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Electric Circuits Analysis Guide: Fundamentals, Laws, and Applications

This guide covers the basic concepts of analyzing electric circuits with sources, resistors, capacitors, and inductors. Topics include Kirchhoff's laws, power ratings, Ohm's Law, equivalent resistance computation, voltage dividers, current dividers, and ideal vs. real voltage sources. Practical examples and computations are provided to enhance understanding and application in circuit analysis.

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Electric Circuits Analysis Guide: Fundamentals, Laws, and Applications

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  1. ECE 4991 Electrical and Electronic CircuitsChapter 2

  2. Hitchhikers Guide to the Galaxy • Chapter 2 - The basic concepts and practice at analyzing simple electric circuits with sources and resistors • Chapter 3 – More harder networks to analyze and the notion of equivalent circuits • Chapter 4 – Capacitors and inductors added to the mix • Chapter 5 – Analyzing transient situations in complex passive networks • Chapter 8 – New subject – the wonders of operational amplifiers as system elements • Chapter 9 – Introduction to semiconductors – the basics and diodes – more network analysis • Chapter 10 – Bipolar junction transistors and how they work – now you can build your own op amp

  3. What’s Important in Chapter 2 • Definitions • KCL & applications • KVL & applications • Electric power / power ratings • Ohm’s Law • Equivalent resistance computation • Voltage Dividers / Current Dividers • Ideal v real voltage sources

  4. 1. Definitions • Voltage • Current • Charge • Power • Energy • Network • Branch • Node • Loop • Mesh

  5. 2. KCL & Applications • First, note that for current to flow, there must be a closed circuit • Kirchhoff’s Current Law (KCL)  in = 0

  6. 2. Applying KCL • Find nodes • Label currents • Write node equations

  7. 2 ½ . Current Speed • Metals are seas of electrons – each atom gives up an electron which can move and be part of the current • i = dq/dt = charge density/length of wire * carrier velocity • Therefore carrier velocity = v = i / charge density • Charge density = e * ~3x1023/m3 = ~5x104 Coul/m3 • For a 1 amp current, v = ~ 2x10-5 m/s = ~ .02 mm/s !

  8. 3. KVL & Applications • First, note that for KVL to work, there must be a closed circuit • Kirchhoff’s Voltage Law (KVL) vn = 0

  9. 3. Applying KVL • Label voltages • Pick loops • Write loop equations

  10. 4. Electric Power / Power Ratings • Power is work done per unit time • For an electronic element, Power is the product of the voltage across the element and the current flowing through it P = VI • “Positive Power” is dissipated by a load • “Negative Power” is provided by an energy source

  11. 4 ½. I-V Characteristics i v

  12. 5. Ohm’s Law • A resistor is a passive electronic circuit element with the following property – the voltage developed across it is directly proportional to the electric current through it V = IR • R is measured in volts per amp • 1 volt/amp = 1 ohm (Ω) • What are some ways to calculate the power dissipated in resistor R?

  13. 5. Working with Ohm’s Law

  14. 6. Equivalent Resistance Computation

  15. 6. Equivalent R • For series resistors Req =  Ri • For parallel resistors 1 / Req =  1/Ri

  16. 6. Equivalent R Practice

  17. 7. Voltage & Current Dividers • A voltage divider accesses a fraction of a voltage • A current divider accesses a fraction of a current

  18. I I 8. Ideal v Real Sources • Ideal sources are independent of loading • Real sources have equivalent series or parallel internal resistances

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