lecture 1 basics of electric circuits
TRANSCRIPT
![Page 1: Lecture 1 Basics of Electric Circuits](https://reader038.vdocuments.site/reader038/viewer/2022102802/588174971a28abf7478b6953/html5/thumbnails/1.jpg)
Lectures on Electrical
and Instrument
Engineering
Focused, To-The-Point and Practical!
![Page 2: Lecture 1 Basics of Electric Circuits](https://reader038.vdocuments.site/reader038/viewer/2022102802/588174971a28abf7478b6953/html5/thumbnails/2.jpg)
Personal IntroductionEngr. Arslan Ahmed Amin is a professional Electrical and
Instrumentation Engineer serving Pakistan’s pioneer Oil and Gas
Organization, Pakistan Petroleum Limited. He obtained his Bachelor's
degree in Electrical Engineering from the prestigious University of
Engineering and Technology, Lahore in 2010 and started his
professional career with Pakistan Petroleum Limited. He has served
this organization for more than 5 years and achieved lots of
accomplishments in the development of the systems of newly installed
210 MMSCFD gas compression facility. He actively contributed his
services in commissioning, testing, maintenance and upgradation of
the E&I systems. He completed his Master’s in Business Administration
(M.B.A.) in 2014 from Virtual University of Pakistan, Lahore through
distance learning and afterwards obtained Masters (M.Sc.) in Electrical
Engineering from University of Engineering and Technology, Lahore in
2015.
![Page 3: Lecture 1 Basics of Electric Circuits](https://reader038.vdocuments.site/reader038/viewer/2022102802/588174971a28abf7478b6953/html5/thumbnails/3.jpg)
M.Sc. Electrical Engineering (University of Engineering
and Technology, Lahore)
M.B.A. Online (Virtual University of Pakistan, Lahore)
B.Sc. Electrical Engineering with Honors (University of
Engineering and Technology, Lahore)
Education
![Page 4: Lecture 1 Basics of Electric Circuits](https://reader038.vdocuments.site/reader038/viewer/2022102802/588174971a28abf7478b6953/html5/thumbnails/4.jpg)
05 years’ experience in industrial process controls and
electrical power systems domain with Pakistan
Petroleum Limited (PPL) in CMMS (SAP) environment.
Experience of commissioning, testing and maintenance
of latest systems regarding Power Generation, Field
Instrumentation, Distributed Control System, Safety
Instrumented System, Gas Turbines, PLCs, Analyzers and
Utility packages.
Experience
![Page 5: Lecture 1 Basics of Electric Circuits](https://reader038.vdocuments.site/reader038/viewer/2022102802/588174971a28abf7478b6953/html5/thumbnails/5.jpg)
‘Circuits and Electronics’ from Massachusetts Instituteof Technology (MIT) USA.
‘Project Management’ from Virtual University ofPakistan (VU).
‘Production and Operations Management’ from VirtualUniversity of Pakistan (VU).
‘Conflict Management’ from Virtual University ofPakistan (VU).
‘Crisis Management’ from Virtual University of Pakistan(VU).
Professional Courses
![Page 6: Lecture 1 Basics of Electric Circuits](https://reader038.vdocuments.site/reader038/viewer/2022102802/588174971a28abf7478b6953/html5/thumbnails/6.jpg)
QMS 9001, ISO 14001 EMS and OHSAS 18001, ERP System, Cost ofQuality, Productivity Improvement Techniques, Process SafetyManagement, Hazard Identification and Risk Assessment, HAZOP,SIL systems, Occupational health and Safety, Permit to worksystem, Safety Modules (Complete), Communication Skills, TeamWork Skills, Decision Making Skills (Organized by PPL)
SAP System (R3P version) Maintenance Work Orders Processing,Contracts Management, Spares and Material.
‘Instrumentation and Controls Fundamentals’ from OMS Institute ofManagement and Technology, Lahore.
Installation, calibration and maintenance of Fire and Gas detectorsby Det-tronics.
Generation, Transmission and Distribution at WAPDAEngineering Academy Faisalabad.
Professional Trainings
![Page 7: Lecture 1 Basics of Electric Circuits](https://reader038.vdocuments.site/reader038/viewer/2022102802/588174971a28abf7478b6953/html5/thumbnails/7.jpg)
Among Top 10 students in the session of 240 students in B.Sc.Electrical Engineering.
Received Dean’s Honor Role award in consecutive fivesemesters for excellent academic performance in B.Sc.Electrical Engineering.
Overall Topped in F.Sc. in Board of Intermediate andSecondary Education, Faisalabad 2006.
Winner of Quaid-e-Azam Scholarship.
Gold medal winner in District Science Quiz CompetitionFaisalabad.
Represented as ‘Talent of Pakistan Youth’ in China in 2007 byMinistry of Youth, Pakistan.
Academic Achievements
![Page 8: Lecture 1 Basics of Electric Circuits](https://reader038.vdocuments.site/reader038/viewer/2022102802/588174971a28abf7478b6953/html5/thumbnails/8.jpg)
Lets Start!
Lecture-1
Basics of Electric Circuits
![Page 9: Lecture 1 Basics of Electric Circuits](https://reader038.vdocuments.site/reader038/viewer/2022102802/588174971a28abf7478b6953/html5/thumbnails/9.jpg)
Electric Circuit
An electric circuit is an interconnection of
electrical elements.
![Page 10: Lecture 1 Basics of Electric Circuits](https://reader038.vdocuments.site/reader038/viewer/2022102802/588174971a28abf7478b6953/html5/thumbnails/10.jpg)
Systems of UNITS
Quantity Basic Unit Symbol
Length meter m
Mass kilogram kg
Time second s
Electric current ampere A
Thermodynamic
Temperature
kelvin K
Luminous
intensity
candela cd
![Page 11: Lecture 1 Basics of Electric Circuits](https://reader038.vdocuments.site/reader038/viewer/2022102802/588174971a28abf7478b6953/html5/thumbnails/11.jpg)
The SI Prefixes
![Page 12: Lecture 1 Basics of Electric Circuits](https://reader038.vdocuments.site/reader038/viewer/2022102802/588174971a28abf7478b6953/html5/thumbnails/12.jpg)
Charge and Current
![Page 13: Lecture 1 Basics of Electric Circuits](https://reader038.vdocuments.site/reader038/viewer/2022102802/588174971a28abf7478b6953/html5/thumbnails/13.jpg)
Electric Current
![Page 14: Lecture 1 Basics of Electric Circuits](https://reader038.vdocuments.site/reader038/viewer/2022102802/588174971a28abf7478b6953/html5/thumbnails/14.jpg)
Electric Current
Current is the flow of
electricity, much like
the flow of water in a
pipe. It is measured in
Amperage as opposed
to gallons per minute
of water.
![Page 15: Lecture 1 Basics of Electric Circuits](https://reader038.vdocuments.site/reader038/viewer/2022102802/588174971a28abf7478b6953/html5/thumbnails/15.jpg)
Conductors
Free Electrons (e)
Easily Directed
Usually metals
Copper
Aluminum
Gold
Platinum
-
-
-
-
-
--
--
-
-
-
-
-
-
-
-
-
-
-
--
--
-
-
-
-
-
-
- +
![Page 16: Lecture 1 Basics of Electric Circuits](https://reader038.vdocuments.site/reader038/viewer/2022102802/588174971a28abf7478b6953/html5/thumbnails/16.jpg)
Semi-Conductors
Dielectrics
4 Valence Electrons
Polarize with Some
Electron Flow due to
Electrical Fields
+
-
![Page 17: Lecture 1 Basics of Electric Circuits](https://reader038.vdocuments.site/reader038/viewer/2022102802/588174971a28abf7478b6953/html5/thumbnails/17.jpg)
Insulators
No Free Electrons
No Current Flow with
Field
+
-
![Page 18: Lecture 1 Basics of Electric Circuits](https://reader038.vdocuments.site/reader038/viewer/2022102802/588174971a28abf7478b6953/html5/thumbnails/18.jpg)
Why Does Current Flow?
A voltage source provides the energy (or work) required to produce a current
Volts = joules/Coulomb = dW/dQ
A source takes charged particles (usually electrons) and raises their potential
so they flow out of one terminal into and through a transducer (light bulb or
motor) on their way back to the source’s other terminal
![Page 19: Lecture 1 Basics of Electric Circuits](https://reader038.vdocuments.site/reader038/viewer/2022102802/588174971a28abf7478b6953/html5/thumbnails/19.jpg)
Voltage
Voltage is a measure of the potential energy that causes a current to flow
through a transducer in a circuit
Voltage is always measured as a difference with respect to an arbitrary
common point called ground
Voltage is also known as electromotive force or EMF outside engineering
![Page 20: Lecture 1 Basics of Electric Circuits](https://reader038.vdocuments.site/reader038/viewer/2022102802/588174971a28abf7478b6953/html5/thumbnails/20.jpg)
Voltage (Volts - V or E)
Voltage is the electrical
pressure in the system,
much like water pressure.
Electrical pressure is
measured in Volts as
opposed to Pounds per
Square Inch. (ie: 110V like
water from a tap, 4160 like
a fire hose)
![Page 21: Lecture 1 Basics of Electric Circuits](https://reader038.vdocuments.site/reader038/viewer/2022102802/588174971a28abf7478b6953/html5/thumbnails/21.jpg)
Voltage
![Page 22: Lecture 1 Basics of Electric Circuits](https://reader038.vdocuments.site/reader038/viewer/2022102802/588174971a28abf7478b6953/html5/thumbnails/22.jpg)
Resistance (Ohms - R or Ω)
Resistance is simply the
restriction of current
flow in a circuit.
Smaller wire
(conductors) and poor
conductors have higher
resistance.
![Page 23: Lecture 1 Basics of Electric Circuits](https://reader038.vdocuments.site/reader038/viewer/2022102802/588174971a28abf7478b6953/html5/thumbnails/23.jpg)
Resistance
ee
e ee
ee
e
e
ee
ee
e
Many Collisions = Heat!
Fewer Collisions = Less Heat!
![Page 24: Lecture 1 Basics of Electric Circuits](https://reader038.vdocuments.site/reader038/viewer/2022102802/588174971a28abf7478b6953/html5/thumbnails/24.jpg)
Ohm’s Law
Current, Voltage, and Resistance relate as follow:
I = E / R
![Page 25: Lecture 1 Basics of Electric Circuits](https://reader038.vdocuments.site/reader038/viewer/2022102802/588174971a28abf7478b6953/html5/thumbnails/25.jpg)
A Circuit Current flows from the higher voltage
terminal of the source into the higher
voltage terminal of the transducer before
returning to the source
+
SourceVoltage
-
I
+ Transducer -Voltage
The source expendsenergy & the transducerconverts it into something useful
I
![Page 26: Lecture 1 Basics of Electric Circuits](https://reader038.vdocuments.site/reader038/viewer/2022102802/588174971a28abf7478b6953/html5/thumbnails/26.jpg)
Passive Devices
A passive transducer device functions only when energized by a source in a
circuit
Passive devices can be modeled by a resistance
Passive devices always draw current so that the highest voltage is present on
the terminal where the current enters the passive device
+ V > 0 -
I > 0
Notice that the voltage ismeasured across the device Current is measured
through the device
![Page 27: Lecture 1 Basics of Electric Circuits](https://reader038.vdocuments.site/reader038/viewer/2022102802/588174971a28abf7478b6953/html5/thumbnails/27.jpg)
Active Devices
Sources expend energy and are considered active devices
Their current normally flows out of their highest voltage terminal
Sometimes, when there are multiple sources in a circuit, one overpowers
another, forcing the other to behave in a passive manner
![Page 28: Lecture 1 Basics of Electric Circuits](https://reader038.vdocuments.site/reader038/viewer/2022102802/588174971a28abf7478b6953/html5/thumbnails/28.jpg)
Power
The rate at which energy is transferred from an active source or used by a
passive device
P in watts = dW/dt = joules/second
P= V∙I = dW/dQ ∙ dQ/dt = volts ∙ amps = watts
W = ∫ P ∙ dt – so the energy (work in joules) is equal to the area under the
power in watts plotted against time in seconds
![Page 29: Lecture 1 Basics of Electric Circuits](https://reader038.vdocuments.site/reader038/viewer/2022102802/588174971a28abf7478b6953/html5/thumbnails/29.jpg)
Power
The power consumed or created is just the Voltage
multiplied by the Current
P = V x I
Eg:
If 3 amps flowing through a component
generate 12 volts across the component
the power is 3 x 12 = 36 watts
![Page 30: Lecture 1 Basics of Electric Circuits](https://reader038.vdocuments.site/reader038/viewer/2022102802/588174971a28abf7478b6953/html5/thumbnails/30.jpg)
Some power calculations
Current
I
Voltage
V
Power
P
2 Amps 5 Volts
9 Amps 36 Watts
10 Watts
4 Volts
![Page 31: Lecture 1 Basics of Electric Circuits](https://reader038.vdocuments.site/reader038/viewer/2022102802/588174971a28abf7478b6953/html5/thumbnails/31.jpg)
Conservation of Power
Power is conserved in a circuit - ∑ P = 0
We associate a positive number for power as power absorbed or used by a
passive device
A negative power is associated with an active device delivering power
I
+
V
-
If I=1 amp
V=5 volts
Then passive
P=+5 watts
(absorbed)
If I= -1 amp
V=5 volts
Then active
P= -5 watts
(delivered)
If I= -1 amp
V= -5 volts
Then passive
P=+5 watts
(absorbed)
![Page 32: Lecture 1 Basics of Electric Circuits](https://reader038.vdocuments.site/reader038/viewer/2022102802/588174971a28abf7478b6953/html5/thumbnails/32.jpg)
Example
A battery is 11 volts and as it is charged, it increases to 12 volts, by a current
that starts at 2 amps and slowly drops to 0 amps in 10 hours (36000 seconds)
The power is found by multiplying the current and voltage together at each
instant in time
In this case, the battery (a source) is acting like a passive device (absorbing
energy)
![Page 33: Lecture 1 Basics of Electric Circuits](https://reader038.vdocuments.site/reader038/viewer/2022102802/588174971a28abf7478b6953/html5/thumbnails/33.jpg)
Energy
The energy is the area under the power curve
Area of triangle = .5 ∙ base ∙ height
W=area= .5 ∙ 36000 sec. ∙ 22 watts = 396000 J.
W=area= .5 ∙ 10 hr. ∙ .022 Kw. = 110 Kw.∙hr
So 1 Kw.∙hr = 3600 J.
Since 1 Kw.∙hr costs about $0.10, the battery costs $11.00 to charge
![Page 34: Lecture 1 Basics of Electric Circuits](https://reader038.vdocuments.site/reader038/viewer/2022102802/588174971a28abf7478b6953/html5/thumbnails/34.jpg)
AC and DC Current
•DC Current has a constant value
•AC Current has a value that changes sinusoidally
Notice that AC current
changes in value and
direction
No net charge is
transferred
![Page 35: Lecture 1 Basics of Electric Circuits](https://reader038.vdocuments.site/reader038/viewer/2022102802/588174971a28abf7478b6953/html5/thumbnails/35.jpg)
AC v DC
• DC can be produced chemically or mechanically; AC must be produced mechanically
• DC can be easily stored; AC cannot
• AC is easier, and thus cheaper, to produce
• AC can easily be transformed to other voltages
• AC can be transmitted more economically
![Page 36: Lecture 1 Basics of Electric Circuits](https://reader038.vdocuments.site/reader038/viewer/2022102802/588174971a28abf7478b6953/html5/thumbnails/36.jpg)
Polarity
• Some components (like a bulb) can be connected either way round – they will still work
![Page 37: Lecture 1 Basics of Electric Circuits](https://reader038.vdocuments.site/reader038/viewer/2022102802/588174971a28abf7478b6953/html5/thumbnails/37.jpg)
Polarity
• Some components (like a diode) can be connected either way round – they work one way but not the other
![Page 38: Lecture 1 Basics of Electric Circuits](https://reader038.vdocuments.site/reader038/viewer/2022102802/588174971a28abf7478b6953/html5/thumbnails/38.jpg)
Passive Sign Convention
![Page 39: Lecture 1 Basics of Electric Circuits](https://reader038.vdocuments.site/reader038/viewer/2022102802/588174971a28abf7478b6953/html5/thumbnails/39.jpg)
PSC: Example I
![Page 40: Lecture 1 Basics of Electric Circuits](https://reader038.vdocuments.site/reader038/viewer/2022102802/588174971a28abf7478b6953/html5/thumbnails/40.jpg)
PSC: Example II
![Page 41: Lecture 1 Basics of Electric Circuits](https://reader038.vdocuments.site/reader038/viewer/2022102802/588174971a28abf7478b6953/html5/thumbnails/41.jpg)
PSC: Example III
![Page 42: Lecture 1 Basics of Electric Circuits](https://reader038.vdocuments.site/reader038/viewer/2022102802/588174971a28abf7478b6953/html5/thumbnails/42.jpg)
Circuit Elements
Ideal Independent Source: provides a specified
voltage or current that is completely independent of
other circuit variables
Ideal Independent Voltage Source:
![Page 43: Lecture 1 Basics of Electric Circuits](https://reader038.vdocuments.site/reader038/viewer/2022102802/588174971a28abf7478b6953/html5/thumbnails/43.jpg)
Circuit Elements
Ideal independent current source
![Page 44: Lecture 1 Basics of Electric Circuits](https://reader038.vdocuments.site/reader038/viewer/2022102802/588174971a28abf7478b6953/html5/thumbnails/44.jpg)
Circuit Elements
Ideal dependent voltage source
Ideal dependent current source
![Page 45: Lecture 1 Basics of Electric Circuits](https://reader038.vdocuments.site/reader038/viewer/2022102802/588174971a28abf7478b6953/html5/thumbnails/45.jpg)
Automotive circuits
![Page 46: Lecture 1 Basics of Electric Circuits](https://reader038.vdocuments.site/reader038/viewer/2022102802/588174971a28abf7478b6953/html5/thumbnails/46.jpg)
Equivalent electrical circuit
Vbatt
(b)
+
–
Ihead
Ibatt
Itail Istart Ifan Ilocks Idash
![Page 47: Lecture 1 Basics of Electric Circuits](https://reader038.vdocuments.site/reader038/viewer/2022102802/588174971a28abf7478b6953/html5/thumbnails/47.jpg)
Electrical vehicle battery
pack
DC-AC converter(electric drive)
12 V12 V12 V12 V12 V
AC motor
(a)
Vbatt1 Vbatt2 Vbattn
![Page 48: Lecture 1 Basics of Electric Circuits](https://reader038.vdocuments.site/reader038/viewer/2022102802/588174971a28abf7478b6953/html5/thumbnails/48.jpg)
Various representations of an
electrical system
HeadlightCar
battery
+ –
R
i
i
+
–v
So
urc
e
Lo
ad
(a) Conceptualrepresentation
Power flow
(b) Symbolic (circuit)representation
(c) Physicalrepresentation
+_
i
+
–
vVS
![Page 49: Lecture 1 Basics of Electric Circuits](https://reader038.vdocuments.site/reader038/viewer/2022102802/588174971a28abf7478b6953/html5/thumbnails/49.jpg)
Volt-ampere characteristic of
a tungsten light bulb
0.1
0.2
0.3
0.5
0.4
–0.5
–0.4
–0.3
–0.2
0–20–30–40–50–60 –10 5040302010 60
–0.1
i (amps)
v (volts)
Variablevoltagesource
Currentmeter
+
–
v
i
![Page 50: Lecture 1 Basics of Electric Circuits](https://reader038.vdocuments.site/reader038/viewer/2022102802/588174971a28abf7478b6953/html5/thumbnails/50.jpg)
The resistance element
i
R v
+
–
A
l 1/R
i
v
i-v characteristicCircuit symbolPhysical resistorswith resistance R.
Typical materials arecarbon, metal film.
R =l
A
![Page 51: Lecture 1 Basics of Electric Circuits](https://reader038.vdocuments.site/reader038/viewer/2022102802/588174971a28abf7478b6953/html5/thumbnails/51.jpg)
Resistor color code
b 4 b 3 b 2 b 1
Color bands
blackbrownredorangeyellowgreen
012345
bluevioletgraywhitesilvergold
6 7 8 9
10%5%
Resistor value = ( b 1 b 2 ) 10b3;b4 = % tolerance in actual value
![Page 52: Lecture 1 Basics of Electric Circuits](https://reader038.vdocuments.site/reader038/viewer/2022102802/588174971a28abf7478b6953/html5/thumbnails/52.jpg)
The current
1.5 V+_
R
v+ –
v– +
+
–
vi
R
i flows through each of the four series elements. Thus, by KVL,
1.5 = v1+ v2+ v3
R 1
R 2
R 3
R n
R N
R EQ
N series resistors are equivalent to a single resistor equal to the sum of the individual resistances.
![Page 53: Lecture 1 Basics of Electric Circuits](https://reader038.vdocuments.site/reader038/viewer/2022102802/588174971a28abf7478b6953/html5/thumbnails/53.jpg)
Parallel circuits
+
–
v
KCL applied at this node
The voltage v appears across each parallel
element; by KCL, iS = i1 + i 2+ i 3
N resistors in parallel are equivalent to a single equivalent resistor with resistance equal to the inverse of the sum of
the inverse resistances.
RN REQR1 R2 R3 Rn
i1 i2 i3
iS R1 R2 R3
![Page 54: Lecture 1 Basics of Electric Circuits](https://reader038.vdocuments.site/reader038/viewer/2022102802/588174971a28abf7478b6953/html5/thumbnails/54.jpg)
Wheatstone bridge circuits
c
R2
R3R1
v S a+_
(a)
Rx
v bva b
d
c
R2
R3R1+_
(b)
R x
v bva b
d
avS
![Page 55: Lecture 1 Basics of Electric Circuits](https://reader038.vdocuments.site/reader038/viewer/2022102802/588174971a28abf7478b6953/html5/thumbnails/55.jpg)
A force-measuring instrument
R2
R3R1
vS
R4
vbva
d
c
+
–
ia ib
h
w
Beam cross section
R2 , R3 bondedto bottom surface
F
![Page 56: Lecture 1 Basics of Electric Circuits](https://reader038.vdocuments.site/reader038/viewer/2022102802/588174971a28abf7478b6953/html5/thumbnails/56.jpg)
Practical voltage source
R L
rSi S
+_vS
+
–
v L
Practical
voltagesource
iS =vS
rS + R L
lim iS =vS
rSRL 0
r S i S max
vS
+
–
vL
The maximum (short circuit) current which can be supplied by a practical voltage source is
iS max = vS
rS
+_
![Page 57: Lecture 1 Basics of Electric Circuits](https://reader038.vdocuments.site/reader038/viewer/2022102802/588174971a28abf7478b6953/html5/thumbnails/57.jpg)
Practical current source
R Li S
+
–
v Sr S
A model for practical current sources consists of an ideal source in parallel with an internal resistance.
i S
+
–
v Sr S
Maximum output voltage for practical current source with open-circuit load:
vS max = iS rS
![Page 58: Lecture 1 Basics of Electric Circuits](https://reader038.vdocuments.site/reader038/viewer/2022102802/588174971a28abf7478b6953/html5/thumbnails/58.jpg)
Measurement of current
R2
R1
+_vS
A seriescircuit
R2
R1
+_vS
A
A
Symbol forideal ammeter
Circuit for the measurementof the current i
i i
![Page 59: Lecture 1 Basics of Electric Circuits](https://reader038.vdocuments.site/reader038/viewer/2022102802/588174971a28abf7478b6953/html5/thumbnails/59.jpg)
Measurement of voltage
R2
R1
+_vS
A seriescircuit
R1
+_ VV
Idealvoltmeter
Circuit for the measurementof the voltage v2
i
v2
+
–i
R2v2
+
–v2
+
–
vS
![Page 60: Lecture 1 Basics of Electric Circuits](https://reader038.vdocuments.site/reader038/viewer/2022102802/588174971a28abf7478b6953/html5/thumbnails/60.jpg)
Models for practical ammeter
and voltmeter
rm
A
Practicalammeter
V
Practicalvoltmeter
rm
![Page 61: Lecture 1 Basics of Electric Circuits](https://reader038.vdocuments.site/reader038/viewer/2022102802/588174971a28abf7478b6953/html5/thumbnails/61.jpg)
Measurement of power
i
R1
+_
Internal wattmeter connections
R2v 2
+
–
vS
iR1
+_
Measurement of the powerdissipated in the resistor R2:
P2 = v2 i
vS
W
R 2v2
+
–
V
A
![Page 62: Lecture 1 Basics of Electric Circuits](https://reader038.vdocuments.site/reader038/viewer/2022102802/588174971a28abf7478b6953/html5/thumbnails/62.jpg)
Definition of a branch
a
rm
A
Practicalammeter
Idealresistor
Rv
A battery
A branch
Branchvoltage
Branchcurrent
+
–
b
i
Examples of circuit branches
![Page 63: Lecture 1 Basics of Electric Circuits](https://reader038.vdocuments.site/reader038/viewer/2022102802/588174971a28abf7478b6953/html5/thumbnails/63.jpg)
Definition of a node
Examples of nodes in practical circuits
Node a
Node b
vS iS
Node c Node a
Node b
Node
![Page 64: Lecture 1 Basics of Electric Circuits](https://reader038.vdocuments.site/reader038/viewer/2022102802/588174971a28abf7478b6953/html5/thumbnails/64.jpg)
Definition of a loop
Loop 1 Loop 2
Loop 3
vS
R
1-loop circuit 3-loop circuit(How many nodes in
this circuit?)
Note how two different loopsin the same circuit may in-clude some of the same ele-ments or branches.
iSR1 R2
![Page 65: Lecture 1 Basics of Electric Circuits](https://reader038.vdocuments.site/reader038/viewer/2022102802/588174971a28abf7478b6953/html5/thumbnails/65.jpg)
Magnetics
NorthSouth
Magnetic Flux
Magnet
![Page 66: Lecture 1 Basics of Electric Circuits](https://reader038.vdocuments.site/reader038/viewer/2022102802/588174971a28abf7478b6953/html5/thumbnails/66.jpg)
Current Flow in Conductor
- +
Current Flowing in a Conductor
![Page 67: Lecture 1 Basics of Electric Circuits](https://reader038.vdocuments.site/reader038/viewer/2022102802/588174971a28abf7478b6953/html5/thumbnails/67.jpg)
Generated Field Around
Conductor
+
![Page 68: Lecture 1 Basics of Electric Circuits](https://reader038.vdocuments.site/reader038/viewer/2022102802/588174971a28abf7478b6953/html5/thumbnails/68.jpg)
Magnetic Field With Coil
+
-
+
-
North Magnetic Pole
South Magnetic Pole
![Page 69: Lecture 1 Basics of Electric Circuits](https://reader038.vdocuments.site/reader038/viewer/2022102802/588174971a28abf7478b6953/html5/thumbnails/69.jpg)
Interaction with Medium
NorthSouth
Magnetic Flux
MagnetMetal NS
![Page 70: Lecture 1 Basics of Electric Circuits](https://reader038.vdocuments.site/reader038/viewer/2022102802/588174971a28abf7478b6953/html5/thumbnails/70.jpg)
Electrical Properties
Frequency
Inductance (L)
Mutual
Inductive Reactance (XL)
Capacitance (C)
Capacitive Reactance (XC)
Phase Angle/Power Factor
Impedance (Z)
![Page 71: Lecture 1 Basics of Electric Circuits](https://reader038.vdocuments.site/reader038/viewer/2022102802/588174971a28abf7478b6953/html5/thumbnails/71.jpg)
Frequency
0 90 180 270 360
![Page 72: Lecture 1 Basics of Electric Circuits](https://reader038.vdocuments.site/reader038/viewer/2022102802/588174971a28abf7478b6953/html5/thumbnails/72.jpg)
Inductance
Stores electromagnetic energy
in its magnetic field
mH
dt
diLV
t
idvL
i0
)0()(1
2
2
1LiW
I lags V
![Page 73: Lecture 1 Basics of Electric Circuits](https://reader038.vdocuments.site/reader038/viewer/2022102802/588174971a28abf7478b6953/html5/thumbnails/73.jpg)
Mutual Inductance
When 2 coils in close
proximity, a changing
current in one coil will
induce a voltage in a
second coil
0 90 180 270 360
N1 = 5 Turns
100 Volts
N2 = 5 Turns
100 Volts
![Page 74: Lecture 1 Basics of Electric Circuits](https://reader038.vdocuments.site/reader038/viewer/2022102802/588174971a28abf7478b6953/html5/thumbnails/74.jpg)
Inductive Reactance XL
Inductive Reactance is
the AC Resistance of a
coil
Presented as a
resistance in Ohms
Frequency and
Inductance Dependant
fLX L 2
![Page 75: Lecture 1 Basics of Electric Circuits](https://reader038.vdocuments.site/reader038/viewer/2022102802/588174971a28abf7478b6953/html5/thumbnails/75.jpg)
Capacitance
Stores energy in an electric field
Dielectric between 2 plates
The charged condition is maintained until a discharge path is present
Causes current to lead voltage
+
-
![Page 76: Lecture 1 Basics of Electric Circuits](https://reader038.vdocuments.site/reader038/viewer/2022102802/588174971a28abf7478b6953/html5/thumbnails/76.jpg)
Capacitive Reactance XC
fCX C
2
1
![Page 77: Lecture 1 Basics of Electric Circuits](https://reader038.vdocuments.site/reader038/viewer/2022102802/588174971a28abf7478b6953/html5/thumbnails/77.jpg)
Phase Angle / Power Factor
In a coil or motor,
current lags behind
voltage
This is represented as
an angle or a fraction
of ‘unity’
Adding C can improve
PF
IV
0 90 180 270 360
![Page 78: Lecture 1 Basics of Electric Circuits](https://reader038.vdocuments.site/reader038/viewer/2022102802/588174971a28abf7478b6953/html5/thumbnails/78.jpg)
Impedance Z
fCX C
2
1fLX L 2
DC
Resistance
Complex
AC
Resistance
22 )( CL XXRZ
![Page 79: Lecture 1 Basics of Electric Circuits](https://reader038.vdocuments.site/reader038/viewer/2022102802/588174971a28abf7478b6953/html5/thumbnails/79.jpg)
Summary
Atomic Structure and Electron Movement
Conductors, Semi-Conductors, Insulators
Basic Electricity: Current, Voltage and Resistance
Electrical and Magnetic Fields
Alternating Current Electricity: L, C, XL, XC, Z
![Page 80: Lecture 1 Basics of Electric Circuits](https://reader038.vdocuments.site/reader038/viewer/2022102802/588174971a28abf7478b6953/html5/thumbnails/80.jpg)
Generation & Distribution
Generator
10.6 KV
GT220 KV
Step down
transformer
Distribution
Power plant Transmission
systemDistribution system
![Page 81: Lecture 1 Basics of Electric Circuits](https://reader038.vdocuments.site/reader038/viewer/2022102802/588174971a28abf7478b6953/html5/thumbnails/81.jpg)
• AC generators (“alternators”) generate
electricity
• Electricity generated at 9-13 KV
• Power generated from 67.5 to 1000 MW
• Power stations: generating transformers
(GTs) to increase voltage to 132-400 KV
• Substations: step-down transformers to
reduce voltage before distribution
Generation & Distribution
![Page 82: Lecture 1 Basics of Electric Circuits](https://reader038.vdocuments.site/reader038/viewer/2022102802/588174971a28abf7478b6953/html5/thumbnails/82.jpg)
Benefits of high voltage transmission
• Less voltage drop: good voltage regulation
• Less power loss: high transmission
efficiency
• Smaller conductor: lower costs
Generation & Distribution
![Page 83: Lecture 1 Basics of Electric Circuits](https://reader038.vdocuments.site/reader038/viewer/2022102802/588174971a28abf7478b6953/html5/thumbnails/83.jpg)
83
Single phase AC circuit:
• Two wires connected
to electricity source
• Direction of current
changes many times
per second
Phase of Electricity
3-phases of an electric system
Three phase systems:
• 3 lines with electricity from 3 circuits
• One neutral line
• 3 waveforms offset in time: 50-60 cycles/second
![Page 84: Lecture 1 Basics of Electric Circuits](https://reader038.vdocuments.site/reader038/viewer/2022102802/588174971a28abf7478b6953/html5/thumbnails/84.jpg)
Star connection
Phase of Electricity
Delta connection
![Page 85: Lecture 1 Basics of Electric Circuits](https://reader038.vdocuments.site/reader038/viewer/2022102802/588174971a28abf7478b6953/html5/thumbnails/85.jpg)
Review of Phasors
Goal of phasor analysis is to simplify the
analysis of constant frequency ac systems
v(t) = Vmax cos(wt + qv)
i(t) = Imax cos(wt + qI)
Root Mean Square (RMS) voltage of sinusoid
2 max
0
1( )
2
TV
v t dtT
![Page 86: Lecture 1 Basics of Electric Circuits](https://reader038.vdocuments.site/reader038/viewer/2022102802/588174971a28abf7478b6953/html5/thumbnails/86.jpg)
Phasor Representation
j
( )
Euler's Identity: e cos sin
Phasor notation is developed by rewriting
using Euler's identity
( ) 2 cos( )
( ) 2 Re V
V
j t
j
v t V t
v t V e
q
w q
q q
w q
![Page 87: Lecture 1 Basics of Electric Circuits](https://reader038.vdocuments.site/reader038/viewer/2022102802/588174971a28abf7478b6953/html5/thumbnails/87.jpg)
Then drop the constant terms
( ) Re 2
V cos sin
I cos sin
V
V
jV
jj t
V V
I I
V V e V
v t Ve e
V j V
I j I
q
qw
q
q q
q q
![Page 88: Lecture 1 Basics of Electric Circuits](https://reader038.vdocuments.site/reader038/viewer/2022102802/588174971a28abf7478b6953/html5/thumbnails/88.jpg)
Advantages of Phasor Analysis
0
2 2
Resistor ( ) ( )
( )Inductor ( )
1 1Capacitor ( ) (0)
C
Z = Impedance
R = Resistance
X = Reactance
XZ = =arctan( )
t
v t Ri t V RI
di tv t L V j LI
dt
i t dt v V Ij C
R jX Z
R XR
w
w
Device Time Analysis Phasor
![Page 89: Lecture 1 Basics of Electric Circuits](https://reader038.vdocuments.site/reader038/viewer/2022102802/588174971a28abf7478b6953/html5/thumbnails/89.jpg)
RL Circuit Example
2 2
( ) 2 100cos( 30 )
60Hz
R 4 3
4 3 5 36.9
100 30
5 36.9
20 6.9 Amps
i(t) 20 2 cos( 6.9 )
V t t
f
X L
Z
VI
Z
t
w
w
w
![Page 90: Lecture 1 Basics of Electric Circuits](https://reader038.vdocuments.site/reader038/viewer/2022102802/588174971a28abf7478b6953/html5/thumbnails/90.jpg)
Complex Power
max
max
max max
( ) ( ) ( )
v(t) = cos( )
(t) = cos( )
1cos cos [cos( ) cos( )]
2
1( ) [cos( )
2
cos(2 )]
V
I
V I
V I
p t v t i t
V t
i I t
p t V I
t
w q
w q
q q
w q q
Power
![Page 91: Lecture 1 Basics of Electric Circuits](https://reader038.vdocuments.site/reader038/viewer/2022102802/588174971a28abf7478b6953/html5/thumbnails/91.jpg)
max max
0
max max
1( ) [cos( ) cos(2 )]
2
1( )
1cos( )
2
cos( )
= =
V I V I
T
avg
V I
V I
V I
p t V I t
P p t dtT
V I
V I
q q w q q
q q
q q
q q
Power Factor
Average
P
Angle
ower
![Page 92: Lecture 1 Basics of Electric Circuits](https://reader038.vdocuments.site/reader038/viewer/2022102802/588174971a28abf7478b6953/html5/thumbnails/92.jpg)
P
Q
S
Power Triangle Inductive Load, lagging Power
Factor.
![Page 93: Lecture 1 Basics of Electric Circuits](https://reader038.vdocuments.site/reader038/viewer/2022102802/588174971a28abf7478b6953/html5/thumbnails/93.jpg)
P
QS
Power Triangle Capacitive load, Leading
Power Factor
![Page 94: Lecture 1 Basics of Electric Circuits](https://reader038.vdocuments.site/reader038/viewer/2022102802/588174971a28abf7478b6953/html5/thumbnails/94.jpg)
*
[cos( ) sin( )
P = Real Power (W, kW, MW)
Q = Reactive Power (var, kvar, Mvar)
S = Complex power (VA, kVA, MVA)
V I V IS V I j
P
I
jQ
V
q q q q
![Page 95: Lecture 1 Basics of Electric Circuits](https://reader038.vdocuments.site/reader038/viewer/2022102802/588174971a28abf7478b6953/html5/thumbnails/95.jpg)
Power Factor (pf) = Cosø
If current leads voltage then pf is leading
If current lags voltage then pf is lagging
![Page 96: Lecture 1 Basics of Electric Circuits](https://reader038.vdocuments.site/reader038/viewer/2022102802/588174971a28abf7478b6953/html5/thumbnails/96.jpg)
1
Relationships between real, reactive and complex power
cos
sin
Example: A load draws 100 kW with a leading pf of 0.85.What are (power factor angle), Q and S?
-cos 0.85 31.8
100117.6
0.85
P S
Q S
kWS
kVA
117.6sin( 31.8 ) 62.0 kVarQ
![Page 97: Lecture 1 Basics of Electric Circuits](https://reader038.vdocuments.site/reader038/viewer/2022102802/588174971a28abf7478b6953/html5/thumbnails/97.jpg)
Conservation of Power
At every node (bus) in the system
Sum of real power into node must equal zero
Sum of reactive power into node must equal zero
This is a direct consequence of Kirchoff’s
current law, which states that the total
current into each node must equal zero.
Conservation of power follows since S = VI*
![Page 98: Lecture 1 Basics of Electric Circuits](https://reader038.vdocuments.site/reader038/viewer/2022102802/588174971a28abf7478b6953/html5/thumbnails/98.jpg)
Conversation of Power
Example
Earlier we found
I = 20-6.9 amps
*
*R
2
*L
2
100 30 20 6.9 2000 36.9 VA
36.9 pf = 0.8 lagging
S 4 20 6.9 20 6.9
1600
S 3 20 6.9 20 6.9
1200var
R
L
S V I
V I
W I R
V I j
I X
![Page 99: Lecture 1 Basics of Electric Circuits](https://reader038.vdocuments.site/reader038/viewer/2022102802/588174971a28abf7478b6953/html5/thumbnails/99.jpg)
Power Consumption in
Devices
2Resistor Resistor
2Inductor Inductor L
2
Capacitor Capacitor C
Capacitor
Resistors only consume real power
P
Inductors only consume reactive power
Q
Capacitors only generate reactive power
1Q
Q
C
I R
I X
jI X X
j C Cw w
2
Capacitor
C
V
X
![Page 100: Lecture 1 Basics of Electric Circuits](https://reader038.vdocuments.site/reader038/viewer/2022102802/588174971a28abf7478b6953/html5/thumbnails/100.jpg)
Example
*
40000 0400 0 Amps
100 0
40000 0 (5 40) 400 0
42000 16000 44.9 20.8 kV
S 44.9 20.8 400 0
17.98 20.8 MVA 16.8 6.4 MVA
VI
V j
j
V I
j
First solve
basic circuit
![Page 101: Lecture 1 Basics of Electric Circuits](https://reader038.vdocuments.site/reader038/viewer/2022102802/588174971a28abf7478b6953/html5/thumbnails/101.jpg)
Example
Now add additional
reactive power load
and resolve
70.7 0.7 lagging
564 45 Amps
59.7 13.6 kV
S 33.7 58.6 MVA 17.6 28.8 MVA
LoadZ pf
I
V
j
![Page 102: Lecture 1 Basics of Electric Circuits](https://reader038.vdocuments.site/reader038/viewer/2022102802/588174971a28abf7478b6953/html5/thumbnails/102.jpg)
Balanced 3 Phase () Systems
A balanced 3 phase () system has
three voltage sources with equal magnitude, but with an angle shift of 120
equal loads on each phase
equal impedance on the lines connecting the generators to the loads
Bulk power systems are almost exclusively 3
Single phase is used primarily only in low voltage, low powersettings, such as residential and some commercial
![Page 103: Lecture 1 Basics of Electric Circuits](https://reader038.vdocuments.site/reader038/viewer/2022102802/588174971a28abf7478b6953/html5/thumbnails/103.jpg)
Balanced 3 -- No Neutral Current
* * * *
(1 0 1 1
3
n a b c
n
an an bn bn cn cn an an
I I I I
VI
Z
S V I V I V I V I
![Page 104: Lecture 1 Basics of Electric Circuits](https://reader038.vdocuments.site/reader038/viewer/2022102802/588174971a28abf7478b6953/html5/thumbnails/104.jpg)
Advantages of 3 Power
Can transmit more power for same amount of
wire (twice as much as single phase)
Torque produced by 3 machines is constant
Three phase machines use less material for
same power rating
Three phase machines start more easily than
single phase machines
![Page 105: Lecture 1 Basics of Electric Circuits](https://reader038.vdocuments.site/reader038/viewer/2022102802/588174971a28abf7478b6953/html5/thumbnails/105.jpg)
Three Phase - Wye Connection
There are two ways to connect
3 systems
Wye (Y)
Delta ()
an
bn
cn
Wye Connection Voltages
V
V
V
V
V
V
+
![Page 106: Lecture 1 Basics of Electric Circuits](https://reader038.vdocuments.site/reader038/viewer/2022102802/588174971a28abf7478b6953/html5/thumbnails/106.jpg)
Wye Connection Line Voltages
Van
Vcn
Vbn
VabVca
Vbc
-Vbn
(1 1 120
3 30
3 90
3 120
ab an bn
bc
ca
V V V V
V
V V
V V
Line to line
voltages are
also balanced
![Page 107: Lecture 1 Basics of Electric Circuits](https://reader038.vdocuments.site/reader038/viewer/2022102802/588174971a28abf7478b6953/html5/thumbnails/107.jpg)
Wye Connection
Define voltage/current across/through device
to be phase voltage/current
Define voltage/current across/through lines to
be line voltage/current
6
3
3 1 30 3
3
j
Line Phase Phase
Line Phase
Phase Phase
V V V e
I I
S V I
![Page 108: Lecture 1 Basics of Electric Circuits](https://reader038.vdocuments.site/reader038/viewer/2022102802/588174971a28abf7478b6953/html5/thumbnails/108.jpg)
Delta Connection
IcaIc
IabIbc
Ia
Ib
a
b
a
3
For the Delta
phase voltages equal
line voltages
For currents
I
3
I
I
3
ab ca
ab
bc ab
ca bc
Phase Phase
I I
I
I I
I I
S V I
![Page 109: Lecture 1 Basics of Electric Circuits](https://reader038.vdocuments.site/reader038/viewer/2022102802/588174971a28abf7478b6953/html5/thumbnails/109.jpg)
Three Phase Transmission Line
![Page 110: Lecture 1 Basics of Electric Circuits](https://reader038.vdocuments.site/reader038/viewer/2022102802/588174971a28abf7478b6953/html5/thumbnails/110.jpg)
Wye Connection Line Voltages
Van
Vcn
Vbn
VabVca
Vbc
-Vbn
(1 1 120
3 30
3 90
3 150
ab an bn
bc
ca
V V V V
V
V V
V V
Line to line
voltages are
also balanced
![Page 111: Lecture 1 Basics of Electric Circuits](https://reader038.vdocuments.site/reader038/viewer/2022102802/588174971a28abf7478b6953/html5/thumbnails/111.jpg)
Wye Connection Line Voltage
Define voltage/current across/through device to be phase
voltage/current
Define voltage/current across/through lines to be line
voltage/current
6
3
3 1 30 3
3
j
Line Phase Phase
Line Phase
Phase Phase
V V V e
I I
S V I
![Page 112: Lecture 1 Basics of Electric Circuits](https://reader038.vdocuments.site/reader038/viewer/2022102802/588174971a28abf7478b6953/html5/thumbnails/112.jpg)
Delta Connection
IcaIc
IabIbc
Ia
Ib
3
For the Delta
phase voltages equal
line voltages
For currents
I
3
I
I
3
a ab ca
ab
b bc ab
a ca bc
Phase Phase
I I
I
I I
I I
S V I
![Page 113: Lecture 1 Basics of Electric Circuits](https://reader038.vdocuments.site/reader038/viewer/2022102802/588174971a28abf7478b6953/html5/thumbnails/113.jpg)
Three Phase Example
Assume a -connected load is supplied from a 3 13.8 kV
(L-L) source with Z = 1020W
13.8 0
13.8 0
13.8 0
ab
bc
ca
V kV
V kV
V kV
13.8 0138 20
138 140 138 0
ab
bc ca
kVI amps
I amps I amps
![Page 114: Lecture 1 Basics of Electric Circuits](https://reader038.vdocuments.site/reader038/viewer/2022102802/588174971a28abf7478b6953/html5/thumbnails/114.jpg)
*
138 20 138 0
239 50 amps
239 170 amps 239 0 amps
3 3 13.8 0 kV 138 amps
5.7 MVA
5.37 1.95 MVA
pf cos 20 lagging
a ab ca
b c
ab ab
I I I
I I
S V I
j
![Page 115: Lecture 1 Basics of Electric Circuits](https://reader038.vdocuments.site/reader038/viewer/2022102802/588174971a28abf7478b6953/html5/thumbnails/115.jpg)
Delta-Wye Transformation
Y
phase
To simplify analysis of balanced 3 systems:
1) Δ-connected loads can be replaced by 1
Y-connected loads with Z3
2) Δ-connected sources can be replaced by
Y-connected sources with V3 30
Line
Z
V
![Page 116: Lecture 1 Basics of Electric Circuits](https://reader038.vdocuments.site/reader038/viewer/2022102802/588174971a28abf7478b6953/html5/thumbnails/116.jpg)
Per Phase Analysis
Per phase analysis allows analysis of balanced 3 systems
with the same effort as for a single phase system
Balanced 3 Theorem: For a balanced 3 system with
All loads and sources Y connected
No mutual Inductance between phases
![Page 117: Lecture 1 Basics of Electric Circuits](https://reader038.vdocuments.site/reader038/viewer/2022102802/588174971a28abf7478b6953/html5/thumbnails/117.jpg)
Per Phase Analysis
Then
All neutrals are at the same potential
All phases are COMPLETELY decoupled
All system values are the same sequence assources. The sequence order we’ve been using(phase b lags phase a and phase c lags phase a) isknown as “positive” sequence; later in the coursewe’ll discuss negative and zero sequence systems.
![Page 118: Lecture 1 Basics of Electric Circuits](https://reader038.vdocuments.site/reader038/viewer/2022102802/588174971a28abf7478b6953/html5/thumbnails/118.jpg)
Per Phase Analysis Procedure
To do per phase analysis
1. Convert all load/sources to equivalent Y’s
2. Solve phase “a” independent of the other phases
3. Total system power S = 3 Va Ia*
4. If desired, phase “b” and “c” values can be
determined by inspection (i.e., ±120° degree phase
shifts)
5. If necessary, go back to original circuit to
determine line-line values or internal values.
![Page 119: Lecture 1 Basics of Electric Circuits](https://reader038.vdocuments.site/reader038/viewer/2022102802/588174971a28abf7478b6953/html5/thumbnails/119.jpg)
Per Phase Example
Assume a 3, Y-connected generator with Van = 10volts supplies a -connected load with Z = -j through a transmission line with impedance of j0.1 per phase. The load is also connected to a -connected generator with Va”b” = 10 through a second transmission line which also has an impedance of j0.1per phase.
Find
1. The load voltage Va’b’
2. The total power supplied by each
generator, SY andS
![Page 120: Lecture 1 Basics of Electric Circuits](https://reader038.vdocuments.site/reader038/viewer/2022102802/588174971a28abf7478b6953/html5/thumbnails/120.jpg)
Per Phase Example
First convert the delta load and source to equivalent
Y values and draw just the "a" phase circuit
![Page 121: Lecture 1 Basics of Electric Circuits](https://reader038.vdocuments.site/reader038/viewer/2022102802/588174971a28abf7478b6953/html5/thumbnails/121.jpg)
Per Phase Example
' ' 'a a a
To solve the circuit, write the KCL equation at a'
1(V 1 0)( 10 ) V (3 ) (V j
3j j
![Page 122: Lecture 1 Basics of Electric Circuits](https://reader038.vdocuments.site/reader038/viewer/2022102802/588174971a28abf7478b6953/html5/thumbnails/122.jpg)
Per Phase Example
' ' 'a a a
'a
' 'a b
' 'c ab
To solve the circuit, write the KCL equation at a'
1(V 1 0)( 10 ) V (3 ) (V j
3
10(10 60 ) V (10 3 10 )
3
V 0.9 volts V 0.9 volts
V 0.9 volts V 1.56
j j
j j j j
volts
![Page 123: Lecture 1 Basics of Electric Circuits](https://reader038.vdocuments.site/reader038/viewer/2022102802/588174971a28abf7478b6953/html5/thumbnails/123.jpg)
Per Phase Example
*'*
ygen
*" '"
S 3 5.1 3.5 VA0.1
3 5.1 4.7 VA0.1
a aa a a
a agen a
V VV I V j
j
V VS V j
j
![Page 124: Lecture 1 Basics of Electric Circuits](https://reader038.vdocuments.site/reader038/viewer/2022102802/588174971a28abf7478b6953/html5/thumbnails/124.jpg)
124
Delta-Star Transformation
![Page 125: Lecture 1 Basics of Electric Circuits](https://reader038.vdocuments.site/reader038/viewer/2022102802/588174971a28abf7478b6953/html5/thumbnails/125.jpg)
125
Start-Delta Transformation
![Page 126: Lecture 1 Basics of Electric Circuits](https://reader038.vdocuments.site/reader038/viewer/2022102802/588174971a28abf7478b6953/html5/thumbnails/126.jpg)
THANK YOU!
For Contact
Email: [email protected]
LinkedIn: https://pk.linkedin.com/pub/arslan-ahmed-amin-p-e-b-sc-ee-m-sc-ee-m-b-a/24/853/68