electric and electronic principles. circuit symbols
TRANSCRIPT
Electric and Electronic Principles
Circuit symbols
Circuit symbols
Transformer
Resistors
Diode
Op Amp
Earth
Transistor
LED
Thermistor
Definitions
EMFElectromotive "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
Current The flow of electric chargeResistance The resistance to currentCapacitorsStore charge in circuit
Simple circuit
The ammeter is in series with components in the circuit
The voltmeter is connected in parallel with the components in the circuit
Current in a series circuit
Current stays the same all the way round a series circuit
voltage 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
Current in a parallel circuit
The total current is shared by the components in a parallel circuit
Resistance
Electron drift
Resistance
The electrical resistance of an electrical conductor is the opposition to the passage of an electric current through that conductor
Temperature coefficient of resistance
αΔT = ΔR/R₀
ΔR = αR₀ΔT
Question
Question A copper wire has a resistance of 400 Ω at
0o C1, Calculate the resistance at 30oC if the
temperature coefficient of copper is 0.0043/oC
superconductors
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.
The thermistors we normallyrefer to are NTC where the resistance increases when thetemperature decreases
PTC thermistor resistorsIncrease 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 ofVL against IL
VL
VO/C
ILCalculating the gradient of the graph gives us the internal resistance of the source
PL
Graph ofPL against RL
RL
RL = RS
The peak (maximum power) is where the load resistance is equal to the internal resistance of the source
r
R
VL
VI
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
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
Basic voltage divider circuit
V out = V in x R2/ R1 +R2
Internal or source resistance is always less thanthe lowest of R1 or R2 When measured in a half voltage test
This system is effectively a variable voltage divider
Capacitors
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 platesD = distance between the plates
Capacitors
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
Permittivity
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
Vacuum
Relative permittivity, er
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
Capacitors
Energy stored in a capacitor
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)
Example question
A 2.0kV power supply unit has an internal 2.6μF capacitor connected across the output.
a) Calculate the charge storedb) Calculate the energy storedc) State how stored charge creates a
hazardd) Describe how the hazard may be
reduced
Variable capacitor
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 controlledThe 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.
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 inthe airspace between the plates
Capacitors in parallel
CT = C1 + C2 etc
Capacitors in series
1/CT = 1/C1 + 1/C2 + 1/C3 etc
Capacitor Charging
current
Voltage
V max
Time
C = Q/V Q = CV
Q = CVmax (1 – e-t/RC)
I = (V/R) – e-t/RC
Discharging a Capacitor
RC 2RC 3RC
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/RCCR (capacitance x resistance) is the time constant. For each period of RC half decay will take place
time
Magnetism
Magnetism
Solenoid
Magnetic field strength equation in a coil 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).
Magnetism
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/HPermeabilty 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 = BAUnits of flux: weber, Wb.
‘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
Magnetism
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
Right hand rule
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
N S
N S
Inducing a current in a coil
Pushing a magnet into a coil induces a current in the coil wire
Pulling the magnet out of the coil induces a current in the opposite direction
Inductors
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/dtIn a purely inductive circuit the applied pd leads the current by 90o
An inductor which has zero resistance is called pure Inductance
This type of device is called and Inductor
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
Inductors
a) L proportional to N2 L = 1.5 x (400/200)2 mH = 6.0 mH
b) L proportional to μr L = 1.5 x 270 mH = 405 mH
c) An air gap would reduce inductance depending on width.
Inductors
Energy stored in an inductor
Inductors
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)
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
coil
Centre limb 50x40mm
Side limb 25 x 4 0mm
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 DetermineA, The MmfB, Flux in the side limbC, Flux density in the centre limbD, 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
AC Theory
Peak value
Peak value
Peak to peakvalue
Currentor voltage
Time
Time period T
Frequency (f) = 1/T
Rotational vector representation
ωt
90o
180o
270o
360o
ωt = angle ( radians)
ω/t = angular velocity
Consider arrow rotating anticlockwise
AC Theory
Resultant waveform
V1
V2
Angular difference between V1 and V2 =40o
40o
V2 lags V1 by 40o
AC Theory
V1
V2
40o
Phasor diagram representing two alternating voltages V1 and V2. V2 lags V1 by 40o
AC Theory
V1
V2
Resultant voltage VR
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
V/IVoltage
Current
R
V
IV
Waveform and phase diagram for a purely resistive circuit. Voltage and current are in phase
t
AC Theory
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
currentvoltage
V/I
V
C
t
Waveform and phase diagram for a purely capacitive circuit. current leads voltage by 90o
I
V
AC Theory
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
voltage
current
V/I
V
L
Waveform and phase diagram for a purely inductive circuit. Voltage leads current by 90o
t
I
V
Measures of AC
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
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 / + (XL – XC)2
Irms would be at a maximum when XL = XC
Fundamental frequency
XL = 2πfoL and XC = 1/2πfoC
fo = fundamental frequency
fo = 1
2πLC
Fundamental frequency
Irms
ffo
Low RHigh Q
High RLow Q
Q = quality factor
Fundamental frequency
V
VC
VL
VR (=V)
Conditions for resonance
LCR Circuits
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
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 radiansω = 2π/T (T = time period)
ω = 2πf (f = frequency)
Q = 2πfoL/R
LCR Series Resonsnce circuit
IVin
VL
VC
At resonance Vc lags Vin by 90o
At resonance VL leads Vin by 90o
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
factorvoltage
magnification factor or sharpness of
tuning
LCR Parallel Resonance Circuit
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
Frequency filters
Low pass filterBy definition, a low-pass filter is a circuit offering easy passage to low-frequency
signals and difficult passage to high-frequency signals.
High pass filterA High pass filter does the opposite
Low pass filter
Low pass filter
capacitive low-pass filter (one resistor, one capacitor),
the cut off frequency is given as: fcut off = 1/2
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 frequency response plot
High pass filter
High pass filter
fcut off = 1/2
Capacitive high pass filter (one resistor, one capacitor),
the cutoff frequency is given as:
Frequencies above the cut off frequency are allowed to pass
High Pass Filter frequency response plot
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