Supernode: In Figure below; the branch current through the 6 V source is certainly no known and cannot be directly expressed using Ohm's law; a 6 V 4 mA 6 mA 6KD 312 kn. To solve this problem, we recall that (N-1) linearly independent equations are required to determine the (N-1) nonreference node voltages in an N-node circuit. Since our network has three nodes (Le /N-3), we need two lincarly independent equations. Now note that if somehow.one of the node.voltages is known, we immediately know the other (i.e., if , is known, then VV-6. If is known, then V=Vz+6, Therefore, the difference in potential between the two nodes is constrained by the voltage source and, hence; V-V6----(1) This constraint equation is one of the two lincarly independent equations needed to determine the node voltages. Next consider the network in Figure below, in which the 6V source is completely enclosed within the dashed surface. Juper node 6 V 36 kl 312 k 4 mA The constraint equation governs this dashed portion of the network. The emaining equation is obtained by applying KCL to this dashed surface, which is ommonly called a supernode Now we can apply KCL for the supernode as: 6 10-+ 6 10 4 10-3 =0 12-10

Supernode: In Figure below; the branch current through the 6 V source is certainly no known and cannot be directly expressed using Ohm's law; a 6 V 4 mA 6 mA 6KD 312 kn. To solve this problem, we recall that (N-1) linearly independent equations are required to determine the (N-1) nonreference node voltages in an N-node circuit. Since our network has three nodes (Le /N-3), we need two lincarly independent equations. Now note that if somehow.one of the node.voltages is known, we immediately know the other (i.e., if , is known, then VV-6. If is known, then V=Vz+6, Therefore, the difference in potential between the two nodes is constrained by the voltage source and, hence; V-V6----(1) This constraint equation is one of the two lincarly independent equations needed to determine the node voltages. Next consider the network in Figure below, in which the 6V source is completely enclosed within the dashed surface. Juper node 6 V 36 kl 312 k 4 mA The constraint equation governs this dashed portion of the network. The emaining equation is obtained by applying KCL to this dashed surface, which is ommonly called a supernode Now we can apply KCL for the supernode as: 6 10-+ 6 10 4 10-3 =0 12-10

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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Concept explainers

Thevenin Theorem

Any linear circuit, no matter how complex, maybe simplified to an equivalent circuit utilizing only a single voltage source and series resistance coupled to a load, according to Thevenin's Theorem. The superposition principle says that all foundational equations must be linear, and the notion of "linear" is still the same (i.e., there should not be any exponentials or roots). This is particularly the case when operating with passive elements like resistors, inductors, and capacitors. However, some components (particularly some gaseous and semiconductor devices like tunnel diode, Schottky diode, transistors like BJT, MOSFET) are nonlinear, meaning their current resistance fluctuates with voltage and current. As a result, circuits made up of these parts are known as nonlinear circuits.

Question

Supernode:
In Figure below; the branch current through the 6 V source is certainly no
known and cannot be directly expressed using Ohm's law
6 V
4 mA
6 mA
312 kn.
To solve this problem, we recall that (N-1) linearly independent equations
are required to determine the (N-1) nonreference node voltages in an N-node
circuit. Since our network has three nodes (Le /N-3), we ned two lincarly
independent equations. Now note that if somehow.one of the node.voltages is
known, we immediately know the other (i.e., if K, is known, then FV-6. If V
is known, then V=Vz+6, Therefore, the difference in potential between the two
nodes is constrained by the voltage source and, hence,
This constraint equation is one of the two linearly independent equations
needed to determine the node voltages. Next consider the network in Figure
below, in which the 6V source is completely enclosed within the dashed surface.
kelivo
Juper node
6 V
36 kn
$12 k
4 mA
The constraint equation governs this dashed portion of the network. The
remaining equation is obtained by applying KCL to this dashed surface, which is
commonly called a supernode Now we can apply KCL for the supernode as:
610-3+
6+10
+ 4 - 10-3 = 0
(2)
12-10

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