ECE 4991 Electrical and Electronic Circuits Chapter 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

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

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

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

2. Applying KCL Find nodes Label currents Write node equations

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 !

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

3. Applying KVL Label voltages Pick loops Write loop equations

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

4 ½. I-V Characteristics i v

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?

5. Working with Ohm’s Law

6. Equivalent Resistance Computation

6. Equivalent R For series resistors Req =  Ri For parallel resistors

6. Equivalent R Practice

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

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