- Title Pages
- Preface
- Contents
- 1 Some essential mathematics
- 2 Static electric fields in vacuum
- 3 The electrostatics of conductors
- 4 Static magnetic fields in vacuum
- 5 Quasi-static electric and magnetic fields in vacuum
- 6 Ohm’s law and electric circuits
- 7 Electromagnetic fields and waves in vacuum
- 8 The electromagnetic potentials
- 9 Static electric and magnetic fields in matter
- 10 Some applications of Maxwell’s equations in matter
- 11 Electromagnetic radiation
- 12 Electromagnetism and special relativity
- Appendix A Vectors and Cartesian tensors
- Appendix A Vectors and Cartesian tensors
- Appendix B Cartesian coordinates
- Appendix C Spherical polar coordinates
- Appendix D Cylindrical polar coordinates
- Appendix E The Dirac delta function
- Appendix E The Dirac delta function
- Appendix F Legendre polynomials
- Appendix F Legendre polynomials
- Appendix G Bessel functions
- Appendix G Bessel functions
- Appendix H Parametric representation of a surface
- Appendix H Parametric representation of a surface
- Appendix I The Cauchy–Riemann equations
- Appendix I The Cauchy–Riemann equations
- Appendix J Questions involving computational work
- Glossary of symbols
- Index

# Ohm’s law and electric circuits

# Ohm’s law and electric circuits

- Chapter:
- (p.285) 6 Ohm’s law and electric circuits
- Source:
- Solved Problems in Classical Electromagnetism
- Author(s):
### J. Pierrus

- Publisher:
- Oxford University Press

This chapter considers various simple dc and ac circuits which contain at least one active element (always a voltage source) and passive elements (resistors, capacitors and inductors) arranged in different combinations to form a bilateral network. The notions of complex voltage, complex current and complex impedance are introduced and then used in the ensuing analysis. Some standard ‘network theorems’ including Kirchhoff’s rules, the delta-star transformation, Thevenin’s theorem and the superposition theorem are employed. Included in the questions are circuits involving bridges, filters, audio amplifiers and transformers. Important topics such as series and parallel resonance in *LRC* circuits are also considered along the way. Much of the laborious algebra involved in manipulating the complex quantities above is avoided by relegating this task to *Mathematica*.

*Keywords:*
passive circuit resistance, reactance impedance, Ohm’s law Kirchhoff’s rules, The venin’s theorem resonance, filter transformer

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- Title Pages
- Preface
- Contents
- 1 Some essential mathematics
- 2 Static electric fields in vacuum
- 3 The electrostatics of conductors
- 4 Static magnetic fields in vacuum
- 5 Quasi-static electric and magnetic fields in vacuum
- 6 Ohm’s law and electric circuits
- 7 Electromagnetic fields and waves in vacuum
- 8 The electromagnetic potentials
- 9 Static electric and magnetic fields in matter
- 10 Some applications of Maxwell’s equations in matter
- 11 Electromagnetic radiation
- 12 Electromagnetism and special relativity
- Appendix A Vectors and Cartesian tensors
- Appendix A Vectors and Cartesian tensors
- Appendix B Cartesian coordinates
- Appendix C Spherical polar coordinates
- Appendix D Cylindrical polar coordinates
- Appendix E The Dirac delta function
- Appendix E The Dirac delta function
- Appendix F Legendre polynomials
- Appendix F Legendre polynomials
- Appendix G Bessel functions
- Appendix G Bessel functions
- Appendix H Parametric representation of a surface
- Appendix H Parametric representation of a surface
- Appendix I The Cauchy–Riemann equations
- Appendix I The Cauchy–Riemann equations
- Appendix J Questions involving computational work
- Glossary of symbols
- Index