Download Problem 3.63 Apply the source-superposition method to the circuit in

Problem 3.63 Apply the source-superposition method to the circuit in Fig. P3.63
to determine:
(a) Vx′ , the component of Vx due to the 1-A current source alone.
(b) Vx′′ , the component of Vx due to the 10-V voltage source alone.
(c) Vx′′′ , the component of Vx due to the 3-A current source alone.
(d) The total voltage Vx = Vx′ +Vx′′ +Vx′′′ .
+ Vx _
18 Ω
15 Ω
1A
+
_
12 Ω
10 V
5Ω
+
_
10 Ω
3A
3Ω
Figure P3.63: Circuit of Problem 3.63.
Solution:
(a) 1-A source alone:
+ Vx′ _
18 Ω
15 Ω
1A
12 Ω
5Ω
3Ω
Fig. P3.63 (a)
Because the 1-A current source is across a short circuit, it will flow entirely through
it. Hence,
Vx′ = 0.
(b) Voltage source alone:
+ Vx′′ _
18 Ω
15 Ω
12 Ω
+
_
10 V
5Ω
3Ω
Fig. P3.63 (b)
Voltage division yields
Vx′′ =
10 × 15
= 5 V.
15 + 10 + 5
(c) 3-A source alone:
c
All rights reserved. Do not reproduce or distribute. 2013
National Technology and Science Press
+ Vx′′′ _
18 Ω
15 Ω
12 Ω
10 Ω
5Ω
3A
3Ω
Fig. P3.63 (c)
Current division yields
I=
3 × 10
= 1 A.
15 + 10 + 5
Hence,
Vx′′′ = 15(−1) = −15 V.
(d)
Vx = Vx′ +Vx′′ +Vx′′′
= 0 + 5 − 15 = −10 V.
c
All rights reserved. Do not reproduce or distribute. 2013
National Technology and Science Press