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ELEC130
Electrical Engineering 1
Week 4
Module 2
DC Circuit Tools
1
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
2
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
3
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
4
Basic Construction
- Capacitor
 Consider two parallel
conductive plates of area A,
separated by an insulting
material called a dielectric by
a distance d.
d
dielectric
plates
(plate area A)

C
OH Slide - Floyd Figure 13-2
A
d
 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
5
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
6
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
7
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
8
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
9
The Formula
d
i( t )  q( t )
dt
dvc ( t )
ic ( t )  C
dt
 vc(t) constant means ic (t) = 0
 vc(t) cannot change instantaneously (else ic (t)   )
 vc(t) changing quickly means ic (t) is large
10
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
11
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
12
RC Circuits / Transients

Derivation of general formula …..
t

 Charging and discharging exponential
curves
foran
RC
v V

(
V
V
)
e
F
i
F
circuit.
 General Formula:

[where: F - Final value & i - initial value]
(v = steady state + transient)
 Response is made up of transient & steady state
t
 Special Case

Charging from zero (Vi = 0)
Discharging to Zero (VF = 0)
v  V F (1  e
v  Vi e

RC
)
t
RC
13
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
14
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
15
RC Example
 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
[A]
16
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
17
Basic Construction
 A coil of wire forms an
inductor.
N
i
+ VL -
dN di
VL

dt
dt
di
VL  L
dt
 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.
18
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
19
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)
di
VL  L
dt
Symbol:
 1 Henry = 1 volt sec / ampere
 Common size units are H to H
 Energy Stored: W = ½ LI2

Show in Matrix - Circuits & Components
20
Series & Parallel Inductors
 Series:
LT=L1+ L2+ …….+ Ln
 Parallel:
1/LT = 1/L1+ 1/L2 +….+ 1/Ln
21
The Formula
di
VL  L
dt
 iL(t) constant means vL  0
 iL(t) cannot change instantaneously (else vL (t)   )
 iL(t) changing quickly means vL (t) is large
t
 Derivation similar to that of C’s:
1
iL (t )  iL (t0 )   vL dt
L to
22
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
23
RL Circuits / Transients
 Time Constant:
 General Formula:
 = L/R sec
[where: F - Final value & i - initial value]
i  I F  ( I i  I F )e

t

(i = steady state + transient)
 Response is made up of transient & steady state
Rt
 Special Case

Charging from zero (Ii = 0)
Discharging to Zero (IF = 0)
i  I F (1  e
i  Iie
L
)
Rt

L
24
Inductor Applications
 Power Supply Filter
 RF Choke
 Tuned Circuit
25