5. 5
21EES101T-ELECTRICAL AND
ELECTRONICSENGINEERING
UNIT 1
Unit-1 -Electric Circuits
Introduction to basic terminologies in DC circuit, Kirchhoff’s Current law, Kirchhoff’s Voltage law,
Mesh Current Analysis, Nodal Voltage Analysis, Thevenin’s Theorem, Maximum power transfer
Theorem, Superposition Theorem.
Basic terminologies of AC -RMS and Average value of half wave and Full wave alternating quantity,
Fundamentals of single-phase AC circuits- Analysis of R-L, R-C, R-L-C series circuits-
Fundamentals of three phase AC system, Three-Phase Winding Connections, Relationship of Line
and Phase Voltages, and Currents in a Delta and Star-connected System
PRACTICAL LEARNING: Practice on Theorems, Halfwave, Full wave bridge rectifier circuits.
6. CONTENTS COVERED
Introduction to Basic Terminologies pertaining to
DC Circuit
Ohm’s Law
Kirchhoff's Current and Voltage Law
Mesh Current Analysis
Nodal Voltage Analysis
Superposition Theorem
Thevenin’s Theorem
Maximum Power Transfer Theorem
6
10. OHM’S LAW
Georg Simon Ohm (1787-1854),
German physicist. Ohm published his
most important work in 1827, after
many years researching the
relationship between electrical current
and potential difference
Ohm's law states that the current through a conductor between two points
is directly proportional to the voltage across the two points, keeping the
physical conditions constant.
𝑽𝜶𝑰
Introducing the constant of proportionality, the resistance, one arrives at the
usual mathematical equation that describes this relationship:
𝑽 = 𝑰R
11. 11
The voltage-current ratios of
resistors are reasonably constant
only within certain ranges of
current, voltage, or power, and
depend also on temperature and
other environmental factors
12. 12
VOLTAGE / POTENTIAL DIVIDER RULE
In general, if a voltage divider has N resistors (R1, R2 ,……., RN ) in series with the source
voltage v, the nth resistor Rn will have a voltage drop of
v
N
R
.........
R
R
n
R
n
v
2
1
The source voltage v is divided among the resistors
in direct proportion to their resistances; the larger
the resistance, the larger the voltage drop. This is
called the principle of voltage division
14. 14
CURRENT DIVIDER RULE
In parallel circuits, current is divided
depending upon the value of resistors and the
number of branches.
Current in each branch of a parallel circuit
is inversely proportional to its resistance.
This shows that the total current i is
shared by the resistors in inverse
proportion to their resistances. This is
known as the principle of current
division, and the circuit is known as a
current divider. Notice that the larger
current flows through the smaller
resistance.
For a parallel combination of N resistors, the current
through resistor Rk is given by:
18. 18
KIRCHHOFF’S LAWS
KIRCHHOFF’S CURRENT LAW KIRCHHOFF’S VOLTAGE LAW
Gustav Robert Kirchhoff (1824–1887), a German
physicist, stated two basic laws in 1847 concerning the
relationship between the currents and voltages in an electrical
network. Kirchhoff’s laws, along with Ohm’s law, form the
basis of circuit theory.
Born the son of a lawyer in Konigsberg, East
Prussia, Kirchhoff entered the University of Konigsberg at age 18
and later became a lecturer in Berlin. His collaborative work in
spectroscopy with German chemist Robert Bunsen led to the
discovery of cesium in 1860 and rubidium in 1861. Kirchhoff
was also credited with the Kirchhoff law of radiation. Thus
Kirchhoff is famous among engineers, chemists, and physicists.
19. 19
KIRCHHOFF’S CURRENT LAW
Also known as Kirchhoff’s point or junction law.
KCL is a consequence of Law of Conservation of Charge (i.e. charge can neither be created nor be destroyed).
A point at which two or more elements have a common connection is called a node or junction.
KCL states that
“The Algebraic Sum of the Currents Entering or Leaving any Node is Zero”.
OR
“The Sum of the Currents Entering a Node is Equal to the Sum of the Currents Leaving the Node”.
Mathematically, KCL implies that
where N is the number of branches connected to the node, and in is the nth current entering
(or leaving the node). By this law, currents entering a node may be regarded as positive,
while currents leaving the node may be taken as negative or vice versa.
N
n
n
i 0
5
2
1
4
3 i
i
i
i
i
OR
0
5
4
3
2
1
)
i
(
i
i
)
i
(
i
20. 20
KIRCHHOFF’S VOLTAGE LAW
Also known as Kirchhoff’s work or energy law.
KCL is a consequence of Law of Conservation of Energy (i.e. energy can neither be created nor be destroyed).
A Loop is a closed conducting path through which an electric current either flows or is intended to flow. (A
loop is a closed path formed by starting at a node, passing through a set of nodes, and returning to the starting node
without passing through any node more than once).
KVL states that
“The Algebraic Sum of all Voltages Around a Closed Path (or Loop) is Zero”.
OR
“Around a Closed Path or Loop the Sum of the Voltage Drops = Sum of the Voltage Rises”
Mathematically, KVL implies that
M
m
m
v
1
0
The phrase algebraic sum indicates that we must take polarity into account as we add up the voltages of
elements that comprise a loop.
KVL can be applied in two ways: by taking either a clockwise or a counter-clockwise trip around the loop.
Either way, the algebraic sum of voltages around the loop is zero.
where M is the number of voltages in the loop (or the
number of branches in the loop) and vm is the mth
voltage.
22. 22
While traversing a closed path,
if we move from + terminal to –
terminal there is a voltage
drop. If we move from –
terminal to + terminal, there is
a voltage rise. A voltage rise
indicates positive voltage and
a voltage drop indicates a
negative voltage
23. MESH / LOOP ANALYSIS
Mainly or Basically used to determine the Mesh or Loop Currents. Although other variables can also be
determined.
KVL is used to determine the Mesh or Loop Currents.
A Loop is a closed conducting path through which an electric current either flows or is intended to flow.
While travelling a Loop no element should be encountered more than once
Mesh is also a Loop that contains no other Loop in it.
Loop -1
Loop - [A-B-E-F-A]
Loop -2
Loop - [B-C-D-E-B]
Loop -3 (Outermost Path)
Loop - [A-B-C-D-E-F-A)
NOTE / MOST IMPORTANT:
A closed loop is defined
as any path that
originates at a point,
travels around a circuit,
and returns to the
original point without
retracing any segments
(i.e. no element is
encountered more than
once)
24. Loop -1
Loop - [A-B-E-F-A]
Loop -2
Loop - [B-C-D-E-B]
Loop -3 (Outermost Path)
Loop - [A-B-C-D-E-F-A)
Mesh -1
Mesh - [A-B-E-F-A]
Mesh -2
Mesh - [B-C-D-E-B]
This loop is not a mesh because it
contains two other loops in it.
Mesh is defined as a Loop
that contains no other Loop
in it.
ALERT: In any case / situation / circumstance, while solving the
numericals to determine the mesh or loop currents, we have to count or
identify the number of meshes only.
25. NODAL ANALYSIS
Mainly or Basically used to determine the NODE VOLTAGES (or Voltages of non –
reference node). Other variables then can also be determined (if required).
KCL is used to determine the Node Voltages.
A NODE or JUNCTION is a point in a circuit at which two or more than branches or
elements are connected. [The term Node is commonly used to refer to a junction of
two or more branches].
Each current path is called a BRANCH.
ALERT: All the points connected together by a simple
wire represents the same node or only one single node.
26.
27. 1.Determine the number of nodes within the network.
2.Pick a reference node (or datum node or ground node), and label
each remaining node with a subscripted value of voltage: V1 (or Va),V2
(or Vb) and so on. [The negative of the battery is chosen as reference or datum node / The
node to which the maximum number of elements are connected is selected as datum or
reference or ground node].
3.Apply Kirchhoff’s current law at each node except the reference
node. Assume that all unknown currents leave the node for each
application of Kirchhoff’s current law. Each node is to be treated as
a separate entity, independent of the application of Kirchhoff’s
current law to the other nodes.
4.Solve the resulting equations for the nodal voltages.
28. SPECIAL CASE OF MESH ANALYSIS
(CONCEPT OF SUPERMESH)
Current source is in the
outermost mesh (i.e. not
common to two meshes)
Current source common to two
meshes (i.e. 6 A is common to
Mesh 1 and Mesh 2)
By observation, i2 = - 5 A [Since direction of
current i2 and current source are in opposite
direction, that’s why place a minus sign]
Amp
i
or
i
or
i
or
)
(
i
or
i
i
i
or
)
i
i
(
i
2
10
20
30
10
10
10
5
6
10
10
6
6
4
0
10
6
4
1
1
1
1
2
1
1
2
1
1
ANSWER
When a current source is common to two meshes, then
such numericals or situations can be solved by the concept
of SUPERMESH
A SUPERMESH results (or formed) when two
meshes have a current source in common.
SUPERMESH is formed from two meshes that have a
current source as a common element; the current source is
in the interior of the supermesh.
30. 30
SUPERPOSITION THEOREM
If a circuit has two or more independent sources, one way to determine the value of a specific
variable (voltage or current) is to use nodal or mesh analysis. Another way is to determine the
contribution of each independent source to the variable and then add them up. The latter
approach is known as the SUPERPOSITION.
32. 32
THEVENIN’S THEOREM
It often occurs in practice that a particular element in a circuit is variable (usually called the
load) while other elements are fixed. As a typical example, a household outlet terminal may be
connected to different appliances constituting a variable load. Each time the variable element is
changed, the entire circuit has to be analyzed all over again. To avoid this problem, Thevenin’s
theorem provides a technique by which the fixed part of the circuit is replaced by an equivalent
circuit.
42. ELECTRICAL AND ELECTRONICS ENGINEERING
21EES101T
UNIT – I – SINGLE PHASE AC
42
By:
Dr. Pavan Khetrapal
Associate Professor
Department of Electrical and
Electronics Engineering
43. CONTENTS COVERED
Generation of AC
Introduction to Basic Terminologies pertaining to
AC Circuit
RMS Value and Mean Value
Phasor and Its Significance
Series R, L and C Circuit
Series R-L, R-C and R-L-C Circuit
43
44. 44
GENERATION OF ALTERNATING EMF
❑ The term alternating indicates that the waveform alternates between two
prescribed levels in a set time sequence.
OR
❑ The term alternating indicates that the waveform changes periodically both in
magnitude and direction.
Changes after certain
time period or interval
Follows
Sine Law
45. 45
A single turn coil
rotated in the influence
of a magnetic field
produced by the
magnetic poles (North
and South).
46. 46
Instantaneous value of emf induced in the coil,
Where N is the number of turns of the coil;
Ømax is the maximum value of the flux which links with the coil;
ω is the angular velocity with which the coil is rotating; (Also referred to angular
frequency) = 2πf
t is an instant of time;
θ is the angular displacement.
48. 48
DEFINITIONS PERTAINING TO AC:
❑ Amplitude / Peak Value / Maximum Value:
❑ Instantaneous Value: The value attained by the
alternating quantity at any particular instant is called as
instantaneous value. It is denoted by small letter – i, v.
v = Vmaxsinωt
or i= Imaxsinωt
49. 49
❑ Cycle: One complete set of positive and negative values span or spread over 2π radians
or 360 degrees.
❑ Alteration: One complete set of either positive or negative values span or
spread over π radians or 180 degrees.
51. 51
❑ Angular Velocity (ω): The rate at which the coil rotates is called its angular
velocity. If the coil rotates through an angle of 300 in 1 second, for example, its
angular velocity is 300 per second. Angular velocity is denoted by the Greek letter ω
(omega).
52. 52
❑ Phase: The phase of a sine wave is an angular measurement that specifies the
position of that sine wave relative to a reference.
⮚ If a sine wave does not pass through zero at t = 0 s, it has a phase shift.
Waveforms may be shifted to the left or to the right
54. 54
❑ When two sine waves are considered having the
same frequency and their waveforms pass
through zero at different times, and when they
do not reach maximum positive amplitude at
the same time, they are out of phase with each
other.
❑ When two sine waves are considered having the
same frequency, and when their wave forms
pass through zero and reach maximum positive
amplitude at the same time, they are in phase
with each other.
61. Ques: Represent the following sinusoidal ac voltage graphically and through phasor
representation:
Solution:
Graphical or Waveform Representation
Comparing the given sinusoidal ac voltage with
standard instantaneous equation of sinusoidal
ac voltage, we have Vmax = 20 volts and ω = 314
Phasor diagram
drawn in terms of
maximum value
Phasor diagram
drawn in terms of
RMS value
Graphical Representation
Phasor Representation
62. 62
Pure Resistive Circuit Connected to Sinusoidal AC Supply Pure Inductive Circuit Connected
to Sinusoidal AC Supply
72. NOMENCLATURE OF PHASES:
R, Y, B [Red, Yellow, Blue] a, b, c / A, B, C 1, 2, 3
72
REPRESENTATION OF THREE PHASE VOLTAGE:
)
t
(
sin
max
V
v
)
t
(
sin
max
V
v
t
sin
max
V
aa
v
'
cc
'
bb
'
0
240
0
120
EQUATION METHOD WAVEFORM METHOD PHASOR REPRESENTATION
73.
74. INTERCONNECTION OF THREE PHASES / WINDINGS:
• STAR CONNECTION
• Similar ends are joined together.
• The common point is called as Neutral point or
Star point.
• DELTA CONNECTION
• Dissimilar ends are joined together.
• Neutral point is not available
74
The voltages acting between two line is called as line voltage.
The voltage acting between one line and neutral is called as phase voltage or the voltage across the
phase is called as phase voltage.
