Chapter 3 Voltage and Current Laws Engineering Circuit Analysis Sixth Edition W.H. Hayt, Jr., J.E. Kemmerly, S.M. Durbin Copyright © 2002 McGraw-Hill, Inc. All Rights Reserved. User Note: Run View Show under the Slide Show menu to enable slide selection. Fig. 3.1 “A circuit containing three nodes and five branches …” Fig. 3.2Example node to illustrate the application of KCL. Fig “Addition of multiple voltage or current sources.” Fig Examples of circuits with multiple sources,... Fig (a) Series combination of N resistors. Fig (a) A circuit with N resistors in parallel. Fig An illustration of voltage division. Fig. 3.32Circuit for Practice Problem Fig. 3.33An illustration of current division. Fig “Determine the current I x if I 1 = 100 mA.”

Fig. 3.1 A circuit containing three nodes and five branches... W.H. Hayt, Jr., J.E. Kemmerly, S.M. Durbin, Engineering Circuit Analysis, Sixth Edition. Copyright ©2002 McGraw-Hill. All rights reserved. (a) A circuit containing three nodes and five branches. (b) Node 1 is redrawn to look like two nodes; it is still one node.

Fig. 3.2 Example node to illustrate the applicaton of Kirchhoff’s current law W.H. Hayt, Jr., J.E. Kemmerly, S.M. Durbin, Engineering Circuit Analysis, Sixth Edition. Copyright ©2002 McGraw-Hill. All rights reserved. Figure 3.2

(a) Series connected voltage sources can be replaced by a single source. (b) Parallel current sources can be replaced by a single source. Fig “Addition of multiple voltage or current sources.” W.H. Hayt, Jr., J.E. Kemmerly, S.M. Durbin, Engineering Circuit Analysis, Sixth Edition. Copyright ©2002 McGraw-Hill. All rights reserved.

Fig Examples of circuits with multiple sources, some of which violate Kirchhoff’s laws. W.H. Hayt, Jr., J.E. Kemmerly, S.M. Durbin, Engineering Circuit Analysis, Sixth Edition. Copyright ©2002 McGraw-Hill. All rights reserved. Examples of circuits with multiple sources, some of which are “illegal” as they violate Kirchhoff’s laws.

(a) Series combination of N resistors. (b) Electrically equivalent circuit. Fig (a) Series combination of N resistors. (b) Electrically equivalent circuit. W.H. Hayt, Jr., J.E. Kemmerly, S.M. Durbin, Engineering Circuit Analysis, Sixth Edition. Copyright ©2002 McGraw-Hill. All rights reserved.

Fig (a) A circuit with N resistors in parallel. (b) Equivalent circuit. W.H. Hayt, Jr., J.E. Kemmerly, S.M. Durbin, Engineering Circuit Analysis, Sixth Edition. Copyright ©2002 McGraw-Hill. All rights reserved. (a) A circuit with N resistors in parallel. (b) Equivalent circuit. Beginning with a simple KCL equation, or Thus, A special case worth remembering is

Fig An illustration of voltage division. W.H. Hayt, Jr., J.E. Kemmerly, S.M. Durbin, Engineering Circuit Analysis, Sixth Edition. Copyright ©2002 McGraw-Hill. All rights reserved. An illustration of voltage division. We may find v 2 by applying KVL and Ohm’s law: so Thus, or For a string of N series resistors, we may write:

Fig Circuit from Practice Problem W.H. Hayt, Jr., J.E. Kemmerly, S.M. Durbin, Engineering Circuit Analysis, Sixth Edition. Copyright ©2002 McGraw-Hill. All rights reserved. Use voltage division to determine v x in the adjacent circuit.

Fig An illustration of current division. W.H. Hayt, Jr., J.E. Kemmerly, S.M. Durbin, Engineering Circuit Analysis, Sixth Edition. Copyright ©2002 McGraw-Hill. All rights reserved. An illustration of current division. The current flowing through R 2 is For a parallel combination of N resistors, the current through R k is or

Determine the current I x if I 1 = 100 mA. Fig Determine the current I x if I 1 = 100 mA. W.H. Hayt, Jr., J.E. Kemmerly, S.M. Durbin, Engineering Circuit Analysis, Sixth Edition. Copyright ©2002 McGraw-Hill. All rights reserved.