BEEE Unit I Material

EECE1001: BASIC ELECTRICAL AND ELECTRONICS ENGINEERING
Unit I
1
Unit I
Syllabus
DC Circuits: Basic circuit elements and sources, Ohms law,
Kirchhoff’s laws, series and parallel connection of circuit
elements, Node voltage analysis, Mesh current analysis,
Superposition ,Thevenin’s and maximum power transfer theorem.
2
Basis For Comparison Electrical Device Electronics Device
Definition It is defined as the device which uses the The device which controls the flow
electrical energy for performing the work. of electrons for performing the
particular task is known as the
electronics devices.
Material Used Metals like copper and aluminium are used for Semiconductor material like silicon,
the conduction of current. germanium etc.
Operating Principle Convert the electrical energy into other forms of Uses the electrical energy for
energy. performing the particular task.
Current Alternating Current Direct Current
Voltage Works on high voltage. Works on low voltage
Power consumption More Less
Required Space More Less
Uses For doing mechanical work. For amplifying the weak signal or for
coding and decoding the
information.
Examples Transformer, motor, generator etc. Transistor, diode, microprocessor,
flip-flop, amplifier, etc. 3
Introduction GITAM
Deemed to be University
• In electrical engineering, we are often interested in
transferring energy from one point to another point.
• To do this, we require interconnection of electrical devices and
such interconnection is known as electric circuit.
• Each component of the electric circuit is known as circuit
element.
• A circuit element is a mathematical representation of a simple
two terminal electrical device characterized by its specific
voltage current relationship. Examples: Resistors, Capacitors,
Inductors etc.
4
Electric Charge GITAM
5
GITAM
• The most basic quantity of electric circuit is electric charge. Charge
is the electrical property of atomic particles of which matter consists
measured in Coulombs.
• Some important characteristics of electric charge:
• Charge is bipolar and is described in either positive or negative
charges.
• The charge that occur in nature are integral multiples of electric
charge 𝑒 = −1.602 ∗ 10−19 coulombs.
• Law of conservation of charge states that charge can neither be
created nor destroyed, only transferred.
6
Electric Charge GITAM
• How much charge is represented by 6524 electrons?

Solution:
Each electron has 𝑒 = −1.602𝑥10−19 𝑐𝑜𝑢𝑙𝑜𝑚𝑏𝑠
Hence 6524 electrons will have
−19
𝑐𝑜𝑢𝑙𝑢𝑚𝑏𝑠
𝑞 = −1.602𝑥10 ∗ 6524 𝑒𝑙𝑒𝑐𝑡𝑟𝑜𝑛𝑠
𝑒𝑙𝑒𝑐𝑡𝑟𝑜𝑛
𝑞 = −1.04514𝑥10−15 𝑐𝑜𝑢𝑙𝑜𝑚𝑏𝑠
7
GITAM
• The unique property of electric charge is that it can be transferred from
one place to another, that means it is mobile in nature.
• Charge in motion represents current.
• The convention is to take the current flow as the movement of positive
charges. That is, opposite to the flow of negative charges.
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Current GITAM
• The electrical effects caused by charge in motion depends on

the rate of charge flow.
• The rate of charge flow is known as ‘electric current’.
• The mathematical relation between current, charge and time
𝑑𝑞
is 𝑖 = where i is current in Amps
𝑑𝑡
q is charge in Coulombs
t is time in seconds
1 Amp = 1 coulomb/Second
9
Current GITAM
• Charge transferred between time to and t is
𝑡
𝑞= ‫𝑖 𝑡׬‬ 𝑑𝑡
𝑜
• Current ‘i’ need not be a constant value function.
• When a current is constant with time, that is direct current (dc). Thus, a
direct current (dc) is a current that remains constant with time.
• A current that varies with time, reversing direction periodically, is called
alternating current (ac).
• Thus, an alternating current (ac) is current that varies with time
periodically. ac is used in our household to run Fans, bulbs, refrigerators,
TV’s, air conditioners, water heaters and other electrical appliances.
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Current GITAM
• Figure shows a dc current and a sinusoidal ac current versus

time.
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Current GITAM
• Figure shows other types of time varying currents such as the

triangular and square waveforms.
12
Current GITAM
• Graphical representation of current:
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Current GITAM
• Graphical representation of current:
14
GITAM
15
Voltage GITAM
• To move an electron in a conductor in a particular direction requires some

work or energy transfer.
• Work done in moving unit charge in electric field is stored in it in the form
of electric potential known as potential difference or voltage.
• Thus the voltage V12 between two points 1 and 2 in an electric circuit is
the energy or work needed to move a unit charge from 1 to 2.
𝑑𝑤
• The voltage 𝑣 = 𝑉12 =
𝑑𝑞
𝑤 𝑖𝑠 𝑒𝑛𝑒𝑟𝑔𝑦 𝑖𝑛 𝑗𝑜𝑢𝑙𝑒𝑠
𝑞 𝑖𝑠 𝑐ℎ𝑎𝑟𝑔𝑒 𝑖𝑛 𝑐𝑜𝑢𝑙𝑢𝑚𝑠
𝑣 = 𝑉12 𝑖𝑠 𝑡ℎ𝑒 𝑣𝑜𝑙𝑡𝑎𝑔𝑒 𝑖𝑛 𝑣𝑜𝑙𝑡𝑠
1 volt = 1 joule / 1 Coulomb
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Voltage GITAM
• Voltage has polarity. Plus ‘+’ and minus ‘-’ are used to represent
reference direction or voltage polarity.
• The Voltage V12 can be interpreted as:

a) Point 1 is at a potential of V12 volts higher than point 2.
Or
b) potential at point 1 with respect to point 2 is V12 volts.
• There fore logically it follows that V12 = - V21
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GITAM
• Power is the time rate of expending or absorbing energy.

• Power is measured in watts (W).
𝑑𝑤
• Power 𝑝 = where p is the power in Watts
𝑑𝑡
w is the energy in Joules
and t is the time in seconds.
1 Watt = 1 Joule/ 1 second
𝑑𝑤 𝑑𝑤 𝑑𝑞
• 𝑝= = ∗ =𝑣 ∗𝑖
𝑑𝑡 𝑑𝑞 𝑑𝑡
• Thus power associated with a basic circuit element is the product
of the current in the element and the voltage across it.
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Power and Energy GITAM
• If the power has + sign, power is delivered to or absorbed by the element.

• On the other hand, if the power has – sign, power is being supplied or delivered by
the element.
• Polarity of voltage and direction of current play major role in determining the sign
of power.
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• According to Passive sign convention:

power absorbed by an element is positive, when current
enters through its + terminal.
i.e. p is +ve.
power absorbed by an element is negative when current
enters through its –ve terminal.
i.e. p is –ve.
In general Power absorbed = – Power delivered.
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21
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• In an electric circuit, law of conservation of energy must be

obeyed.
• For this reason, at any instant of time, algebraic sum power
must be zero. i.e. σ 𝑝 = 0.
• i.e. total power supplied to the circuit must balance total
power absorbed.
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• Energy supplied or absorbed by a circuit element between

instants to and t is
𝑡 𝑡
𝐸 = න 𝑝 𝑑𝑡 = න 𝑣𝑖 𝑑𝑡
𝑡𝑜 𝑡𝑜
• Energy is the capacity to do work. Measured in Joules.
• The electric power companies measure energy in Kilo-watt-
hours (KWh)
• 1KWh = 36x105 Joules.
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Active and passive circuit elements GITAM
• There are two types of elements found in electric circuits based

on energy delivered to or by them.
• Passive elements are those whose average power delivered is
always zero or negative.
Examples: Resistors, inductors, capacitors
• Active elements are those whose average power delivered is
always positive.
Examples: Voltage and current sources.
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Independent Voltage source GITAM
• An independent voltage source is two terminal element that maintains a
specific voltage between its terminal.
• The voltage is completely independent of the current through it.
• Sources such as generators and batteries may be regarded as
approximations to ideal voltage sources.
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Independent Current source GITAM
• An independent current source is a two terminal element that

provides a specific current independent of voltage across the
source.
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Dependent sources GITAM
• Dependent sources are designated by diamond shaped

symbols.
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Dependent voltage sources GITAM
• In a dependent or controlled voltage source, the voltage across

the source terminals is a function of other voltages or currents
in the circuit.
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Dependent voltage sources GITAM
• A voltage controlled voltage source is a voltage source having a

terminal voltage equal to a constant times the voltage (vx)
across a pair of terminals elsewhere in the network.
• A current controlled voltage source is a voltage source having a
terminal voltage equal to a constant times the current (ix)
through some other element in the circuit.
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Dependent current sources GITAM
• The current flowing through a dependent current source is

determined by a current or voltage elsewhere in the circuit.
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Dependent current sources GITAM
• A current controlled current source is a current source having

the source current equal to a constant times the current (ix)
through some other element in the circuit.
• A voltage controlled current source is a current source having
the source current equal to a constant times a constant times
the voltage (vx) across a pair of terminals elsewhere in the
network.
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Dependent or controlled sources GITAM
• Controlled voltage and current sources are useful in
constructing circuit models for many types of real world
devices such as transistors, transformers, electrical machines
and electronic amplifiers.
• There are four kinds of controlled sources:
a) Voltage controlled voltage sources (VCVS)
b) Current controlled voltage sources (CCVS)
c) Current controlled current sources (CCCS)
d) Voltage controlled current sources (VCVS)
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GITAM
• Ohm’s law states that the voltage ‘v’ across an element is directly
proportional to the current ‘i’ flowing through it. i.e. v ∝ i or v=R i.
where R is a proportionality constant known as resistance.
• Resistance is the property of the material to restrict the flow of
current. It depends on type of material and its dimensions.
• This property is used in many applications such as heaters, irons,
toasters and electric stoves.
• In the process of flow of electrons through a material, they loose
some of their energy due to the resistive property of materials,
resulting in heat generation.
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Ohms law GITAM
35
GITAM
36
GITAM
18 October 2021 Department of EECE, GIT Course Code and Course Title:19EEE131-BEEE 37
Resistance GITAM
𝜌𝑙
• Resistance of an element, 𝑅 = and its units are Ohm or Ω
𝐴
• An element with low resistance is a conductor. Ex. Copper, aluminum, silver etc.
• An element with very high resistance is known as Insulator. Ex. Wood, mica, paper, glass
etc.
• An element with R=0 is considered as short circuit.
• An element with R=∞ is considered as open circuit.
Resistance GITAM
• A resistor that obeys Ohm’s law is known as linear resistor.

• A resistor that does not obey Ohm’s law is known as nonlinear resistor. Ex. Filament in a lamp and
diodes
Electrical Resistance is the property of a
material by virtue of which it opposes the
flow of electrons through the material
Resistance restricts the flow of electric

Resistance current through the material
The Unit of resistance (R) being Ohm Ω
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Inductance is property of a material by virtue of
which it opposes any change of magnitude or
direction of electric current passing through the
conductor
Inductance
Inductance A pure inductor doesnot dissipate energy but
stores energy in the form of electromagnetic
form
The Unit of inductance (L) being ‘henry’ given by

faradays laws of electro magnetic induction
Dept of EECE, GIT , GITAM deemed to be University

18 October 2021 41
19EEE131 : Basic Electrical and Electronics Engineering
Capacitance is property of a material by virtue
of which it opposes any sudden change of
magnitude electric voltage across the conductor
It is the capability of an element to store

Capacitance electric charge within it
The Unit of Capacitance (C) being ‘farad’ [F]
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Voltage-Current Relation ship of Circuit Elements
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GITAM
• Elements of electric circuit can be interconnected in several ways.

• Interconnection of two or more circuit elements is known as a
NETWORK.
• A network having one or more closed paths is known as ELECTRIC
CIRCUIT.
• A BRANCH represents a two terminal element in a circuit.
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NODE GITAM
A NODE is a point where two or more circuit elements or branches are

connected.
45
Branches GITAM
An element or number of elements connected between two nodes constitute a

BRANCH
46
Path GITAM
a PATH is a sequence of nodes

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Closed path or Loop GITAM
A LOOP is a closed path starting at anode and proceeding through

circuit elements, eventually returning to the starting node.
48
Mesh GITAM
MESH is the most elementary form of a loop and cannot be

further divided into other loops.
A loop that do not have any internal loops in it, is a mesh.
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Nodes, branches and loops GITAM
• A Node is a point where two or more circuit elements or branches are

connected.
• Here the nodes are represented by dots a, b and c.
• A loop is a closed path starting at anode and proceeding through circuit

elements, eventually returning to the starting node.
• A loop that do not have any internal loops in it, is a mesh.
• Number of meshes 𝑚 = 𝑏 − 𝑛 + 1,
where b − number of branches, n − number of nodes
50
GITAM
• Kirchhoff’s laws were first introduced in 1847 by the German physicist Gustav
Robert Kirchhoff.
➢Kirchhoff’s Current law (KCL)
➢Kirchhoff’s Voltage law (KVL)
51
GITAM
• Kirchhoff’s current law (KCL) is based on law of conservation of charge.

• Kirchhoff’s current law (KCL) states that the algebraic sum of currents
entering a node is zero.
• Mathematically KCL can be written as σ𝑁 𝑘=1 𝑖𝑘 = 0,
where N is the number of branches connected to the node k,
ik is the kth current entering or leaving the node.
• While writing KCL currents entering are taken +ve and
leaving –ve.
𝑖1 + −𝑖2 + 𝑖3 + 𝑖4 + −𝑖5 = 0
𝑖1 + 𝑖3 + 𝑖4 = 𝑖2 + 𝑖5
Thus the sum of currents entering a node is equal to sum of
currents leaving the node
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Kirchhoff’s laws GITAM
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GITAM
• Kirchhoff’s Voltage law (KVL) is based on law of conservation

of energy.
• Kirchhoff’s Voltage law (KVL) states that algebraic sum of
voltages around closed path or a loop is zero.
• KVL can be expressed as σ𝑀 𝑝=1 𝑣𝑝 = 0, where M is number of
branches in the loop and vp is the corresponding branch
voltage.
54
GITAM
• While writing KVL, we encounter various voltages in the loop.

Some of them carry positive sign and other carry negative sign
in the algebraic sum.
• While writing KVL, we can start with any branch and go
around the loop in either clockwise or counter clockwise.
• The elements that are encountered first with +ve terminal are
taken positive voltage and –ve terminal are taken –ve voltage
in algebraic sum.
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Kirchhoff’s laws GITAM
• Let us consider this circuit.

• Start moving in clockwise direction in the loop shown with arrow.
• Then voltages will be +v2 , +v3 , - v4 , - v5 and – v1.
• Thus KVL yields 𝑣2 + 𝑣3 − 𝑣4 − 𝑣5 − 𝑣1 = 0.
• Rearranging them, 𝑣2 + 𝑣3 = 𝑣1 + 𝑣4 + 𝑣5
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Resistors in Series
Using KVL shows:
Req = R1 + R2 + … + RN
57
ies combination of
Electrically
it.
(a) Series combination of N resistors. (b) Electrically equivalent circuit.
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Resistors in Parallel
Using KCL shows:
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Two Resistors in Parallel
Two resistors in parallel can be combined using the
product / sum shortcut.
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• Classification of a network is done based on the type of elements being
used in that network. The operational characteristics of a network
depend on the behaviour of its elements.
• Elements which supply the energy to the circuit are known as active
elements. A network which contains active elements is known as active
networks.
➢ Ex: batteries, generators, transistors etc.
• Elements which absorb the energy are known as passive elements. A
network containing only passive elements is known as passive network.
➢Ex: resistors, inductors and capacitors.
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• An element whose operational behaviour is dependent on the direction
of flow of current through is known as unilateral elements. Elements
like semiconductor diode, which allow the current to pass through
them only in one direction.
• An element whose behaviour is same irrespective of the direction of

flow of current through it is known as bilateral element. Passive
elements that allow the current to pass through them in both
directions are known as bilateral elements.
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• Networks consisting of elements which can be physically separated are
known as lumped networks. Most of the networks we deal with, are
lumped in nature and consists of R, L,C and sources.
• Networks, like transmission lines, having inseparable elements are
known as distributed networks
• A linear element is one which has linear output/input relation and

always follows superposition and homogeneity principles. Ohm’s can
be applied to such networks.
• The element that which does not follow these is known as a nonlinear
element. Ohm’s law cannot be applied to such networks.
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Voltage Division
Resistors in series “share” the voltage applied to them.
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Current Division
Resistors in parallel “share” the current through them.
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Source transformation GITAM
A voltage source can be transformed to its equivalent current

source.
𝑣
𝑖=
𝑅
Source Transformation Source transformation is a circuit analysis technique in which

we transform voltage source in series with resistor into a current source in parallel with
the resistor and vice versa.
18 October 2021 Department of EECE, GIT Course Code and Course Title:19EEE131- BEEE 66
Source transformation GITAM
A current source can be transformed to its equivalent voltage

source.
𝑣 = 𝑖𝑅
Nodal and Mesh analysis GITAM
• Two powerful techniques that aid in analysis of complex circuits are:

a) Nodal Analysis
b) Mesh analysis
a)Nodal analysis: it is based on systematic application of Kirchhoff’s current

law.
b) Mesh Analysis: it is based on the systematics application of Kirchhoff’s
voltage law.
Using above two methods we can solve for voltages and currents in any linear
circuit.
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Nodal Analysis GITAM
• In nodal analysis node voltages are the variables.

Procedure:
• Consider a network without voltage sources.
• Identify the nodes and number them in the network.
• Select one of the node as a reference node.
• Assign the voltages to remaining ‘n-1’ non reference nodes with respect to
the reference node
as ex: v1, v2,v3,…..vn.
• Apply KCL at each of the ‘n-1’ non-reference nodes.
• Express branch current in terms of node voltages using ohms law.
• Solve the simultaneous equations to obtain the node voltages.
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Nodal analysis GITAM
• Determine node voltages for the following circuit
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• Applying KCL at node1: 10 = i1+i2+6

• Applying KCL at node2: i2+6 = i3,
• Using ohm’s law: i1=v1/R1 , i2=(v1-v2)/R2,
i3=v2/R3.
• Substituting i1,i2 and i3:
𝑉1 𝑉1 −𝑉2
• 10 = + +6
𝑅1 𝑅2
𝑉1 −𝑉2 𝑉2
• +6=
𝑅2 𝑅3
• Rewriting the equations:
1 1 1
• v1 + − v2 =4
𝑅1 𝑅2 𝑅2
1 1 1
• −v1 + v2 + =6
𝑅2 𝑅2 𝑅3
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• Applying KCL at node 1:

𝑣1 𝑣1 − 𝑣2
2.5 = +
4 8
Applying KCL at node 2:
𝑣2 𝑣2 − 𝑣1
5= + + 2.5
12 8
2𝑣1 + 𝑣1 − 𝑣2 = 20; 3𝑣1 − 𝑣2 = 20
2𝑣2 + 3𝑣2 − 3𝑣1 = 30 − 3𝑣1 + 5𝑣2 = 30
Solving, 𝑣1 = 13.33𝑉 𝑎𝑛𝑑 𝑣2 = 20𝑉
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Mesh analysis GITAM
• Mesh analysis is a general method to analyze electric circuits using

mesh currents of the circuit.
• In mesh analysis we apply KVL to obtain unknown currents.
• Mesh analysis is applicable to planar networks.
• A circuit that can be drawn on a plain paper with no branches crossing
one another is called a planar circuit.
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Mesh analysis GITAM
Determine the branch currents for the following circuit.
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Mesh analysis GITAM
• Number of node, n=4 • Applying KVL around mesh 1:

• Number of branches=5 • −42 + 𝑉1 + 𝑉2 = 0 − 42 + 6𝐼1 + 3 𝐼1 − 𝐼2 = 0
• Number of meshes, m=b-n+1=5-4+1=2 • Applying KVL around mesh 2:

• 𝑉3 − 10 − 𝑉2 = 0 4𝐼2 − 10 − 3 𝐼1 − 𝐼2 = 0
• 9𝐼1 − 3𝐼1 − 42 = 0
• −3𝐼1 + 7𝐼2 − 10 = 0
• 𝐼1 = 6𝐴 𝑎𝑛𝑑 𝐼2 = 4𝐴
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Network Theorem GITAM
• We have used Kirchhoff's laws, nodal and mesh analysis to

analyze various circuit. The main advantage of using them is, we
can analyze a circuit without tampering with its original
configuration.
• Major drawback of this approach is, it involves tedious
computations for large and complex circuits.
• To handle the complexity of circuits, circuit theorems are
developed by engineers to simplify the analysis.
• Such theorems include: Superposition theorem, Thevenin’s,
Maximum power transfer theorem
Superposition theorem GITAM
• Superposition theorem:
States that current through (voltage across) an element in a linear
circuit is the algebraic sum of the currents through (or voltages
across ) that element due to each independent source acting alone.
To apply super position theorem:
1. Consider one independent source at a time while all other
independent sources are turned off.
2. Dependent sources are controlled by control variables and hence
they will be left intact.
Super position theorem GITAM
First, take the source V1 alone and short circuit the V2 source
as shown in the circuit diagram below:
Now, activating the voltage source V2 and deactivating the voltage source V1 by
short-circuiting it, find the various currents, i.e. i1’’, i2’’, i3’’ flowing in the circuit
diagram shown below:
As per the superposition theorem, the value of current i1, i2, i3 is now calculated as:
Using super position theorem, determine current flowing through 3ohms

resistor for the following circuit.
Department of EECE, GIT Course Code and Course
18 October 2021 82
Title:19EEE231- Electric circuit analysis
GITAM
Statement:
• Thevenin’s theorem states that any two terminal linear network having a number
of voltage current sources and resistances can be replaced by a simple equivalent
circuit consisting of a single voltage source in series with a resistance.
• The value of the voltage source is equal to the open-circuit voltage across the
two terminals of the network,
• Resistance is equal to the equivalent resistance measured between the terminals
with all the energy sources are replaced by their internal resistances.
Department of EECE, GIT Course Code and Course Title:19EEE131- BEEE 83

Explanation of Thevenin’s Theorem
Let us consider a simple DC circuit as shown in the
figure above, where we have to find the load
current IL by the Thevenin’s theorem.
In order to find the equivalent voltage source, rL is
removed from the circuit as shown in the figure
below and Voc or VTH is calculated.
84
• Now, to find the internal resistance of the network (Thevenin’s
resistance or equivalent resistance) in series with the open-
circuit voltage VOC , also known as Thevenin’s voltage VTH, the
voltage source is removed or we can say it is deactivated by a
short circuit
85
Equivalent Thevenin’s circuit
• As per Thevenin’s Statement, the load current is determined by
the circuit shown above and the equivalent Thevenin’s circuit is
obtained.
The load current IL is given as:
Where,
VTH is the Thevenin’s equivalent voltage. It is an
open circuit voltage across the terminal AB known
as load terminal
RTH is the Thevenin’s equivalent resistance, as
seen from the load terminals where all the sources
are replaced by their internal impedance
rL is the load resistance
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87
GITAM
According to Maximum power transfer theorem, power transferred to the

load is maximum when the load resistance is equal to source resistance.

Maximum power transfer theorem
𝑉𝑠
GITAM
Load current, 𝐼𝐿 = Deemed to be University
𝑅𝑠 +𝑅𝐿
2
2 𝑉𝑠
Power absorbed by load, 𝑃𝐿 = 𝐼𝐿 𝑅𝐿 = 𝑅𝐿
𝑅𝑠 +𝑅𝐿
Differentiating PL with respect to RL,
The amount of maximum power transferred to

𝑉𝑠 2
load is: 𝑃𝐿𝑚𝑎𝑥 =
4𝑅𝑠

In the circuit shown determine the value of load resistance
when the load resistance draws maximum power. Also find the
value of the maximum power
The source delivers the maximum power
when load resistance is equal to the source
resistance.
RL = 25 ohms
I = 50/(25 + RL) = 50/50 = 1 A
The maximum power delivered to the load P =
I2RL = 25 W
90
Maximum power transfer theorem GITAM
Find the maximum power transferred to the load in following

circuit.

Assume current ‘i’ ,20 + 30 + 2000𝑖 + 2000𝑖 = 0

50
𝑖=− = −12.5𝑚𝐴
4000
𝑉2 = −12.5𝑚 𝑥 2000 = −25𝑉
Applying KVL in outer loop:
40 + 𝑉𝑇ℎ − 𝑉2 − 30 = 0
𝑉𝑇ℎ = 15𝑉.
Thevenin’s resistance: 𝑅𝑇ℎ = 1𝐾Ω

Maximum power transferred to load:

2
𝑉𝑇ℎ 152
𝑃𝐿𝑚𝑎𝑥 = = = 56.25𝑚𝑊
4𝑅𝑇ℎ 4𝑥1000
𝑅𝐿 = 𝑅𝑠 = 𝑅𝑇ℎ = 1𝐾Ω

BEEE Unit I Material

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EECE1001: BASIC ELECTRICAL AND ELECTRONICS ENGINEERING

• How much charge is represented by 6524 electrons?

• The electrical effects caused by charge in motion depends on

• Figure shows a dc current and a sinusoidal ac current versus

• Figure shows other types of time varying currents such as the

• Graphical representation of current:

• Graphical representation of current:

• To move an electron in a conductor in a particular direction requires some

• The Voltage V12 can be interpreted as:

• Power is the time rate of expending or absorbing energy.

• If the power has + sign, power is delivered to or absorbed by the element.

• According to Passive sign convention:

• In an electric circuit, law of conservation of energy must be

• Energy supplied or absorbed by a circuit element between

• There are two types of elements found in electric circuits based

• An independent current source is a two terminal element that

• Dependent sources are designated by diamond shaped

• In a dependent or controlled voltage source, the voltage across

• A voltage controlled voltage source is a voltage source having a

• The current flowing through a dependent current source is

• A current controlled current source is a current source having

• A resistor that obeys Ohm’s law is known as linear resistor.

Resistance restricts the flow of electric

The Unit of resistance (R) being Ohm Ω

The Unit of inductance (L) being ‘henry’ given by

Dept of EECE, GIT , GITAM deemed to be University

It is the capability of an element to store

The Unit of Capacitance (C) being ‘farad’ [F]

• Elements of electric circuit can be interconnected in several ways.

A NODE is a point where two or more circuit elements or branches are

An element or number of elements connected between two nodes constitute a

a PATH is a sequence of nodes

A LOOP is a closed path starting at anode and proceeding through

MESH is the most elementary form of a loop and cannot be

• A Node is a point where two or more circuit elements or branches are

• A loop is a closed path starting at anode and proceeding through circuit

➢Kirchhoff’s Current law (KCL)

➢Kirchhoff’s Voltage law (KVL)

• Kirchhoff’s current law (KCL) is based on law of conservation of charge.

• Kirchhoff’s Voltage law (KVL) is based on law of conservation

• While writing KVL, we encounter various voltages in the loop.

• Let us consider this circuit.

Using KVL shows:

(a) Series combination of N resistors. (b) Electrically equivalent circuit.

Using KCL shows:

• An element whose behaviour is same irrespective of the direction of

• A linear element is one which has linear output/input relation and

Resistors in parallel “share” the current through them.

A voltage source can be transformed to its equivalent current

Source Transformation Source transformation is a circuit analysis technique in which

A current source can be transformed to its equivalent voltage

• Two powerful techniques that aid in analysis of complex circuits are:

a)Nodal analysis: it is based on systematic application of Kirchhoff’s current

• In nodal analysis node voltages are the variables.

• Determine node voltages for the following circuit

• Applying KCL at node1: 10 = i1+i2+6

• Applying KCL at node 1:

• Mesh analysis is a general method to analyze electric circuits using