I would like to know the steps to solve the problem to get Equation 10.1.2 in detail, thank you in advance for the answer.

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I would like to know the steps to solve the problem to get Equation 10.1.2 in detail, thank you in advance for the answer.
Thus, the frequency-domain equivalent circuit is as shown in Fig. 10.2.
or
20/0° V
Figure 10.2
At node 2,
10 92
www
Applying KCL at node 1,
20 - V₁
10
By simplifying, we get
A₁ =
20
0
Frequency-domain equivalent of the circuit in Fig. 10.1.
But Ix = V₁/-j2.5. Substituting
2V₁
-j2.5
V₁
We obtain the determinants as
Δ=
V₁ =
j2.5
15
V₂ =
21x +
(1 + j1.5)V₁ + j2.5V₂ = 20
-j2.5 Q
Δι
A
1+j1.5 j2.5
11
= 300,
42
A
V₁
-j2.5
11V₁ +15V₂ = 0
Equations (10.1.1) and (10.1.2) can be put in matrix form as
25][]-[20]
+
j4 92
m
V₁ - V₂ V₂
j4
j2
this gives
V₁ - V₂
j4
15
1+j1.5
11
+
j2.5
15
300
15 - j5
21₁
-220
15 - j5
Δ2 =
=
V₂2₂
V₁ - V₂
j4
V₂
j2
= 15 - j5
1+j1.5 20
11
0
18.97/18.43° V
= ¹ +
j2 92
13.91/198.3° V
(10.1.1)
(10.1.2)
= -220
Transcribed Image Text:Thus, the frequency-domain equivalent circuit is as shown in Fig. 10.2. or 20/0° V Figure 10.2 At node 2, 10 92 www Applying KCL at node 1, 20 - V₁ 10 By simplifying, we get A₁ = 20 0 Frequency-domain equivalent of the circuit in Fig. 10.1. But Ix = V₁/-j2.5. Substituting 2V₁ -j2.5 V₁ We obtain the determinants as Δ= V₁ = j2.5 15 V₂ = 21x + (1 + j1.5)V₁ + j2.5V₂ = 20 -j2.5 Q Δι A 1+j1.5 j2.5 11 = 300, 42 A V₁ -j2.5 11V₁ +15V₂ = 0 Equations (10.1.1) and (10.1.2) can be put in matrix form as 25][]-[20] + j4 92 m V₁ - V₂ V₂ j4 j2 this gives V₁ - V₂ j4 15 1+j1.5 11 + j2.5 15 300 15 - j5 21₁ -220 15 - j5 Δ2 = = V₂2₂ V₁ - V₂ j4 V₂ j2 = 15 - j5 1+j1.5 20 11 0 18.97/18.43° V = ¹ + j2 92 13.91/198.3° V (10.1.1) (10.1.2) = -220
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