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Example Problem. Find currents I
x
, I
2
, and I
3
.
20
Ω
6V
2
Ω
8
Ω
5
Ω
16
Ω
10
Ω
8V
I
X
I
2
I
3
AB
C
We first examine the circuit and select the node at the bottom of the circuit diagram as the
reference. We do this since there is one voltage source connected to this node as well as three
resistors.
We then identify the other essential nodes as A, B, and C.
We also note that a voltage source connects nodes A and B so we cannot use Ohm's law to
calculate the current in this voltage source. We will use the
Unknown Current Method
to
compute the current through the 6V voltage source. (We note that this unknown current is I
x
which the problem is already asking us to find.)
We write the equation for the currents leaving node A:
()
1)
(Eq.
8
.
0
=
I
+
V
15
.
0
or
10
8
=
I
+
10
V
+
20
V
:
terms
grouping
and
ng
Substituti
8V.
=
V
that
observe
We
0
=
I
+
8
+
2
V

V
+
20
V
x
A
x
A
A
C
X
C
A
A
We next focus on node B:
3)
(Eq.
2.4
=
V
(0.2625)
+
V
0.15
2,
Eq.
and
1
Eq.
Adding
2)
(Eq.
1.6
=
I

V
(0.2625)
or
0
=
I

5
8

V
+
16
V
B
A
X
B
X
B
B
We now deal with the constraint equation. We know that the voltage between nodes A and B will
ALWAYS be 6V since a voltage source is connected between them. In fact, we can state this
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 Fall '06
 MCCANN
 Volt

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