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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