten as:
R
eq
= R
1
+ R
2
+ R
3
=
V
s
I
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Where, the equivalent resistance,
R
eq
, is the sum of three resister in figure 25 which is called
equivalent resistance. In general, if there are
N
resisters in series, their equivalent resistance
is equal to the sum of all resistance, namely:
R
eq
=
∑
i=1
N
R
i
Figure 26. A parallel circuit
Two or more resisters are said to be parallel if the same voltage is across each of resisters.
Consider the three parallel resisters as illustrated in figure 26, a equivalent circuit for figure 26
is derived through Kirchoff’s Current Law as
− I +
V
s
R
1
+
V
s
R
2
+
V
s
R
3
=0
Above equivalent resistance can be also rewritten as:
R
eq
=
V
s
I =
1
1
R
1
+
1
R
2
+
1
R
3
In general, if there are
N
resisters in parallel,
R
eq
=
V
s
I =
1
1
R
1
+
1
R
2
+ ⋯ +
1
R
N
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