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1
ELEC130 Electrical Engineering 1
Week 4Module 2
DC Circuit Tools
2
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
3
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
4
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
5
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
6
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
7
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
8
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
9
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
10
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( )( )
11
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
12
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
13
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
14
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
15
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
16
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
17
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
18
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
19
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
20
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
21
Series & Parallel Inductors
Series:
LT=L1+ L2+ …….+ Ln
Parallel:
1/LT = 1/L1+ 1/L2 +….+
1/Ln
22
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
23
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
24
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
25
Inductor Applications
Power Supply Filter RF Choke Tuned Circuit