ECE 4991 Electrical and Electronic ECE 4991 Electrical and Electronic CircuitsCircuits

Chapter 4Chapter 4

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Where are we?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

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What’s Important in What’s Important in Chapter 4Chapter 4

1. Definitions, Concepts & Units

2. Capacitor characteristics

3. Inductor characteristics

4. LCR circuits in steady-state conditions

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1. Definitions, Concepts & 1. Definitions, Concepts & UnitsUnits

• Capacitor• Farad• Dielectric• Capacitor i-v

relationship• Capacitor

energy storage

• Inductor• Henry• Inductor i-v

relationship• Inductor energy

storage

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• 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 Characteristics2. Capacitor Characteristics

idt

dq

t

dttiC

)(1

dt

dvCti )(

+

+

+

+

+

-

-

-

-

-

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Combining CapacitorsCombining Capacitors• Capacitors in series combine like

resistors in parallel

• Capacitors in parallel combine like resistors in series

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Energy Storage in Energy Storage in CapacitorsCapacitors

• Energy is the integral of power, and P = IV

• An RC circuit

2

2

1)()()()( CVdttV

dt

dVCdttVtIdttPW

C

R

V

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3. Inductors3. 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,

t

dtvL

i1

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Combining InductorsCombining Inductors• Inductors combine like resistors

Energy Storage in Energy Storage in InductorsInductors

• Energy is the integral of power

2

2

1)()()()( LIdt

dt

dILtIdttVtIdttPW

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Working with Capacitors and Working with Capacitors and Inductors - CombinationsInductors - Combinations

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Working with Capacitors and Working with Capacitors and Inductors - CombinationsInductors - Combinations

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

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

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Working with Capacitors and Inductors Working with Capacitors and Inductors – Transient Circuit Analysis– Transient Circuit Analysis

I

R1V

C

R3R2

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Working with Capacitors and Inductors Working with Capacitors and Inductors – Transient Circuit Analysis– Transient Circuit Analysis

I

R1

LR2

V

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Working with Capacitors and Inductors Working with Capacitors and Inductors – Steady State Circuit Analysis– Steady State Circuit Analysis

I

R1

L

C

R2

V

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Steady State SolutionsSteady State Solutions• V = 8 volts, I = 2 amps, R1 = 16 ohms, R2 = 4 ohms, L = 2 H

and C = 100 F. At t ,

• IR1 =

• WC =

• VL =

• WL =

•PR2 =

•PV =

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For Next TimeFor Next Time

1. Practice problems – 4.1, 4.2 a &b, 4.4, 4.7, 4.10, 4.11, 4.15

2. Do some equivalent capacitance and inductance problems

3. Learn about Chapter 5a) Writing differential equations for first-

order circuits

b) Initial and final circuit conditions