Ecc203 a 2

©M. S. Ramaiah University of Applied Sciences
1
Faculty of Engineering & Technology
Basic Network Concepts

2
Lecture 2
Basic Circuit Elements and Energy
Sources
Lecture delivered by:
Kiran Kumar B M

3
Topics
• Basic Circuit Elements
• (Energy Sources) Active Elements
• Independent sources
• Dependent sources

4
Objectives
At the end of this lecture, student will be able to:
Explain basic circuit elements
Explain current, voltage, resistance, capacitance and inductance
Classify various energy sources
Describe Independent sources
Explain dependent sources

5
Faculty of Engineering & Technology©M. S. Ramaiah University of Applied Sciences
5
Basic Circuit Elements

6
6
Resistor
 Resistance is the physical property of an element or device that resist the
flow of current: it is represented by the symbol R
 Resistors dissipate electrical energy, converting it to heat
 Resistors lower voltage across an active circuit; the voltage on the positive
end will be higher than the voltage on the negative end
Resistance of a wire element is calculated using the relation:

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7
Resistor symbols:
I
L
A
V
R
Ohm’s law
Voltage difference  current
IRV 
R=Resistance Ω[ohms]

8
8
Inductor
 An inductor is a circuit element that develops a magnetic field as current
flows through it.
 It stores energy in its magnetic field and this field resists and slows the
movement of electrons in the inductor
 The amount that an inductor resists electrical current is proportional to the
rate of change of current flowing through
+
-
Lv
where L is the inductance in henrys (H)
Note* Inductance is the property whereby an inductor exhibits opposition to the change of current
flowing through it


1
1
t
t
LL
L
o
dtv
L
i
dt
di
Lv
B field

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9
Sign Convention
 The sign convention used with an inductor is the same as for
a power dissipating device.
When current flows into the positive side of the voltage
across the inductor, it is positive and the inductor is
dissipating power.
When the inductor releases energy back into the circuit,
the sign of the current will be negative.

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Power and Energy
( )
di
p t vi Li
dt
 
 The energy stored in the magnetic field is thus
( ) ( )
t t
L
di
w t p t dt L i dt L idi
dt 
    
21
( ) ( ) joules
2
Lw t Li t
 The instantaneous power delivered to an inductor is

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11
Inductors in Series
DC
1L 2L NL
1v 2v Nv+ + + -- -
v
i
i
eqLv
+
-
DC
4321eq
4321
4433
2211
4321
L
dt
di
dt
di
dt
di
dt
di
dt
di
dt
di
dt
di
dt
di
dt
di
LLLL
Lv
LLLLv
LvLv
LvLv
vvvvv
eqin
in
in








S
s
seq LL
1

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Inductors in Parallel
         1
4321eq
t
t
t
t4
t
t3
t
t2
t
t1
t
t4
4
t
t3
3
t
t2
2
t
t1
1
4321
1111L
vdt
1
vdt
1
vdt
1
vdt
1
vdt
1
vdt
1
vdt
1
vdt
1
vdt
1
1
o
1
o
1
o
1
o
1
o
1
o
1
o
1
o
1
o











LLLL
L
i
LLLL
i
L
i
L
i
L
i
L
i
iiiii
eq
in
in
in
1
1
1

 







 
P
p p
eq
L
L

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General Equations for Leq
Series Combination Parallel Combination
• If S inductors are in
series, then
• If P inductors are in
parallel, then:
1
1
1

 







 
P
p p
eq
L
L

S
s
seq LL
1
Inductors in series Inductors in parallal

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Capacitors
A capacitor is a passive element that stores energy in its electric field
A capacitor consists of two conducting plates separated by an insulator.
The insulator is called dielectric. (e.g. polystyrene, oil or air)
When a voltage source is connected to the capacitor, the source deposits a
positive charge, +q, on one plate and a negative charge, –q, on the other
+Q –Q

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Capacitance is a measure of a capacitor’s ability to store charge on its plates
Consider any isolated pair of conductors with charge Q
C, called the capacitance of the capacitor
( )
( )
dq dv t
i t C
dt dt
 
q Cv
0
0
1 1 1
( ) ( ) ( ) ( )
t t t
t
v t i x dx i x dx i x dx
C C C 
    
0
0
1
( ) ( ) ( )
t
t
v t v t i x dx
C
  
Contd..

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Energy stored in the capacitor
 The instantaneous power delivered to the capacitor is
( )
t tdv
w p t dt C v dt C vdv
dt 
    
( )
dv
p t vi Cv
dt
 
 The energy stored in the capacitor is thus
21
( ) joules
2
w Cv t

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Capacitors in Series
1
1
1
v idt
C
 
1 2
1 2
1 1 1 1
N
N eq
v v v v idt idt
C C C C
 
       
 
 
1
1 1N
keq kC C
 
The equivalent capacitance of N series connected capacitors is the reciprocal of the sum of
the reciprocals of the individual capacitors. Capacitors in series act like resistors in parallel.
DC
1v 2v Nv
1C 2C NC
v
i
+ + + -- -
i
eqCv
+
-
DC
2
2
1
v idt
C
 
1
N
N
v idt
C
 

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Capacitors in Parallel
i
1i 2i Ni
1C 2C NCv
+
-
i
i
eqCv
+
-
1 1
dv
i C
dt
 2 2
dv
i C
dt
 N N
dv
i C
dt

 1 2 1 2N N eq
dv dv
i i i i C C C C
dt dt
      
1
N
eq k
k
C C

 
Thus, the equivalent capacitance of N capacitors in parallel is the sum of the individual
capacitances. Capacitors in parallel act like resistors in series.

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Active Elements (Energy Sources)
There are two types of energy sources
Independent sources
Dependent sources
Ideal Voltage Source
 An ideal voltage source is a two terminal device whose terminal voltage is
independent of the current drawn by the network connected to its
terminals
 Both the magnitude and wave form of voltage remain unaffected
 This means an ideal voltage source should have zero internal resistance
Sometimes
used
+
-Vs

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 However, in actual practice, there is no voltage source which does not have
internal resistance
 therefore, an actual voltage source is always associated with an internal
resistance
Contd..

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Ideal Current Source
 It is a two terminal device which delivers a constant current to the network
connected across its terminals irrespective of the elements of the network
 The current is independent of the voltage across its terminals
It can be seen that the voltage and current sources are dual in the sense that the roles for
current and voltage are interchanged in the two sources
is

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Dependent Sources (Controlled Sources)
A dependent voltage source (or current source) would have its terminal
voltage (or current) depend on another circuit quantity such as a voltage or
current
Thus four possibilities exist
o Voltage dependent (controlled) voltage source
It produces a voltage as a function of voltages elsewhere in the given circuit
o Current dependent (controlled) voltage source
It produces a voltage as a function of current elsewhere in the given circuit
o Voltage dependent (controlled) current source
It produces a current as a function of voltages elsewhere in the given circuit
o Current dependent (controlled) current source
It produces a current as a function of current elsewhere in the given circuit

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The Circuit Symbols
μ is a multiplying constant that is dimensionless
is a multiplying constant has the dimension volts per ampere
is a multiplying constant has the dimension amperes per volt
is a multiplying constant that is dimensionless

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Summary
 There are various types of basic Circuit Elements
 Inductors and capacitors can be connected in series or parallel
 There are two types of energy sources Independent sources and dependent
sources
 Output of an independent source does not depend upon the voltage or
current of any other part of the network
 There are four possible dependent sources
 Voltage dependent (controlled) voltage source
 Current dependent (controlled) voltage source
 Voltage dependent (controlled) current source
 Current dependent (controlled) current source

Ecc203 a 2

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