ECE 4991 Electrical and Electronic Circuits Chapter 4

2 Where are we? 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 4 1.Definitions, Concepts & Units 2.Capacitor characteristics 3.Inductor characteristics 4.LCR circuits in steady-state conditions

4 1. Definitions, Concepts & Units Capacitor Farad Dielectric Capacitor i-v relationship Capacitor energy storage Inductor Henry Inductor i-v relationship Inductor energy storage

5 A capacitor stores energy in an electric field Electric field caused by separation of charge Ideal Capacitor acts like an open with respect to DC current Q = CV, or q(t) = Cv(t) ; Farad = Coul / Volt But, so Conversely, v(t) = 2. Capacitor Characteristics

6 Combining Capacitors Capacitors in series combine like resistors in parallel Capacitors in parallel combine like resistors in series

7 Energy Storage in Capacitors Energy is the integral of power, and P = IV An RC circuit C R V

8 3. Inductors An inductor stores energy in a magnetic field Magnetic field caused by flow of current Ideal inductor acts like a wire with respect to DC current Maxwell’s equations + Lenz’s Law yields v= L (di/dt); Henry = V-s/A Conversely,

9 Combining Inductors Inductors combine like resistors Energy Storage in Inductors Energy is the integral of power

10 Working with Capacitors and Inductors - Combinations

11 Working with Capacitors and Inductors - Combinations

12 Working with Capacitors and Inductors – Currents/Voltages/ Energies

13 Working with Capacitors and Inductors – Currents/Voltages/ Energies

14 Working with Capacitors and Inductors – Transient Circuit Analysis I R1R1 V C R3R3 R2R2

15 Working with Capacitors and Inductors – Transient Circuit Analysis I R1R1 L R2R2 V

16 Working with Capacitors and Inductors – Steady State Circuit Analysis I R1R1 L C R2R2 V

17 Steady State Solutions V = 8 volts, I = 2 amps, R 1 = 16 ohms, R 2 = 4 ohms, L = 2 H and C = 100  F. At t  , I R1 = W C = V L = W L = P R2 = P V =

18 For Next Time 1.Practice problems – 4.1, 4.2 a &b, 4.4, 4.7, 4.10, 4.11, Do some equivalent capacitance and inductance problems 3.Learn about Chapter 5 a)Writing differential equations for first- order circuits b)Initial and final circuit conditions