var(t)=vab(t)+ vbe(t)+ vea(t)+ vde(t)+ vef(t) Had we chosen the path corresponding to the edge sequence lep,e, e6, e) for the path, we would have obtained t)=vab(r)+ ve(t)+ ver(t) This demonstrates how KCL can be used to determine the voltage between a pair of nodes. It also reveals the fact that the voltage between a pair of nodes is independent of the path between the nodes on which the voltages are measured Kirchhoffs Voltage Law in the Complex domain Kirchhoffs voltage law also applies to the phasors of the voltages in a circuit in steady state and to the Fourier transforms and Laplace transforms of the voltages in a circuit. Importance of KVL and KCL Kirchhoff's current law is used extensively in nodal analysis because it is amenable to computer-based imple mentation and supports a systematic approach to circuit analysis. Nodal analysis leads to a set of algebraic equations in which the variables are the voltages at the nodes of the circuit. This formulation is popular in CAd programs because the variables correspond directly to physical quantities that can be measured easily Kirchhoff's voltage law can be used to completely analyze a circuit, but it is seldom used in large-scale circuit simulation programs. The basic reason is that the currents that correspond to a loop of a circuit do not necessarily correspond to the currents in the individual branches of the circuit. Nonetheless, KVL is frequently used to troubleshoot a circuit by measuring voltage drops across selected components. Defining Terms Branch: A symbol representing a path for current through a component in an electrical circuit. Branch current: The current in a branch of a circuit Branch voltage: The voltage across a branch of a circuit Independent source: A voltage(current) source whose voltage(current)does not depend on any other voltage or current in the circuit Node: A symbol representing a physical connection between two electrical components in a circuit. Node voltage: The voltage between a node and a reference node(usually ground Related Topic 3.6 Graph Theory eferences M.D. Ciletti, Introduction to Circuit Analysis and Design, New York: Holt, Rinehart and winston, 1988 R H. Smith and R.C. Dorf, Circuits, Devices and Systems, New York: Wiley, 1992 Further information Kirchhoff's laws form the foundation of modern computer software for analyzing electrical circuits. The interested reader might consider the use of determining the minimum number of algebraic equations that fully characterizes the circuit. It is determined by KCL, KVL, or some mixture of the two? c 2000 by CRC Press LLC© 2000 by CRC Press LLC vaf(t) = vab (t) + vbc(t) + vcd (t) + vde(t) + vef(t) Had we chosen the path corresponding to the edge sequence {e1, e5 , e6 , e7} for the path, we would have obtained vaf(t) = vab (t) + vbe(t) + vef(t) This demonstrates how KCL can be used to determine the voltage between a pair of nodes. It also reveals the fact that the voltage between a pair of nodes is independent of the path between the nodes on which the voltages are measured. Kirchhoff’s Voltage Law in the Complex Domain Kirchhoff’s voltage law also applies to the phasors of the voltages in a circuit in steady state and to the Fourier transforms and Laplace transforms of the voltages in a circuit. Importance of KVL and KCL Kirchhoff’s current law is used extensively in nodal analysis because it is amenable to computer-based imple￾mentation and supports a systematic approach to circuit analysis. Nodal analysis leads to a set of algebraic equations in which the variables are the voltages at the nodes of the circuit. This formulation is popular in CAD programs because the variables correspond directly to physical quantities that can be measured easily. Kirchhoff’s voltage law can be used to completely analyze a circuit, but it is seldom used in large-scale circuit simulation programs. The basic reason is that the currents that correspond to a loop of a circuit do not necessarily correspond to the currents in the individual branches of the circuit. Nonetheless, KVL is frequently used to troubleshoot a circuit by measuring voltage drops across selected components. Defining Terms Branch: A symbol representing a path for current through a component in an electrical circuit. Branch current: The current in a branch of a circuit. Branch voltage: The voltage across a branch of a circuit. Independent source: A voltage (current) source whose voltage (current) does not depend on any other voltage or current in the circuit. Node: A symbol representing a physical connection between two electrical components in a circuit. Node voltage: The voltage between a node and a reference node (usually ground). Related Topic 3.6 Graph Theory References M.D. Ciletti, Introduction to Circuit Analysis and Design, New York: Holt, Rinehart and Winston, 1988. R.H. Smith and R.C. Dorf, Circuits, Devices and Systems, New York: Wiley, 1992. Further Information Kirchhoff’s laws form the foundation of modern computer software for analyzing electrical circuits. The interested reader might consider the use of determining the minimum number of algebraic equations that fully characterizes the circuit. It is determined by KCL, KVL, or some mixture of the two?