Download Problem 3.4 For the circuit in Fig. P3.4: (a) Apply nodal analysis to

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Transcript
Problem 3.4 For the circuit in Fig. P3.4:
(a) Apply nodal analysis to find node voltages V1 and V2 .
(b) Determine the voltage VR and current I.
V1
1Ω
16 V
+
_
1Ω
V2
1Ω
+ VR
I
_
1Ω
1Ω
Figure P3.4: Circuit for Problem 3.4.
Solution: (a) At nodes V1 and V2 ,
V1 − 16 V1 V1 −V2
+ +
=0
1
1
1
V2 −V1 V2 V2
+ +
=0
1
1
1
Node 1:
Node 2:
(1)
(2)
Simplifying Eqs. (1) and (2) gives:
3V1 −V2 = 16
(3)
−V1 + 3V2 = 0.
(4)
Simultaneous solution of Eqs. (3) and (4) leads to:
V1 = 6 V,
V2 = 2 V.
(b)
VR = V1 −V2 = 6 − 2 = 4 V
I=
V2 2
= = 2 A.
1
1
c
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National Technology and Science Press