Electric Circuit Analysis 2020/2021
Dr. Yaseen H. Tahir
Southern Technical University
Engineering Technical College / Basrah
Electrical Power Technical Engineering Dep.
Second Year
Subject:
Electric Circuit Analysis
Course Objective:
Tech the students the analysis of electric circuits
No. of Weeks, Hours, and Units:
Weekly Hours
Weeks
Theoretical
Practical
Total
Units
2
3
7
30
Distribution of Degrees:
1st Semester
2nd Semester
Theoretical
(Exam)
Practical
(Exam +
Evaluation)
Theoretical
(Exam)
Practical
(Exam +
Evaluation)
10
10
10
10
Annual
Works
10
Final
Theoretical
(Exam)
Practical
(Exam)
40
10
Total
100
50
50
References:
1. “Basic Engineering Circuit Analysis”, J. David Irwin & R. Mark Nelms
2. “Engineering Circuit Analysis”, William H. Hayt, Jack E. Kemmerly,
Steven M. Durbin
3. “Circuit Analysis Theory and Practice”, Robbins and Mille
4. “Fundamentals of Electric Circuits”, David A. Bell.
5. “Electrical Engineering Technology”, Dr. Nil Kanta Datta & Dr. Partha
Priva Datta.
6. “Fundamentals of Electric Circuit”, C. K. Alexander, M. N. O. Sadiku
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Electric Circuit Analysis 2020/2021
Dr. Yaseen H. Tahir
Syllabus of Electric Circuit Analysis Subject
1st, 2nd
3rd
4th
5th, 6th,
7th, 8th
9th, 10th
11th, 12th
13th, 14th
15th, 16th, 17th,
18th, 19th
20th, 21st,
22nd, 23rd
24th, 25th, 26th,
27th, 28th
29th, 30th
Definitions and Units.
Sinusoids, phasors for circuit elements.
Impedance, admittance, impedance combinations.
Sinusoidal steady- state analysis (Kirchhoff's laws, Mesh
analysis, Nodal analysis, Superposition's theorem,
Thevenin's theorem, Norton's theorem, source
transformations).
Source free series and parallel RLC circuits.
Step response of a series and a parallel RLC circuits.
General second-order circuits.
Three-phase circuits: (wye –wye, delta-delta, wye-delta,
delta-wye connections, balanced and unbalanced threephase systems).
Advanced circuit analysis using Laplace transform.
Two-port networks: (impedance, admittance, hybrids,
transmissions parameters, relationships between
parameters, interconnection between networks).
Resonance : Series resonance. Parallel resonance.
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Electric Circuit Analysis 2020/2021
Dr. Yaseen H. Tahir
Useful Information
1. The Standard SI Prefixes:
2. Typical voltage magnitudes
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Electric Circuit Analysis 2020/2021
Dr. Yaseen H. Tahir
3. Greek Alphabet:
4. Roman Numbers:
Roman
none
I,i
II , ii
III , iii
IV , iv
V,v
VI , vi
VII , vii
VIII , viii
IX , ix
X,x
Arabic
0
1
2
3
4
5
6
7
8
9
10
Roman
XI , xi
XII , xii
XIII , xiii
XIV , xiv
XV , xv
XVI , xvi
XVII , xvii
XVIII , xviii
XIX , xix
XX , xx
Arabic
11
12
13
14
15
16
17
18
19
20
5. The Basic SI Units:
Quantity
Length
Mass
Time
Electric Current
Temperature
Luminous Intensity
Quantity
Symbol
l
m
t
i or I
t
4
Unit
Meter
Kilogram
Second
Ampere
Kelvin
Candela
Unit
Symbol
m
kg
s
A
K
cd
Electric Circuit Analysis 2020/2021
Dr. Yaseen H. Tahir
6. The Quantities, Their Symboles, Units, and Units’ Symbols:
Quantity
Velocity
Acceleration
Force
Electrical charge or Electrical
quantity
Resistance
Conductance
Electromotive force
Potential difference or Voltage
Work
Energy
Power
Quantity
Symbol
v
a
F
meters per second
meters per second squared
newton
Unit
Symbol
m/s
m/s2
N
Q
coulomb
C
R
G
E
V
W
E or W
P
ohm
mho or siemen
volt
volt
joule
joule
watt
Unit
Ω
or S
V
V
J
J
W
7. Electric Circuit:
Generally, the electric circuits consist of:
1. Electrical power sources.
2. Loads.
3. Conductors.
8. Standard Symbols for Electrical Components:
In general, the elements are classified as being either active or passive. The
distinction between these two classifications depends on one thing whether
they supply or absorb energy.
 The active element is capable of generating energy. Typical active
elements are batteries and generators.
 The passive element cannot generate energy. The three common passive
elements are resistors, capacitors, and inductors.
 However, later we will show that some passive elements are capable of
storing energy.
Symbols are used for components in electrical circuit diagrams and some of
the more common ones are shown in Figures below.
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Electric Circuit Analysis 2020/2021
Dr. Yaseen H. Tahir
1. Independent voltage source
6. Fixed resistor
or
or
7. Variable resistor
2. Dependent voltage source
or
8. Fixed capacitor
3. Independent current source
or
C
9. Variable capacitor
4. Dependent current source
or
C
10. air-core inductor
5. Ground
or
or
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Electric Circuit Analysis 2020/2021
Dr. Yaseen H. Tahir
11. Iron-core inductor
14. Measurement devices
1. Ammeter
A
2.
Voltmeter
V
3.
12. variable iron-core inductor
Ohmmeter
Ω
15. Lamp
13. Switch
or
9. The Sources
a) Independent Sources
Independent sources generate a constant voltage or current (i.e. (in othe
words), they generate a voltage or current that is not determined by other
voltage or current in the circuit) as shown in Figure below:
Symbols for (a) independent voltage source and (b) independent current source.
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Electric Circuit Analysis 2020/2021
Dr. Yaseen H. Tahir
b) Dependent Sources:
Dependent sources generate a voltage or current that is determined by a
voltage or current at a specified location in the circuit as shown in Figure
below:
Example:
Determine the power supplied to element 1 by the dependent sources in Figures
below.
a)
Solution
b)
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Electric Circuit Analysis 2020/2021
Dr. Yaseen H. Tahir
The Capacitance:
 A capacitor is a circuit element that consists of two conducting surfaces
(plates) separated by a non-conducting, or dielectric material layer. A
simplified capacitor and its electrical symbol are shown in Figures below.
 The capacitance is a passive element but it is capable of storing energy by
store an electric charge.
 Capacitors may be fixed or variable and typically range from thousands
of microfarads (μF) to a few picofarads (pF).
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Electric Circuit Analysis 2020/2021
Dr. Yaseen H. Tahir
 The International System (SI) unit of capacitance is farad (F). “The
farad (F) is the capacitance of a capacitor that contains a charge of 1
coulomb (- 6.242*1018electrons) when the potential difference between
its plates (its terminals) is 1 volt.”
 The insulating material is known as the dielectric. Typical dielectric
materials are air, paper, plastic film, mica, and rubber,.
 The capacitance value of capacitor is a measure of the maximum amount
of electric charge that can be stored in it.
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Electric Circuit Analysis 2020/2021
Dr. Yaseen H. Tahir
 The capacitance value can be calculated from knowledge of the:
1. Plate area, (A in m2).
2. The relative permittivity (‫ )السماحية النسبية‬or dielectric constant
(𝝐𝒓 ).
3. Thickness (d in m) of the dielectric.
𝑨
𝑪 ∝
𝒅
𝑨
𝑪 = 𝝐∗
𝒅
𝑨
𝑪 = 𝝐𝒓 ∗ 𝝐𝟎 ∗
𝒅
where 𝝐𝟎 is the permittivity of free space (𝝐𝟎 = 𝟖. 𝟖𝟒 ∗ 𝟏𝟎 𝟏𝟐 in F/m).
 The quantity of charge stored depends on the:
1. Capacitor value (C).
2. Battery voltage (E).
𝑸 = 𝑪∗𝑬
 Based on the dielectric type, the capacitors are classified as:
a.
b.
c.
d.
e.
f.
g.
Air capacitors.
Paper capacitors.
Plastic film capacitors.
Mica capacitors.
Ceramic capacitors.
Electrolytic capacitors.
Tantalum capacitors.
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Electric Circuit Analysis 2020/2021
Dr. Yaseen H. Tahir
Example: (example 15-2, page 387, David)
Calculate the capacitance of a capacitor with a plate area of 400 cm2
and a dielectric thickness of 1 mm:
a) When the dielectric is air.
b) When the dielectric is mica with relative permittivity of 5.
c) Determine the charge on the capacitor in the case of (a) and (b)
when the applied voltage is 25V.
Solution:
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Electric Circuit Analysis 2020/2021
Dr. Yaseen H. Tahir
Example: (example 15-3, page 388, David) (H. W.)
A 1 ϻF capacitance is to be constructed from rolled-up sheets of
aluminum foil separated by a layer of paper 0.1 mm thick.
Calculate the required area for each sheet of foil if the relative
permittivity of the paper is 6.
Solution:
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Electric Circuit Analysis 2020/2021
Dr. Yaseen H. Tahir
Capacitance connections:
1- Parallel-Connected Capacitors:
𝑬 = 𝒗𝟏 = 𝒗𝟐 = 𝒗𝟑 = ⋯ ⋯ = 𝒗𝑵
𝒊𝑻 = 𝒊 𝟏 + 𝒊 𝟐 + 𝒊𝟑 + ⋯ ⋯ + 𝒊 𝑵
𝑡 ∗ 𝑖 = 𝑡 ∗ 𝑖 + 𝑡 ∗ 𝑖 + 𝑡 ∗ 𝑖 + ⋯⋯+ 𝑡 ∗ 𝑖
𝑸𝑻 = 𝑸𝟏 + 𝑸𝟐 + 𝑸𝟑 + ⋯ ⋯ + 𝑸𝑵
𝑪𝑻 = 𝑪𝟏 + 𝑪𝟐 + 𝑪𝟑 + ⋯ ⋯ + 𝑪𝑵
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Electric Circuit Analysis 2020/2021
Dr. Yaseen H. Tahir
2- Series-Connected Capacitors:
𝑬 = 𝒗𝟏 + 𝒗𝟐 + 𝒗𝟑 + ⋯ ⋯ + 𝒗𝑵
𝒊𝑻 = 𝒊𝟏 = 𝒊 𝟐 = 𝒊𝟑 = ⋯ ⋯ = 𝒊 𝑵
𝑡 ∗ 𝑖 = 𝑡 ∗ 𝑖 = 𝑡 ∗ 𝑖 = 𝑡 ∗ 𝑖 = ⋯⋯ = 𝑡 ∗ 𝑖
𝑸𝑻 = 𝑸𝟏 = 𝑸𝟐 = 𝑸𝟑 = ⋯ ⋯ = 𝑸𝑵
𝟏
𝟏
𝟏
𝟏
𝟏
=
+
+
+⋯⋯+
𝑪𝑻 𝑪𝟏 𝑪𝟐 𝑪𝟑
𝑪𝑵
Note:
For two series-connected capacitors the total capacitor is given by:
1
1
1
= +
𝐶
𝐶
𝐶
1
𝐶 +𝐶
=
𝐶
𝐶 ∗𝐶
𝑪𝑻 =
𝑪𝟏 ∗ 𝑪𝟐
𝑪𝟏 + 𝑪𝟐
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Electric Circuit Analysis 2020/2021
Dr. Yaseen H. Tahir
Example: Determine the total capacitance (CT) in Figure below. (Ans. 1.667 μF)
Solution:
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Electric Circuit Analysis 2020/2021
Dr. Yaseen H. Tahir
Example: Three capacitors have values C1 = 3 ϻF, C2 = 3 ϻF, and C3 = 3 ϻF
are connected across the 50 V supply. Determine the total
capacitance (CT) and the charge on each capacitor when:
a- The three capacitors are connected in parallel.
b- The three capacitors are connected in series.
Solution:
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Electric Circuit Analysis 2020/2021
Dr. Yaseen H. Tahir
Energy Stored in Capacitor:
The energy stored (W) in joules is given as
then
𝑊 = 𝑎𝑣𝑒𝑟𝑎𝑔𝑒 𝑣𝑜𝑙𝑡𝑎𝑔𝑒 ∗ 𝑎𝑣𝑒𝑟𝑎𝑔𝑒 𝑐𝑢𝑟𝑟𝑒𝑛𝑡 ∗ 𝑡
𝟏
𝒂𝒗𝒆𝒓𝒂𝒈𝒆 𝒗𝒐𝒍𝒕𝒂𝒈𝒆 = 𝑬
𝟐
𝑸 𝑪𝑬
𝒂𝒗𝒆𝒓𝒂𝒈𝒆 𝒄𝒖𝒓𝒓𝒆𝒏𝒕 = 𝑰 =
=
𝒕
𝒕
1
𝐶𝐸
𝐸∗
∗𝑡
2
𝑡
𝟏
𝑾 = 𝑪 𝑬𝟐
𝟐
𝑊=
Example: Calculate the energy stored in each of the three series-connected
capacitors in the previous example and total energy stored.
Solution:
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