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ELEC130 Electrical Engineering 1

Week 4Module 2

DC Circuit Tools

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Administration

Laboratory This Week in ES 210 - Using Electronic Workbench Practical Laboratories - Do Not Come Late

Quiz Quiz 1 - results (marks, to be returned) Missed the quiz?

Survey Web site (Access site & PowerPoint viewer) Textbook availability

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Review Week 3

Thevenin & Norton Laboratory 2 Example from last weeks lecture will be

covered in the laboratory Tutorial 1 - Questions 26 to 30

Tutorial problems are for you to do at home

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Capacitors

The capacitor is a device which can store electrical charge, thereby creating an electric field that in turn, stores energy.

The measure of the energy storing ability of a capacitor is its capacitance.

Your Research: to investigate the relationship between force, charge, distance between the plates, capacitance, voltage and energy stored. Floyd chapter 13 Dorf chapter 7 Hambley chapter 3

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Basic ConstructionBasic Construction- Capacitor- Capacitor

Consider two parallel conductive plates of area A, separated by an insulting material called a dielectric by a distance d.

OH Slide - Floyd Figure 13-2

A voltage source connected to the plates transfers charge. That is, electrons are removed from one of the plates and an equal number are deposited on the opposite plate, creating a potential difference.

Electrons only flow through the conductors and voltage source (the dielectric is an insulator)

This transfer will stop when the voltage difference between the plates = the voltage sources

d

plates

(plate area A)

dielectric

d

AC

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Types of Capacitors

Normally classified according to the type of dielectric material

Most common material types used are: mica, ceramic, plastic-film [non-polarised] electrolytic (aluminium oxide & tantalum oxide) [polarised]

and [bi-polar]

Show using Matrix - Parts Gallery

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Properties - Capacitance

The amount of charge that a capacitor can store per unit voltage across its plates is its capacitance

Notation: C Unit: Farads (F) Symbol: C = Q/V 1 Farad is the amount of capacitance when 1 Coulomb of

charge is stored with one volt across the plates Common size units are F to pF Voltage rating - maximum DC voltage that can be applied

without risk of damage to the device. (breakdown voltage) Energy Stored: W = ½ CV2

Show in Matrix - Circuits & Components

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Series Capacitors

Capacitors in series effectively lower the total capacitance as the effective plate separation increases.VT = V1 + V2 +.....+ Vn

QT/CT = Q1/C1 + ..…+ Qn/Cn

Since charges on all the capacitors are equal, the Q term can be factored and cancelled resulting in

1/CT = 1/C1 + 1/C2 ...… +1/Cn

A series connection of charged capacitors acts as a voltage divider

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Parallel Capacitors

Capacitors connected in parallel give a total capacitance of the sum of the individual capacitance's as the effective plate area increases

QT = Q1 + Q2 + ...+ Qn

CTVT = C1V1 + C2V2 +.....+ CnVn

CT= C1 + C2 +......+ Cn

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The Formula

vc(t) constant means ic (t) = 0

vc(t) cannot change instantaneously (else ic (t) )

vc(t) changing quickly means ic (t) is large

i td

dtq t( ) ( )

i t Cdv t

dtc

c( )( )

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Rules (Floyd, pg 511)

Voltage across a capacitor cannot change instantaneously

Current in a capacitive circuit can ideally change instantaneously

A fully charged capacitor appears as an open circuit to non changing current

An uncharged capacitor appears as a short to an instantaneous change in current

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Characteristics of Capacitors in DC Circuits Charging a Capacitor

When a capacitor is fully charged, there is no current A capacitor blocks constant DC When a charged capacitor is disconnected from the source

it will remain charged (except for leakage resistance)

Discharging a Capacitor the energy stored by a capacitor is dissipated in the closed

circuit the charge is neutralised on each plate, at this time the

voltage across the capacitor is zero

Use diagram from Matrix

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RC Circuits / Transients

Derivation of general formula …..

Charging and discharging exponential curves for an RC circuit.

General Formula:[where: F - Final value & i - initial value]

(v = steady state + transient)

Response is made up of transient & steady state Special Case

Charging from zero (Vi = 0)

Discharging to Zero (VF = 0)

v V V V eF i F

t

( )

v V eF

t

RC

( )1

v V ei

t

RC

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Time Constant

Resistance is unavoidable in circuits, whether it be the wires or designed resistance

This resistance introduces the element of time into charging and discharging of a capacitor

The voltage across a capacitor cannot change instantaneously because it takes finite time to move charge from one point to another.

The rate at which the capacitor charges or discharges is determined by the time constant

= RC seconds During one time constant interval, the charge on a capacitor

changes approx. 63% Five (5) time constant intervals, is accepted as the time to fully

charge or discharge a capacitor and is called the transient time Show OH

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Capacitor Applications Electrical Storage

backup voltage source Power supply filtering computer memories

DC blocking and AC coupling Power Line decoupling

decouple voltage transients or spikes

Bypassing bypassing an ac voltage around a resistor without affecting

the dc voltage across the resistor

Signal Filters selecting specific frequencies

Timing Circuits

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RC Example

[A]

Assume switch is in position A for a long time

The switch is moved to position B at t = 0 sec.

At t = 6 milli sec the switch is again placed in position A

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Inductors

The inductor, which is basically a coil of wire, is based on the principle of electromagnetic induction. An electromagnetic field surrounds any conductor when there is a current through it.

Inductance is the property of a coil of wire that opposes a change in current.

Your Research: to investigate the relationship between flux, number of turns, cross section al area, length of core, inductance, current, voltage and energy stored. Floyd chapter 14 Dorf chapter 7 Hambley chapter 3

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Basic ConstructionBasic Construction

A coil of wire forms an inductor.

When current flows through it a electromagnetic field is created.

When current changes, the electromagnetic field changes.

A changing electromagnetic field causes an induced voltage in a direction to oppose the current.

This property is referred to as inductance.

VL

N

+ -

dt

diLV

dt

di

dt

dNV

L

L

i

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Types of Inductors

Two general categories fixed variable

Classified by type of core air iron ferrite

Losses winding resistance winding capacitance

Show using Matrix - Parts Gallery

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Properties Inductance

Inductor and capacitor have similar but opposite properties. (refer Table 7.9 Dorf pg 301)

Induced voltage is determined by the time rate of change of the current and the inductance of the coil

Notation: L Unit: Henry (H) Symbol:

1 Henry = 1 volt sec / ampere Common size units are H to H Energy Stored: W = ½ LI2

Show in Matrix - Circuits & Components

dt

diLVL

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Series & Parallel Inductors

Series:

LT=L1+ L2+ …….+ Ln

Parallel:

1/LT = 1/L1+ 1/L2 +….+

1/Ln

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The Formula

iL(t) constant means vL 0

iL(t) cannot change instantaneously (else vL (t) )

iL(t) changing quickly means vL (t) is large

Derivation similar to that of C’s:

dt

diLVL

dtvL

titit

t

LLL

o

1

)()( 0

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Characteristics of Inductor in DC Circuits Charging a Inductor

When an inductor is fully charged, there is no voltage A inductor acts like a short circuit When a charged inductor is disconnected from the source it

will remain charged (except for winding leakage's)

Discharging a Inductor the energy stored by an inductor is dissipated in the closed

circuit the electromagnetic field collapses, at this time the current

through the inductor is zero

Use diagram from Matrix

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RL Circuits / Transients

Time Constant: = L/R sec General Formula:

[where: F - Final value & i - initial value]

(i = steady state + transient)

Response is made up of transient & steady state Special Case

Charging from zero (Ii = 0)

Discharging to Zero (IF = 0)

t

FiF eIIIi

)(

)1( L

Rt

F eIi

L

Rt

ieIi

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Inductor Applications

Power Supply Filter RF Choke Tuned Circuit