how to solve this equations Five nodes requires four KCL equations in general nodal analysis,but we have reduced this requirement to only two, as we formed twoseparate supernodes. Each supernode required a KVL equation (Eq. [22]and v₁ = −12, the latter written by inspection). Neither dependentsource was controlled by a nodal voltage, so two additional equationswere needed as a result.With this done, we can now eliminate v₁ and vy to obtain a set ofVxfour equations in the four node voltages:-2v₁ +2.5v₂ - 0.5v30.1v₁ - V₂ +0.5v3 + 1.4v4 ==140= -12VI0.201+V3 - 1.2V4 = 0Solving, v₁ = −12 V, v₂ = −4 V, v3 = 0 V, and v4 = −2 V.

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Electrical Engineering

how to solve this equations

Introductory Circuit Analysis (13th Edition)

13th Edition

ISBN:9780133923605

Author:Robert L. Boylestad

Publisher:Robert L. Boylestad

Chapter1: Introduction

Section: Chapter Questions

Problem 1P: Visit your local library (at school or home) and describe the extent to which it provides literature...

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Question

how to solve this equations

Five nodes requires four KCL equations in general nodal analysis,
but we have reduced this requirement to only two, as we formed two
separate supernodes. Each supernode required a KVL equation (Eq. [22]
and v₁ = −12, the latter written by inspection). Neither dependent
source was controlled by a nodal voltage, so two additional equations
were needed as a result.
With this done, we can now eliminate v₁ and vy to obtain a set of
Vx
four equations in the four node voltages:
-2v₁ +2.5v₂ - 0.5v3
0.1v₁ - V₂ +0.5v3 + 1.4v4 =
=
14
0
= -12
VI
0.201
+
V3 - 1.2V4 = 0
Solving, v₁ = −12 V, v₂ = −4 V, v3 = 0 V, and v4 = −2 V.

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