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Electric and Electronic
Principles
Circuit symbols
Diode
Earth
Resistors
Transformer
LED
Op Amp
Transistor
Thermistor
Circuit symbols
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EMF
Electromotive "force" is not considered a
force, as force is measured in newtons, but a
potential, or energy per unit of charge,
measured in volts
PD
Potential difference measured between two
points (eg across a component) if a measure
of the energy of electric charge between the
two points
Definitions

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Current
The flow of electric charge
Resistance
The resistance to current
Capacitors
Store charge in circuit
Definitions
The ammeter is in
series with components
in the circuit
The voltmeter is
connected in parallel
with the components
in the circuit
Simple circuit
Current stays
the same all
the way round
a series circuit
Current in a series circuit
The voltage
(pd) across
the battery
terminals is
shared
between all
the
components
in the circuit
voltage in a series circuit
voltage in a series circuit
The total current is
shared by the
components in a
parallel circuit
Current in a parallel circuit
Resistance
Electron drift
The electrical resistance of an electrical
conductor is the opposition to the passage
of an electric current through that
conductor
Resistance

αΔT = ΔR/R₀

ΔR = αR₀ΔT
Temperature coefficient of
resistance
Question
 A copper wire has a resistance of 400 Ω at
0o C
 1, Calculate the resistance at 30oC if the
temperature coefficient of copper is
0.0043/oC

Question

If mercury is cooled below 4.1 K, it loses all
electric resistance

The critical temperature for superconductors
is the temperature at which the electrical
resistivity of a metal drops to zero. The
transition is so sudden and complete that it
appears to be a transition to a different
phase of matter;. Several materials exhibit
superconducting phase transitions at low
temperatures.
superconductors
The thermistors we normally
refer to are NTC where the
resistance increases when the
temperature decreases
PTC thermistor resistors
Increase resistance with
Increasing temperature
In the above test the open circuit The open circuit voltage
was measured. The decade box was then set to a
maximum and connected as the load. The resistance of the
box was reduced so that the voltage across it decreased
by 10% each time. From this information the load current
and the power in the load was calculated for each voltage.
Graphs of load voltage VL against load current IL and
power in the load PL against load resistance RL were
plotted.
Graph of
VL against IL
VO/C
VL
Calculating the gradient of the graph
gives us the internal resistance of the
source
IL
Graph of
PL against RL
PL
The peak
(maximum
power) is
where the
load
resistance
is equal to
the internal
resistance
of the
source
RL
RL = RS
Using Kirchoff’s
second Law The
sum of all the PD’s
around the circuit is
equal to the e.m.f.
of the source. If the
load resistance is
equal to the
internal resistance
then the PD across
each must be the
same. Thus VL
must be half the
e.m.f. of the cell
r
VI
R
VL
This means that maximum power is obtained when the
load resistance is equal to the internal resistance. As was
show in the experiment
The need for Maximum power transfer is when
there is a high source impedance and power is
scarce. This is contrasted to when power is
abundant (i.e. low source impedance)and a
constant voltage is available
Power is inversely proportional to load
resistance.
That is the higher the load resistance the
lower the power
V out = V in x
R2/ R1 +R2
Basic voltage divider circuit
Internal or source resistance is always less than
the lowest of R1 or R2 When measured in a half voltage
test
This system is effectively a variable voltage
divider
Capacitors
Capacitors

Capacitance is typified by a parallel plate
arrangement and is defined in terms of
charge storage:
Capacitors

A dielectric is an electrical insulator that
can be polarized by an applied electric
field. When a dielectric is placed in an
electric field
Capacitors

A dielectric is an electrical insulator that
can be polarized by an applied electric
field. When a dielectric is placed in an
electric field, electric charges do not flow
through the material as they do in a
conductor but only slightly shift from their
average equilibrium positions causing
dielectric polarization.
Capacitors
Capacitors

In an insulating material, the maximum
electric field strength that it can withstand
intrinsically without breaking down, i.e.,
without experiencing failure of its
insulating properties.
Field strength E = V/d


V = potential across the plates
D = distance between the plates
Capacitors
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
In a test on a 1mm thickness of polymer, it is
ruptured by an applied voltage of 20kV.
a) Calculate the dielectric strength of the
material
b) Describe what happens in the material
when the rupture occurs
c) Explain why a solid insulator with a hairline
crack through it breaks down at a lower
voltage than the rated voltage
Capacitors

The permittivity of a substance is a
characteristic which describes how it
affects any electric field set up in it. A
high permittivity tends to reduce any
electric field present. We can increase the
capacitance of a capacitor by increasing
the permittivity of the dielectric material.
Permittivity

The permittivity of free space (or a vacuum),
e0, has a value of 8.9 × 10-12 F m-1.

The absolute permittivity ε of all other
insulating materials is greater than ε0.

The ratio ε / ε0 is called relative permittivity
of the material and is denoted by K (or εr).


K = ε / ε0 = Absolute permittivity of
medium / Absolute permittivity of air
Permittivity
Material
Relative permittivity, er
Vacuum
1 (by definition)
Air
1.0005
Polythene
2.35
Perspex
3.3
Mica
7
Water
80
Barium Titanate
1200
Permittivity
Capacitance is increased by the use of a dielectgric
Permittivity
Capacitors
The energy stored in a capacitor can be expressed as
W = 1/2 C V2 (1)
where
W = energy stored (Joules)
C = capacitance (Farad)
V = potential difference (Voltage)
Energy stored in a capacitor
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
A 2.0kV power supply unit has an internal
2.6μF capacitor connected across the
output.
a) Calculate the charge stored
b) Calculate the energy stored
c) State how stored charge creates a
hazard
d) Describe how the hazard may be
reduced
Example question

A variable capacitor is a capacitor
whose capacitance may be intentionally
and repeatedly changed mechanically or
electronically
Variable capacitor

Types of variable capacitors

Mechanically controlled In
mechanically controlled variable
capacitors, the distance between the
plates, or the amount of plate surface
area which overlaps, can be changed
Variable capacitor
Electronically controlled
 The thickness of the depletion layer of a
reverse-biased semiconductor diode
varies with the DC voltage applied across
the diode. Any diode exhibits this effect
(including p/n junctions in transistors)


Their use is limited to low signal
amplitudes
Variable capacitor

Transducers

In a capacitor microphone (commonly
known as a condenser microphone), the
diaphragm acts as one plate of a
capacitor, and vibrations produce changes
in the distance between the diaphragm
and a fixed plate, changing the voltage
maintained across the capacitor plates.
Variable capacitor
An air-spaced variable capacitor has semi-circular plates. Minimum
capacitance is 20pF (at 0°)
and maximum capacitance is 400pF when the shaft is rotated
180°.
a) Sketch a graph of capacitance against angle of rotation of the
shaft
b) Calculate the capacitance when the shaft is rotated 90°
c) Calculate the maximum capacitance if a polymer film of relative
permittivity 2.3 is placed in
the airspace between the plates
CT = C1 + C2 etc
Capacitors in parallel
1/CT = 1/C1 + 1/C2 + 1/C3 etc
Capacitors in series
C = Q/V
Q = CV
Q = CVmax (1 – e-t/RC)
V
max
Voltage
I = (V/R) – e-t/RC
current
Time
Capacitor Charging
The Voltage, Current and
Charge all follow the same
kind of decay curve
(exponential)
V = Vmaxe-t/RC
Q = CVmaxe-t/RC
I = (Vmax/R)e-t/RC
RC
2RC 3RC
time
CR (capacitance x resistance) is the time
constant. For each period of RC half decay will
take place
Discharging a Capacitor
Magnetism
Solenoid
Magnetism
coil
Magnetic field strength equation in a
H = (NI) / l
where:
H = magnetic field strength (ampere per
metre)
I = current flowing through coil (amperes)
N = number of turns in coil
l = length of magnetic circuit
Magnetic Flux
The rate of flow of magnetic energy across or through
a (real or imaginary) surface. The unit of flux is the
Weber (Wb)
Magnetic Flux Density
A measure of the amount of magnetic flux in a unit
area perpendicular to the direction of magnetic flow, or
the amount of magnetism induced in a substance
placed in the magnetic field.
The SI unit of magnetic flux density is the Tesla, (T).
One Tesla, (1T), is equivalent to one weber per square
metre (1 Wb/ m2).
The relationship between magnetic field
strength and magnetic flux density is:
B=H×µ
where µ is the magnetic permeability of the
substance
Magnetism
Permeability
Is a measure of how easily a magnetic field
can set up in a material
It is the ratio of the flux density of the
magnetic field within the material to its
field strength.
µ =B/H
Permeabilty of free space µo is 4Pi x10-7
H/m
Magnetism
Relative Permeablity µr
This is how much more permeable the
material is compared to free space (a
vacuum). The permeability of the material
can be calculated by multiplying its
relative permeability by the permeability
of free space.
 µ = µo x µr

Magnetism
The magnetomotive force in an inductor or
electromagnet consisting of a coil of wire is given by:
F = NI
where N is the number of turns of wire in the coil and I is
the current in the wire.
The equation for the magnetic flux in a magnetic circuit,
sometimes known as Hopkinson's law, is:
F = ΦR
where Φ is the magnetic flux and is the reluctance of the
magnetic circuit
Magnetism
The magnetic flux density , B, multiplied
by the area swept out by a conductor, A,
is called the magnetic flux, Φ.
 Φ = BA
 Units of flux: weber, Wb.

Magnetism
‘Hard’ and ‘soft’ magnetic materials
Hard magnets, such as steel, are magnetised, but
afterwards take a lot of work to de-magnetise.
They're good for making permanent magnets, for
example.
Soft magnets are the opposite. With an example
being iron, they are magnetised, but easily lost
their magnetism, be it through vibration or any
other means. These are best for things that only
need to be magnetised at certain points, eg
magnetic fuse/trip switch.
Retentivity –
A measure of the residual flux
density corresponding to the
saturation induction of a magnetic
material. In other words, it is a
material's ability to retain a certain
amount of residual magnetic field
when the magnetizing force is
removed after achieving saturation

Residual Magnetism or Residual Flux the magnetic flux density that remains in
a material when the magnetizing force is
zero.

Coercive Force - The amount of reverse
magnetic field which must be applied to a
magnetic material to make the magnetic
flux return to zero. (The value of H at
point c on the hysteresis curve
Starting with the concept of molecular
magnets in a magnetic material, explain
 a) Relative permeability of a material


b) Loss of magnetisation in a ‘soft’
material

c) Magnetic saturation
Magnetism

a) Relative permeability of a material,
molecular magnets align with applied field

b) Loss of magnetisation in a ‘soft’
material, molecular magnets take up
random alignment

c) Magnetic saturation, molecular
magnets all aligned in field direction
Magnetism
Moving a conductor through a magnetic field can induce an
emf. The faster the conductor moves through the field the
greater the emf and hence the greater the current
Right hand rule
Pushing a magnet into a coil induces a current in the
coil wire
N
N
S
S
Pulling the magnet out of the coil induces a current in
the opposite direction
Inducing a current in a coil
If an Alternating Current is
passed through the coil an
alternating magnetic field is
produced which in turn produces
a back emf given by the equation
E = -l dI/dt
In a purely inductive circuit the
applied pd leads the current by
90o
This type of device is called and Inductor
An inductor which has zero resistance is called pure
Inductance
Inductors

Inductance of a Solenoid
This means that the inductance L of a
solenoid is directly proportional to the
number of turns squared and the area.
It is inversely proportional to the
length of the solenoid
It is also directly proportional to
μo and μr
permiability of free space and relative permiability

An air-cored coil has 200 turns and an inductance of
1.5mH.

a) If the number of turns is increased to 400 calculate the
new value of inductance
b) Calculate the value of inductance if the 200 turn coil is
mounted on a toroidal ferrite core
of μr=270


c) Describe the effect on inductance of an air gap in the
core

a) L proportional to N2 L = 1.5 x
(400/200)2 mH = 6.0 mH

b) L proportional to μr
mH = 405 mH

c) An air gap would reduce inductance
depending on width.
Inductors
L = 1.5 x 270
Energy stored in an
inductor
Inductors


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
A relay coil has inductance of 1.2H,
resistance of 400Ω and operates on 24V dc.
a) Calculate the coil current when the relay is
closed
b) Calculate the energy stored in the coil
when it is operated
c) Describe what happens to the energy
stored when the coil current is switched off
d) State one method for suppressing the
effect in b)
Inductors

a) Operating current = V/R = 24/400 A =
60 mA

b) Energy stored = ½ LI2 = ½ x 1.3 x
0.0602 = 2.34 mJ

c)Back emf developed

d) Parallel diode
Side
limb
25 x 4
0mm
coil
Centre limb
50x40mm
A low frequency inductor, the winding has 2000 turns and the
length of magnetic circuit through the centre limb and side limb is
300mm. A current of 400mA creates a total flux in the centre
limb of 0.92mWb
Determine
A, The Mmf
B, Flux in the side limb
C, Flux density in the centre limb
D, The magnetic field strength H
A) Mmf = NI = 0.4 x 2000 Amp-Turns
= 800 A-T
B) Flux in side limbs Flux = flux density x area so flux in
side limbs is half that in the centre limb 0.92/2 mWb = 0.46
mWb = 460 μWb
C) Flux density in centre limb = Ф/A = 0.92 x 10-3 / 40 x 30
x 10-6 Wb/m2 = 0.77 Wb/m2 or Tesla
D) Magnetic field strength H = NI/length = 800/ 0.3 A-T/m
= 2667 A-T/m
AC Theory
Current
or
voltage
Peak
value
Peak
value
Peak
to
peak
value
Time
Frequency
(f) = 1/T
Time period T
AC Theory
Consider arrow
rotating
anticlockwise
90o
ωt
180o
360o
270o
ωt = angle ( radians)
ω/t = angular velocity
Rotational vector representation
V2
Resultant
waveform
V1
40o
Angular
difference
between V1
and V2 =40o
V2 lags V1 by 40o
AC Theory
Phasor diagram representing
two alternating voltages V1
and V2. V2 lags V1 by 40o
V1
40o
V2
AC Theory
Resultant voltage VR
V1
V2
Phasor of added voltages
AC Theory
When an AC circuit is purely resistive the
current and voltage are in phase
R = V/I
AC Theory
R
V/I
Voltage
V
Current
t
Waveform and phase
diagram for a purely
resistive circuit. Voltage and
current are in phase
AC Theory
I
V
In a purely capacitive circuit the current
leads the voltage by 90o
the opposition to the flow of alternating
current is called the capacitive reactance
Xc
Xc = V/I
AC Theory
V/I
C
voltage
current
V
t
I
Waveform and phase
diagram for a purely
capacitive circuit. current
leads voltage by 90o
AC Theory
V
In a purely inductive circuit the voltage
leads the current by 90o. The opposition to
the flow of alternating current is called
inductive reactance
XL
XL = V/I
AC Theory
L
V/I
voltage
V
current
t
V
I
Waveform and phase diagram
for a purely inductive circuit.
Voltage leads current by 90o
AC Theory
Value
Description
Peak
Maximum value in positive or negative half cycle
Peak to peak
Difference between positive and negative peak
Root mean
square (r.m.s.)
The value of direct current which would provide the same heating
effect as the AC current. For a sine wave the value = 0.707 x
maximum value
Average
The average of the instantaneous measurement in one half cycle.
For a sine wave the average value is 0.637 x maximum value
Instantaneous
The value of the voltage or current at a particular time instant. If
measured at the instant that the cycle polarity is changing the this
value would be zero
Form factor
This is the r.m.s. divided by the average value. For a sine wave the
form factor is 1.11
Peak factor
This is the maximum value divided by the r.m.s. value. For a sine wave the
peak value is 1.41
Measures of AC
Impedance (Z)
Electrical impedance is the measure of the
opposition that a circuit presents to the passage of
ac current
Z= V/I
Total Reactance = XL – XC
Z = R + (XL – XC)
I
rms
= Vrms / R2 + (XL – XC)2
Irms would be at a maximum when XL = XC
XL = 2πfoL
and XC = 1/2πfoC
fo = fundamental frequency
fo
= 1
2π√LC
Fundamental frequency
Irms
Low R
High Q
Q = quality
factor
High R
Low Q
fo
f
Fundamental frequency
Conditions for
resonance
V
VC
VR (=V)
VL
Fundamental frequency

The resonance of a series RLC circuit
occurs when the inductive and
capacitive reactances are equal in
magnitude but cancel each other
because they are 180 degrees apart
in phase. The sharp minimum in
impedance which occurs is useful in
tuning applications. The sharpness of the
minimum depends on the value of R and
is characterized by the "Q" of the circuit
LCR Circuits
LCR Circuits
Phasor Diagram for a Series RLC
Circuit

In a parallel (tank) LC circuit, this means
infinite impedance at resonance as
opposed to the series LC circuit, which
has zero impedance at resonance:
Phasor Diagram for a Parallel RLC
Circuit
ω = angular velocity in radians /sec
a radian is arc length / radius
A full circle is 2π radians
An angle can be referred to as ω t (ω x t)
1 revolution = 2π radians
360o = 2π radians
ω = 2π/T (T = time period)
ω = 2πf (f = frequency)
Q = 2πfoL/R
LCR Series Resonsnce circuit
VL
At resonance VL leads Vin by 90o
At resonance Vc lags Vin by 90o
Vin
VC
I
At resonance
Inductive reactance = Capacitive reactance
XL = XC and would cancel each
other out
therefore impedance, Z is
at a minimum and IRMS is at a
maximum
Because the resistor, capacitor and inductor
are in series, the cancelling out of the
reactance leaves a minimum resistance in
the circuit
Q factor means
Quality or goodness
factor
voltage magnification
factor or sharpness
of
tuning
LCR Parallel Resonance Circuit
Because the resistor, capacitor and inductor
are in parallel, the cancelling out of the
reactance leaves a maximum resistance in
the circuit
In a parallel resonance circuit the voltage
output VP is in phase at resonance, Below
resonance VP leads Vin showing the
reactance is Inductive (VL leads Vin )
Above resonance VP lags Vin showing that
the reactance is Capacitive (VC lags Vin )
LCR Parallel Resonance Circuit
When the input
is a square wave
the tuned circuit
acts as a
bandpass filter
selecting the
fundamental
frequency and
filtering out
harmonics
LCR Parallel Resonance Circuit
Radio Tuner
Low pass filter
By definition, a low-pass filter is a circuit
offering easy passage to low-frequency
signals and difficult passage to highfrequency signals.
 High pass filter
 A High pass filter does the opposite
Frequency filters
Low pass filter
capacitive low-pass filter
(one resistor, one capacitor),
the cut off frequency is given as:
fcut off = 1/2𝛑𝐑𝐂
Frequencies below the cut off
frequency are allowed to pass
Low pass filter
For a half power cut off point, power
out/ power in = 0.5
(Vout/ Vin for same current)
Log10 0.5 = -0.3 decibels (dB)
Half power = -0.3 decibels
Low pass filter
Low Pass
Filter
frequency
response
plot
High pass filter
Capacitive high pass filter
(one resistor, one capacitor),
the cutoff frequency is given as:
fcut off = 1/2𝛑𝐑𝐂
Frequencies above the cut off
frequency are allowed to pass
High pass filter
High Pass Filter
frequency
response plot