BECE203L CIRCUIT THEORY
L T P C
3 1 0 4
Dr. M. Saranya Nair
School of Electronics Engineering
VIT-Chennai Campus
E-mail : saranyanair.m@vit.ac.in
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What is a circuit ?
• Circuits are everywhere in modern world
• A circuit is a series of electrical components or devices connected
together in a loop, allowing electrical current in the form of charged
electrons to flow through it and power the components.
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Circuit Components
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A simple Electric Circuit
• Current ?
• Resistance ?
• Voltage / Potential Difference ?
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What is Voltage ?
• The level of the water inside the tank represents the voltage &
the amount of water flowing out represents current.
• If the level of water inside the tank is very low, there will be
low pressure exerted on the water flowing out. Therefore the
amount of water flowing out in a unit time will be low. If the
water level is high, it will exert high pressure, thus amount of
water flowing out will increase.
• The same idea is used in voltage, where the voltage is the
pressure that flushes the current in an electrical circuit. Greater
the voltage greater will be the current flow though the circuit.
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Voltage
• Every electrical equipment has its voltage requirement mentioned on its
nameplate or its manual.
• In electrical circuit, voltage is the force or pressure that is responsible for
pushing the charge in a closed looped conductor. The flowing of charge is
called current. The voltage is the electric potential between two points; the
greater the voltage the greater will be the current flow through that point. It
is denoted by letter V or E
• Equipment designed for 220 volts won’t operate from a 12V supply &
equipment designed for 12 volts will get damaged if connected with 220V
supply.
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By learning the fundamentals, it is much easier to build electric circuits and to learn more
advanced concepts.
Circuit theory and Electromagnetic theory are the two fundamental theories upon which all
branches of electrical engineering are built.
Course Objectives
1. To prepare the students to analyse the given electrical network using phasors
and graph theory.
2. To introduce the students with the basic knowledge of Laplace transform,
Fourier Transform and Fourier series and to analyse the network using suitable
technique
3. To prepare the students to analyse the two-port networks, passive filters, and
attenuators
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Expected Course Outcome
1. Apply the knowledge of various circuit analysis techniques such as mesh analysis,
nodal analysis, and network theorems to investigate the given network.
2. Analyse the resonance and transient response of the first order, second order
circuits
3. Able to solve the networks using graphical approach.
4. Design and analyse two-port networks, passive filters and attenuators.
5. Able to analyse the given network by transforming from time domain to S domain.
6. Analyse the given network using Fourier series and transforming from time domain
to frequency domain.
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Text/Reference Books
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Evaluation Criteria
• CONTINUOUS ASSESMENT TESTS I & II – 30
• DIGITAL ASSIGMENTS / QUIZ – 30
• FINAL ASSESSMENT – 40
• Others – Flipped Class / Slow Learners Assignments / Practice
Problems
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Review on Basic Concepts
Electric Charge.
Current.
Voltage.
Ohm’s Law
Nodes, Branches, and Loops
Kirchhoff ’s Laws
Series Resistors and Voltage Division
Power and Energy.
Parallel Resistors and Current Division
Circuit Elements.
Wye-Delta Transformations
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Electric charge & Current
Charge is an electrical property of the atomic particles, measured in coulombs (C).
Electric current is the time rate of change of charge, measured in amperes (A).
• The charge on an electron is negative and equal in magnitude to 1.602 x 10-19 C, while a proton carries a
positive charge of the same magnitude as the electron.
• In 1 C of charge, there are 6.24 x 1018 electrons.
• A unique feature of electric charge or electricity is the fact that it is mobile; that is, it can be transferred
from one place to another.
• 1 ampere = 1 coulomb/second. A direct current (dc) is a current that remains constant with time. An
alternating current (ac) is a current that varies sinusoidally with time.
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Circuit Elements
Circuit analysis is the process of determining voltages across (or the currents through) the
elements of the circuit.
• There are two types of elements found in electric circuits: passive elements
and active elements. An active element is capable of generating energy
while a passive element is not. Examples of passive elements are resistors,
capacitors, and inductors.
• The most important active elements are voltage or current sources that
generally deliver power to the circuit connected to them. There are two
kinds of sources: independent and dependent sources.
• An ideal independent source is an active element that provides a specified
voltage or current that is completely independent of other circuit elements.
Physical sources such as batteries and generators may be regarded as
approximations to ideal voltage sources.
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Circuit Elements
• An ideal dependent (or controlled) source is an active element in which
the source quantity is controlled by another voltage or current.
1. A voltage-controlled voltage source (VCVS).
2. A current-controlled voltage source (CCVS).
3. A voltage-controlled current source (VCCS).
4. A current-controlled current source (CCCS).
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Ohm’s Law
Materials in general have a characteristic behavior of resisting the flow of electric charge. This physical
property, or ability to resist current, is known as resistance and is represented by the symbol R . The
resistance of any material with a uniform cross-sectional area A depends on A and its length l
Ohm’s law states that the voltage across a
resistor is directly proportional to the current
flowing through the resistor.
• An element with R=0, is called a short circuit,
v=0
• An element with R= is known as an open
circuit, i = 0
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Nodes, Branches & Loops
A branch represents a single element such as a voltage source or a resistor. A node is the point of
connection between two or more branches. A loop is any closed path in a circuit.
• What is independent loop?
A network with b branches, n nodes, and l independent loops will
satisfy the fundamental theorem of network topology.
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Kirchhoff ’s Laws
Kirchhoff ’s current law (KCL) states that the algebraic sum of currents entering a node is
zero.
Kirchhoff ’s voltage law (KVL) states that the algebraic sum of all voltages around a closed
path (or loop) is zero.
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Series Resistors & Voltage Division
Parallel Resistors & Current Division
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Delta : Wye Conversion
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Kirchhoff ’s Laws
Find currents and voltages in the circuit
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Module I - Sinusoidal Steady-State Analysis
Review of steady state sinusoidal analysis using phasors. Node voltage and Mesh current analysis, special
cases. Network theorems: Superposition, Thevenin, Norton and maximum power transfer theorems.
• We now begin the analysis of circuits in which the source voltage or current is time-varying. In this
chapter, we are particularly interested in sinusoidally time-varying excitation.
• A sinusoid is a signal that has the form of the sine or cosine function.
• Circuits driven by sinusoidal current or voltage sources are called ac circuits.
• First, nature itself is characteristically sinusoidal. We experience sinusoidal variation in the motion
of a pendulum, the vibration of a string, the ripples on the ocean surface, to mention but a few.
• Second, a sinusoidal signal is easy to generate and transmit.
• Third, through Fourier analysis, any practical periodic signal can be represented by a sum of
sinusoids.
• Lastly, a sinusoid is easy to handle mathematically. The derivative and integral of a sinusoid are
themselves sinusoids.
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Sinusoidal Steady-State Analysis
• A sinusoidal forcing function produces both a transient response and a
steady-state response, much like the step function, which we studied.
• The transient response dies out with time so that only the steady-state
response remains.
• When the transient response has become negligibly small compared with
the steady-state response, we say that the circuit is operating at
sinusoidal steady state. It is this sinusoidal steady-state response that is
of main interest to us in this chapter.
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Let us now consider a general expression for the sinusoid,
Both argument and phase can be in radians or degrees.
The starting point of v2 in Fig. occurs first in time. Therefore, we say that v2 leads v1 by  or that v1 lags
v2 by . If   0, the signals are said to be out of phase, If  = 0, the signals are said to be inphase; they
reach their minima and maxima at exactly the same time.
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A phasor is a complex number that represents the
amplitude and phase of a sinusoid.
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A phasor is a complex number that represents the
amplitude and phase of a sinusoid.
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Sinusoid to Phasor
From Eq., we see that to get the phasor representation of a sinusoid, we express it in cosine form and
take the magnitude and phase. Given a phasor, we obtain the time domain representation as the
cosine function with the same magnitude as the phasor and the argument as t plus the phase of the
phasor.
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Determine v0(t) in the circuit
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1. The voltage v = 12 cos (60t+45) is applied to a 0.1-H inductor. Find the steady-state current through
the inductor.
2. Find v(t) and i(t) in the circuit shown
3. Determine the input impedance of the circuit , let  = 10 rad/s
4. Determine v0 in the circuit.
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Circuit Analysis Methods
1. Mesh Current (Mesh) Analysis
A mesh is a loop that does not contain any other loop within it. Mesh analysis use mesh currents as the
circuit variables.
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Mesh Analysis
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2. Nodal (Node-voltage) analysis
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Nodal Analysis
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Superposition Theorem
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Supernode & Supermesh
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Practice Problems
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Thevenin & Norton Theorems
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Determine the Norton equivalent of the circuit in Fig. as seen
from terminals a-b. Use the equivalent to find Io.
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Maximum Power Transfer Theorem
Instantaneous and Average Power
The instantaneous power p(t) absorbed by an element is the product of the instantaneous voltage v(t) across
the element and the instantaneous current i(t) through it.
p(t) = v(t)i(t)
• The instantaneous power changes with time and is therefore difficult to measure. The average power is
more convenient to measure. In fact, the wattmeter, the instrument for measuring power, responds to
average power.
• The average power, in watts, is the average of the instantaneous power over one period.
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Thus, the average power is given by
The first integrand is constant, and the average of a constant is the same constant. The second integrand is a
sinusoid. We know that the average of a sinusoid over its period is zero because the area under the sinusoid
during a positive half-cycle is canceled by the area under it during the following negative half-cycle. Thus, the
second term in Eq. vanishes.
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Note that p(t) is time-varying while P does not depend on time. To find the instantaneous power, we must
necessarily have v(t) and i(t) in the time domain. But we can find the average power when voltage and current are
expressed in the time domain, or when they are expressed in the frequency domain.
When v = i,
When v - i =  90,
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Maximum Average Power Transfer Theorem
We solved the problem of maximizing the power delivered by a resistive network to a load. Representing the
circuit by its Thevenin equivalent, we proved that the maximum power would be delivered to the load if the load
resistance is equal to the Thevenin resistance. We now extend that result to ac circuits.
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In a situation in which the load is purely resistive, the condition for maximum power transfer is obtained by
setting XL = 0 ;
What is the maximum power ?
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Determine the load impedance that maximizes the average power drawn from the circuit. What is the
maximum average power?
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In the circuit in below Fig., find the value of RL that will absorb the maximum average power. Calculate that power.
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In Fig. the resistor RL is adjusted until it absorbs the maximum average power. Calculate RL and the maximum
average power absorbed by it.
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Other Power Relations in AC circuits
Effective or RMS Value
• The effective/rms value of a periodic current is the dc current that delivers the same average power to
a load as the periodic current.
For any periodic function x(t) in general, the rms value is given by
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Apparent Power and Power Factor
The product S is known as the apparent power . The factor is called the power factor (pf).
The apparent power (in VA) is the product of the rms values of voltage and current. The power factor is the
cosine of the phase difference between voltage and current.
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Complex Power
Complex power is important in power analysis because it contains all the information pertaining to the power
absorbed by a given load.
The complex power S absorbed by the ac load is the product of the voltage and the complex conjugate of the
current
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• The voltage across a load is v(t) = 60 cos(t -10) V and the current through the element in the
direction of the voltage drop is i(t) = 1.5 cos(t +50) A. Find: (a) the complex and apparent powers,
(b) the real and reactive powers
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Thank You..
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