I need help with this supernode problem. I do the KCL at the supernode, but then get two equations, and 3 variables. That confuses me. Also, is my equation for i-phi correct? Example 9: Determine is in the circuit shown in the left panel of Figure 17.10 is5Ω ,V3is40NUz-450 V50 N100 N ( ↑)4ARCL forU, - UzSO =0L,C.M²40くu、-8u, t U, - 5Oqu, - 8u2EqualonKCLforHe supemaderUz-V,(0ig -4 =050100Vz-V,Va - UiUz-4=0Uz - U,10 Uz-Y=050100L.C.M= l0200 uz t 2a,400=020 ve -20v, + Zuz t Us-178ua + 1 80 + U3 = 400 Equalion eDid I doS Dan thing unong if I have2 equaHons, butthree varia bles,D,, Uz, tb Uz ? -I just did ore.IsMy ig conut?

Answered: I need help with this supernode…

Introductory Circuit Analysis (13th Edition)

13th Edition

ISBN:9780133923605

Author:Robert L. Boylestad

Publisher:Robert L. Boylestad

Chapter1: Introduction

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I need help with this supernode problem. I do the KCL at the supernode, but then get two equations, and 3 variables. That confuses me. Also, is my equation for i-phi correct?

Example 9: Determine is in the circuit shown in the left panel of Figure 17.
10 is
5Ω ,
V3
is
40N
Uz-4
50 V
50 N
100 N ( ↑)4A
RCL for
U, - Uz
SO =0
L,C.M²40
くu、-8u, t U, - 5O
qu, - 8u2
Equalon
KCL
for
He supemader
Uz-V,
(0ig -4 =0
50
100
Vz-V,
Va - Ui
Uz
-4=0
Uz - U,
10 Uz
-Y=0
50
100
L.C.M= l0
200 uz t 2a,
400=0
20 ve -20v, + Zuz t Us
-178ua + 1 80 + U3 = 400 Equalion e
Did I do
S Dan thing unong if I have
2 equaHons, but
three varia bles,
D,, Uz, tb Uz ? -I just did ore.
Is
My ig conut?

Expert Solution

Step 1

your two equations are correct and third equation which can be written is given below:

$v_{2} = v_{3} + 10 i_{ϕ} v_{2} = v_{3} + 10 \times \frac{v_{2} - v_{1}}{5} v_{2} = v_{3} + 2 v_{2} - 2 v_{1} 2 v_{1} = v_{3} + v_{2} . . . . . (3)$

i hope now you can solve your question with the third equation.

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