# Circuit Laws and Networking Theorems

• Sergey N. Makarov
• Reinhold Ludwig
• Stephen J. Bitar
Chapter

## Abstract

Prerequisites:
• Knowledge of circuit elements, their υ-i characteristics, and Ohm’s law (Chap. 2)

## Keywords:

Electric network Branches of electric network Nodes of electric network Loops of electric network Meshes of electric network Essential mesh Branch currents Branch voltages Series connection Parallel connection Shunt connection Kirchhoff’s current law Kirchhoff’s voltage law Maxwell’s minimum heat theorem Tellegen’s theorem Power conservation law for electric networks One-port network Equivalent electric networks Equivalent electric circuits Series battery bank Battery pack Dual-polarity power supply Common ground of the dual-polarity power supply Virtual ground of the dual-polarity power supply Parallel battery bank Series and parallel combinations (of resistances, of conductances), Equivalent resistance Equivalent circuit element Reduction of resistive networks Voltage divider circuit Voltage division rule Sensor circuit sensitivity Maximum sensitivity of the voltage divider circuit Current limiter Current-limiting resistor Current divider circuit Current division rule Wheatstone bridge (definition of, difference signal, difference voltage, balanced) Linear circuit (definition of, homogeneity, additivity, superposition) Nonlinear circuit (definition of, linearization, dynamic or small-signal resistance) Superposition theorem Superposition principle Y network Δ network Two-terminal networks Three-terminal networks Conversion between Y and Δ networks Replacing a node by a loop Δ to Y transformation Y to Δ transformation Balanced Y network Balanced Δ network Star to delta transformation T network T pad Π network Π pad Two-terminal network (definition of, input port, output port)

## Supplementary material

© Springer Nature Switzerland AG 2019

## Authors and Affiliations

• Sergey N. Makarov
• 1
• Reinhold Ludwig
• 2
• Stephen J. Bitar
• 3
1. 1.ECE DepartmentWorcester Polytechnic InstituteWorcesterUSA
2. 2.ECE DepartmentWorcester Polytechnic InstituteWorcesterUSA
3. 3.Worcester Polytechnic InstituteWorcesterUSA