EE 6201
CIRCUIT THEORY
A. Richard Pravin
ME, MBA, (PhD)
Assistant Professor
Department of Electrical and Electronics Engineering
St. Anne’s College of Engineering and Technology
OVERVIEW
Department : EEE
Year :1
Semester : 2
Regulation : 2013
No. of Credits :4
Lecture + Tutorial : 45 + 15
OBJECTIVES
To introduce electric circuits and its analysis
To impart knowledge on solving circuits
using network theorems
To introduce the phenomenon of resonance
in coupled circuits.
To educate on obtaining the transient
response of circuits.
To draw Phasor diagrams and analysis of
three phase circuits
UNIT - I
BASIC CIRCUITS ANALYSIS
Ohm‘s Law
Kirchoffs laws
DC and AC Circuits
Resistors in series and parallel circuits
Mesh current and node voltage method
of analysis for D.C and A.C. circuits
Phasor Diagram
Power, Power Factor and Energy
UNIT - II
NETWORK REDUCTION AND
NETWORK THEOREMS FOR DC
AND AC CIRCUITS
Network reduction: voltage and
current division, source
transformation
star delta conversion
Thevenins and Novton & Theorem
Superposition Theorem
Maximum power transfer theorem
Reciprocity Theorem
UNIT - III
RESONANCE AND COUPLED CIRCUITS
Series and parallel resonance
frequency response
Quality factor and Bandwidth
Self and mutual inductance
Coefficient of coupling
Tuned circuits – Single tuned circuits.
UNIT - IV
TRANSIENT RESPONSE FOR DC CIRCUITS
Transient response of RL, RC and RLC
Circuits using Laplace transform for DC
input and AC with sinusoidal input
Characterization of two port networks
in terms of Z,Y and h parameters
UNIT - V
THREE PHASE CIRCUITS
Three phase balanced / unbalanced
voltage sources
analysis of three phase 3-wire and 4-
wire circuits with star and delta
connected loads
balanced & un balanced loads
phasor diagram of voltages and
currents
power and power factor measurements
in three phase circuits
TEXT BOOKS &
REFERENCES
William H. Hayt Jr, Jack E. Kemmerly and Steven M. Durbin,
Engineering Circuits Analysis‖, Tata McGraw Hill publishers,
6 edition, New Delhi, 2003.
Joseph A. Edminister, Mahmood Nahri,
―Electric circuits‖, Schaum‘s series, Tata McGraw-
Hill, New Delhi, 2001.
Paranjothi SR, ―Electric Circuits Analysis,‖ New Age
International Ltd., New Delhi, 1996.
Sudhakar A and Shyam Mohan SP, ―Circuits and Network
Analysis and Synthesis‖, Tata McGraw Hill, 2007.
Chakrabati A, ―Circuits Theory (Analysis and synthesis),
Dhanpath Rai & Sons, New Delhi, 1999.
Charles K. Alexander, Mathew N.O. Sadiku, ―Fundamentals
of Electric Circuits‖, Second Edition, McGraw Hill, 2003.
OUTCOMES
Ability to analyse electrical circuits
Ability to apply circuit theorems
Ability to analyse AC and DC Circuits
&
100% Result
First, An Analogy
Force: The difference in the water levels ≡ Voltage
Flow: The flow of the water between the tanks ≡ Current
Opposition: The valve that limits the amount of water ≡ Resistance
Force
Flow
Opposition
VOLTAGE
Voltage is the electrical force that
causes current to flow in a circuit.
It is measured in VOLTS.
Alessandro Volta
1745-1827
Italian Physicist
CURRENT
Current is the flow of electrical charge
through an electronic circuit.
The direction of a current is opposite to
the direction of electron flow.
Current is measured in AMPERES.
Andre Ampere
1775-1836
French Physicist
Flashlight
Switch Switch
Light Light
Bulb Bulb
D - Cell
Battery - +
Battery
Block Diagram Schematic Diagram
Flashlight Schematic
Current
Resistance
- + - +
Voltage
Closed circuit (switch Open circuit (switch open)
closed) No current flow
Current flow
Lamp is off
Lamp is on
Lamp is resistance, but is
Lamp is resistance, uses not using any energy
energy to produce light
(and heat)
CIRCUIT THEORY
An electrical circuit is a connection of circuit
elements into one or more closed loops.
Electrical circuit elements are idealized
models of physical devices that are
defined by relationships between their
terminal voltages and currents. Circuit
elements can have two or more
terminals.
CIRCUIT TOPOLOGY
A circuit consists of a mesh of loops
Represented as branches and nodes in
an undirected graph.
Circuit components reside in the
branches
Connectivity resides in the nodes
CIRCUIT COMPONENTS
Active vs. Passive components
Active ones may generate electrical power.
Passive ones may store but not generate power.
Lumped vs. Distributed Constants
Distributed constant components account for
propagation times through the circuit branches.
Lumped constant components ignore these
propagation times. Appropriate for circuits small
relative to signal wavelengths.
Linear, time invariant (LTI) components are
those with constant component values.
ACTIVE CIRCUIT
COMPONENTS
From non-electrical sources
Batteries (chemical)
Dynamos (mechanical)
Transducers in general (light, sound,
etc.)
From other electrical sources
Power supplies
Power transformers
Amplifiers
PASSIVE LUMPED
CONSTANTS
Classical LTI
Resistors are AC/DC components.
Inductors are AC components (DC short
circuit).
Capacitors are AC components (DC open
circuit).
Other components
Rectifier diodes.
Three or more terminal devices, e.g.
transistors.
Transformers.
CURRENT FLOW
Conventional Current
assumes that current flows Conventional
out of the positive side of Current
the battery, through the
circuit, and back to the
negative side of the
battery. This was the
convention established
when electricity was first
discovered, but it is Electron
incorrect! Flow
Electron Flow is what
actually happens. The
Engineering vs. Science
The direction that the current flows does not affect what the
current is doing; thus, it doesn’t make any difference which
convention is used as long as you are consistent.
Both Conventional Current and Electron Flow are used.
In general, the science disciplines use Electron Flow,
whereas the engineering disciplines use Conventional
Current.
Since this is an engineering course, we will use
Conventional Current .
Electron Conventional
Flow Current
Ohm’s Law
Ohm’s Law:
Current in a resistor varies in direct proportion
to the voltage applied to it and is inversely
proportional to the resistor’s value.
Stated mathematically:
V
V + -
I
R I R
Where: I is the current (amperes)
V is the potential difference (volts)
R is the resistance (ohms)
Ohm’s Law Triangle
V V
I ( amperes , A )
I R R
V V
R (ohms , )
I R I
V
V I R ( volts, V )
I R
Example: Ohm’s Law
Example:
The flashlight shown uses a 6 volt battery and has a bulb
with a resistance of 150 . When the flashlight is on, how
much current will be drawn from the battery?
Example: Ohm’s Law
Example:
The flashlight shown uses a 6 volt battery and has a bulb
with a resistance of 150 . When the flashlight is on, how
much current will be drawn from the battery?
Solution:
Schematic Diagram
IR
V
+
VT = VR I R
-
VR 6V
IR 0.04 A 40 mA
R 150
Circuit Configuration
Components in a circuit can be connected in one of two ways .
Series Circuits Parallel Circuits
Components are connected Both ends of the components
end-to-end. are connected together.
There is only a single path There are multiple paths for
for current to flow. current to flow.
Components
(i.e., resistors, batteries, capacitors, etc.)
Series Circuits
Characteristics of a series circuit
The current flowing through every series component
is equal.
The total resistance (RT) is equal to the sum of all of
the resistances (i.e., R1 + R2 + R3).
The sum of all of the voltage drops (VR1 + VR2 + VR2) is
equal to the total appliedVvoltage
R1
(VT). This is called
IT
Kirchhoff’s Voltage Law.+ -
+ +
VT VR2
- -
- +
RT 28
VR3
Example: Series Circuit
Example:
For the series circuit shown, use the laws of circuit theory to calculate
the following:
• The total resistance (RT)
• The current flowing through each component (IT, IR1, IR2, & IR3)
• The voltage across each component (VT, VR1, VR2, & VR3)
• Use the results to verify Kirchhoff’s
V
Voltage Law.
R1
IT + -
+ IR1 +
VT IR2 VR2
- IR3 -
29
- +
RT
VR3
Example: Series Circuit
Solution:
Total Resistance:
R T R1 R2 R3
R T 220 470 1.2 k
R T 1890 1.89 k
Current Through Each Component:
VT
IT (Ohm' s Law) V
RT
12 v I R
IT 6.349 mAmp
1.89 k
Since this is a series circuit :
IT IR1 IR2 IR3 6.349 mAmp
Example: Series Circuit
Solution:
Voltage Across Each Component:
VR1 IR1 R1 (Ohm' s Law)
VR1 6.349 mA 220 Ω 1.397 volts
VR2 IR2 R2 (Ohm' s Law)
VR2 6.349 mA 470 Ω 2.984 volts V
I R
VR3 IR3 R3 (Ohm' s Law)
VR3 6.349 mA 1.2 K Ω 7.619 volts
Example: Series Circuit
Solution:
Verify Kirchhoff’s Voltage Law:
VT VR1 VR2 VR3
12 v 1.397 v 2.984 v 7.619 v
12 v 12 v
Parallel Circuits
Characteristics of a Parallel Circuit
The voltage across every parallel component is equal.
The total resistance (RT) is equal to the reciprocal of the sum
of the reciprocal:
1 1 1 1 1
RT
RT R1 R 2 R 3 1 1 1
R1 R 2 R 3
The sum of all of the currents in each branch (IR1 + IR2 + IR3)
is equal to the total current (IT). This is called Kirchhoff’s
IT
Current Law.
+ + + +
VT VR1 VR2 VR3
- - - -
33
RT
Example: Parallel Circuit
Example:
For the parallel circuit shown, use the laws of circuit theory to calculate
the following:
• The total resistance (RT)
• The voltage across each component (VT, VR1, VR2, & VR3)
• The current flowing through each component (IT, IR1, IR2, & IR3)
• Use the results to
IT verify Kirchhoff’s Current Law.
IR1 IR2 IR3
+ + + +
VT VR1 VR2 VR3
- - - -
34 34
RT
Example: Parallel Circuit
Solution:
Total Resistance:
1
RT
1 1 1
R1 R 2 R 3
1
RT
1 1 1
470 2.2 k 3.3 k
R T 346.59
Voltage Across Each Component:
Since this is a parallel circuit :
VT VR1 VR2 VR3 15 volts
Example: Parallel Circuit
Solution:
Current Through Each Component:
V
IR1 R1 (Ohm' s Law)
R1
V 15 v
IR1 R1 31.915 mAmps
R1 470
V
V 15 v
IR2 R2 6.818 mAmps
R2 2.2 k I R
VR3 15 v
IR3 4.545 mAmp
R3 3.3 k
VT 15 v
IT 43.278 mAmp
RT 346.59
Example: Parallel Circuit
Solution:
Verify Kirchhoff’s Current Law:
IT IR1 IR2 IR3
43.278 mAmps 31.915 mA 6.818 mA 4.545 mA
43.278 mAmps 43.278 mAmps
Summary of Kirchhoff’s
Laws
Kirchhoff’s Voltage Law (KVL):
The sum of all of the voltage drops in a
series circuit equals the total applied
voltage.
Kirchhoff’s Current Law (KCL):
Gustav Kirchhoff
1824-1887 The total current in a parallel circuit equals
German Physicist the sum of the individual branch currents.
THANK YOU
