Short Notes: Network Elements | Network Theory (Electric Circuits) - Electrical Engineering (EE) PDF Download

 Page 1


 
 
 
 
Active & Passive Elements 
If any elements absorb, dissipate, waste, convert electrical energy it is called as passive element. 
Eg. Resistor, Inductor, Capacitor. 
If any elements energize, deliver, give out, drive the electrical energy it is called as active element. 
Eg. BJT, MOSFET. 
 
Network Technologies 
Node : It is a point of interconnection or junction between two or more components. 
Branch : It is an elemental connection between two nodes. 
Mesh: A mesh is a close path which should not have any further closed path in it. 
Loop : All possible close path. 
 
Ohm’s law 
At constant temperature and for uniform cross section of conductor. 
JE ??
 
s= conductivity, 
? ??
?
 resisti
1
vity . 
? V IR 
?
?
l
R
A
                                                   Circuit Symbol:   
? l lenght of conductor 
A = Area of conductor. 
 
Conductance of circuit elements is 
?
1
G
R
 
Sign Convention  
To apply ohm’s law, we must apply following sign convention. 
 
 
 
 
 
 
Page 2


 
 
 
 
Active & Passive Elements 
If any elements absorb, dissipate, waste, convert electrical energy it is called as passive element. 
Eg. Resistor, Inductor, Capacitor. 
If any elements energize, deliver, give out, drive the electrical energy it is called as active element. 
Eg. BJT, MOSFET. 
 
Network Technologies 
Node : It is a point of interconnection or junction between two or more components. 
Branch : It is an elemental connection between two nodes. 
Mesh: A mesh is a close path which should not have any further closed path in it. 
Loop : All possible close path. 
 
Ohm’s law 
At constant temperature and for uniform cross section of conductor. 
JE ??
 
s= conductivity, 
? ??
?
 resisti
1
vity . 
? V IR 
?
?
l
R
A
                                                   Circuit Symbol:   
? l lenght of conductor 
A = Area of conductor. 
 
Conductance of circuit elements is 
?
1
G
R
 
Sign Convention  
To apply ohm’s law, we must apply following sign convention. 
 
 
 
 
 
 
 
 
 
 
 
 
Short circuit & open circuit 
Voltage across terminals of a short circuit is always zero, regardless of the value of current which 
could be any value. (R = 0) 
The current through an open circuit is always zero, regardless of voltage across the terminals 
which could be any value. ? ? R ?? 
Power of resistor 
2
2
V
P VI I R
R
? ? ?
 
Resistance always absorbs or dissipates power. 
 
Kirchoff’s laws 
? Kirchoff’s current law(KCL) 
It states that any instant the algebraic sum of current leaving any junction (or node) in a network 
is zero. 
In other words, current entering a node is equal to current leaving the node. 
  
            
? ?
?
? n
n
i t 0 
 ?
?? entering leaving
ii 
            
1 3 5 2 4
i i i i i ? ? ? ?
 
 
 
? Kirchoff’s voltage law (KVL) 
It states that any instant the algebraic sum of the voltage around any closed path (or loop) within 
a network is zero. In other words, the sum of voltage drops is equal to sum of voltage rises. 
 
? ?
?
?
n
n
V t 0 
            ?
?? drop rise
VV 
            ? ? ? ? ?
1 2 3 4 5
V V V V V 0 
 
 
 
 
 
Page 3


 
 
 
 
Active & Passive Elements 
If any elements absorb, dissipate, waste, convert electrical energy it is called as passive element. 
Eg. Resistor, Inductor, Capacitor. 
If any elements energize, deliver, give out, drive the electrical energy it is called as active element. 
Eg. BJT, MOSFET. 
 
Network Technologies 
Node : It is a point of interconnection or junction between two or more components. 
Branch : It is an elemental connection between two nodes. 
Mesh: A mesh is a close path which should not have any further closed path in it. 
Loop : All possible close path. 
 
Ohm’s law 
At constant temperature and for uniform cross section of conductor. 
JE ??
 
s= conductivity, 
? ??
?
 resisti
1
vity . 
? V IR 
?
?
l
R
A
                                                   Circuit Symbol:   
? l lenght of conductor 
A = Area of conductor. 
 
Conductance of circuit elements is 
?
1
G
R
 
Sign Convention  
To apply ohm’s law, we must apply following sign convention. 
 
 
 
 
 
 
 
 
 
 
 
 
Short circuit & open circuit 
Voltage across terminals of a short circuit is always zero, regardless of the value of current which 
could be any value. (R = 0) 
The current through an open circuit is always zero, regardless of voltage across the terminals 
which could be any value. ? ? R ?? 
Power of resistor 
2
2
V
P VI I R
R
? ? ?
 
Resistance always absorbs or dissipates power. 
 
Kirchoff’s laws 
? Kirchoff’s current law(KCL) 
It states that any instant the algebraic sum of current leaving any junction (or node) in a network 
is zero. 
In other words, current entering a node is equal to current leaving the node. 
  
            
? ?
?
? n
n
i t 0 
 ?
?? entering leaving
ii 
            
1 3 5 2 4
i i i i i ? ? ? ?
 
 
 
? Kirchoff’s voltage law (KVL) 
It states that any instant the algebraic sum of the voltage around any closed path (or loop) within 
a network is zero. In other words, the sum of voltage drops is equal to sum of voltage rises. 
 
? ?
?
?
n
n
V t 0 
            ?
?? drop rise
VV 
            ? ? ? ? ?
1 2 3 4 5
V V V V V 0 
 
 
 
 
 
 
 
 
 
 
Series resistance or voltage division 
Two or more circuit elements are connected in series means that current through all elements in 
same. If ‘N’ resistors, with resistance 
1 2 n
R ,R ,........R are connected in series 
eq 1 2 N
R R R ...................R ? ? ?
            
? ?
?
?
1
1
12
VR
V
RR
      
? ?
?
?
2
2
12
VR
V
RR
 
 
 
Parallel resistance or current division 
Two or more circuit elements are connected in parallel means that voltage across all elements is 
same. If ‘N’ resistors are connected in parallel 
1 2 N
R ,R ,............R 
eq 1 2 N
1 1 1 1
...........
R R R R
? ? ? ?
 
? ?
?
?
2
1
12
IR
I
RR
 
? ?
?
?
1
2
12
IR
I
RR
 
 
 
Star Delta Conversion 
 
Start to Delta 
 
??
?
1 2 1 3 2 3
a
1
R R R R R R
R
R
 
 
??
?
1 2 1 3 2 3
b
2
R R R R R R
R
R
 
 
??
?
1 2 1 3 2 3
c
3
R R R R R R
R
R
 
Page 4


 
 
 
 
Active & Passive Elements 
If any elements absorb, dissipate, waste, convert electrical energy it is called as passive element. 
Eg. Resistor, Inductor, Capacitor. 
If any elements energize, deliver, give out, drive the electrical energy it is called as active element. 
Eg. BJT, MOSFET. 
 
Network Technologies 
Node : It is a point of interconnection or junction between two or more components. 
Branch : It is an elemental connection between two nodes. 
Mesh: A mesh is a close path which should not have any further closed path in it. 
Loop : All possible close path. 
 
Ohm’s law 
At constant temperature and for uniform cross section of conductor. 
JE ??
 
s= conductivity, 
? ??
?
 resisti
1
vity . 
? V IR 
?
?
l
R
A
                                                   Circuit Symbol:   
? l lenght of conductor 
A = Area of conductor. 
 
Conductance of circuit elements is 
?
1
G
R
 
Sign Convention  
To apply ohm’s law, we must apply following sign convention. 
 
 
 
 
 
 
 
 
 
 
 
 
Short circuit & open circuit 
Voltage across terminals of a short circuit is always zero, regardless of the value of current which 
could be any value. (R = 0) 
The current through an open circuit is always zero, regardless of voltage across the terminals 
which could be any value. ? ? R ?? 
Power of resistor 
2
2
V
P VI I R
R
? ? ?
 
Resistance always absorbs or dissipates power. 
 
Kirchoff’s laws 
? Kirchoff’s current law(KCL) 
It states that any instant the algebraic sum of current leaving any junction (or node) in a network 
is zero. 
In other words, current entering a node is equal to current leaving the node. 
  
            
? ?
?
? n
n
i t 0 
 ?
?? entering leaving
ii 
            
1 3 5 2 4
i i i i i ? ? ? ?
 
 
 
? Kirchoff’s voltage law (KVL) 
It states that any instant the algebraic sum of the voltage around any closed path (or loop) within 
a network is zero. In other words, the sum of voltage drops is equal to sum of voltage rises. 
 
? ?
?
?
n
n
V t 0 
            ?
?? drop rise
VV 
            ? ? ? ? ?
1 2 3 4 5
V V V V V 0 
 
 
 
 
 
 
 
 
 
 
Series resistance or voltage division 
Two or more circuit elements are connected in series means that current through all elements in 
same. If ‘N’ resistors, with resistance 
1 2 n
R ,R ,........R are connected in series 
eq 1 2 N
R R R ...................R ? ? ?
            
? ?
?
?
1
1
12
VR
V
RR
      
? ?
?
?
2
2
12
VR
V
RR
 
 
 
Parallel resistance or current division 
Two or more circuit elements are connected in parallel means that voltage across all elements is 
same. If ‘N’ resistors are connected in parallel 
1 2 N
R ,R ,............R 
eq 1 2 N
1 1 1 1
...........
R R R R
? ? ? ?
 
? ?
?
?
2
1
12
IR
I
RR
 
? ?
?
?
1
2
12
IR
I
RR
 
 
 
Star Delta Conversion 
 
Start to Delta 
 
??
?
1 2 1 3 2 3
a
1
R R R R R R
R
R
 
 
??
?
1 2 1 3 2 3
b
2
R R R R R R
R
R
 
 
??
?
1 2 1 3 2 3
c
3
R R R R R R
R
R
 
 
 
 
 
 
Delta to start conversion 
?
??
bc
1
a b c
RR
R
R R R
 
?
??
ac
2
a b c
RR
R
R R R
 
?
??
ab
3
a b c
RR
R
R R R
 
 
Sources 
Independent Voltage Source 
An ideal independent voltage source maintains a specified voltage across its terminals. The 
voltage is independent of current flowing through it. 
 
Independent current source 
An ideal independent current source maintains a specified current to flow through it. The current 
through this is independent of voltage across it. 
Dependent Source 
Voltage controlled voltage source (VCVS) ; 
X
V AV ? 
Current controlled voltage source (CCVS) ; 
X
V Ai ? 
Voltage controlled current source (VCCS) ; ?
x
i AV 
Current controlled current source (CCCS) ; 
x
i Ai ? 
 
Capacitor 
A capacitor is a combination of a two conducting plates separated by a non-conducting material. 
Capacitance is donated by ‘C’ 
 
 
?= Permittivity of medium 
A = Area of Plates 
D = distance between the plates. 
Charge on Plates,    Q = CV 
V = Potential difference between the plates. 
 
?
?
A
C
d
Page 5


 
 
 
 
Active & Passive Elements 
If any elements absorb, dissipate, waste, convert electrical energy it is called as passive element. 
Eg. Resistor, Inductor, Capacitor. 
If any elements energize, deliver, give out, drive the electrical energy it is called as active element. 
Eg. BJT, MOSFET. 
 
Network Technologies 
Node : It is a point of interconnection or junction between two or more components. 
Branch : It is an elemental connection between two nodes. 
Mesh: A mesh is a close path which should not have any further closed path in it. 
Loop : All possible close path. 
 
Ohm’s law 
At constant temperature and for uniform cross section of conductor. 
JE ??
 
s= conductivity, 
? ??
?
 resisti
1
vity . 
? V IR 
?
?
l
R
A
                                                   Circuit Symbol:   
? l lenght of conductor 
A = Area of conductor. 
 
Conductance of circuit elements is 
?
1
G
R
 
Sign Convention  
To apply ohm’s law, we must apply following sign convention. 
 
 
 
 
 
 
 
 
 
 
 
 
Short circuit & open circuit 
Voltage across terminals of a short circuit is always zero, regardless of the value of current which 
could be any value. (R = 0) 
The current through an open circuit is always zero, regardless of voltage across the terminals 
which could be any value. ? ? R ?? 
Power of resistor 
2
2
V
P VI I R
R
? ? ?
 
Resistance always absorbs or dissipates power. 
 
Kirchoff’s laws 
? Kirchoff’s current law(KCL) 
It states that any instant the algebraic sum of current leaving any junction (or node) in a network 
is zero. 
In other words, current entering a node is equal to current leaving the node. 
  
            
? ?
?
? n
n
i t 0 
 ?
?? entering leaving
ii 
            
1 3 5 2 4
i i i i i ? ? ? ?
 
 
 
? Kirchoff’s voltage law (KVL) 
It states that any instant the algebraic sum of the voltage around any closed path (or loop) within 
a network is zero. In other words, the sum of voltage drops is equal to sum of voltage rises. 
 
? ?
?
?
n
n
V t 0 
            ?
?? drop rise
VV 
            ? ? ? ? ?
1 2 3 4 5
V V V V V 0 
 
 
 
 
 
 
 
 
 
 
Series resistance or voltage division 
Two or more circuit elements are connected in series means that current through all elements in 
same. If ‘N’ resistors, with resistance 
1 2 n
R ,R ,........R are connected in series 
eq 1 2 N
R R R ...................R ? ? ?
            
? ?
?
?
1
1
12
VR
V
RR
      
? ?
?
?
2
2
12
VR
V
RR
 
 
 
Parallel resistance or current division 
Two or more circuit elements are connected in parallel means that voltage across all elements is 
same. If ‘N’ resistors are connected in parallel 
1 2 N
R ,R ,............R 
eq 1 2 N
1 1 1 1
...........
R R R R
? ? ? ?
 
? ?
?
?
2
1
12
IR
I
RR
 
? ?
?
?
1
2
12
IR
I
RR
 
 
 
Star Delta Conversion 
 
Start to Delta 
 
??
?
1 2 1 3 2 3
a
1
R R R R R R
R
R
 
 
??
?
1 2 1 3 2 3
b
2
R R R R R R
R
R
 
 
??
?
1 2 1 3 2 3
c
3
R R R R R R
R
R
 
 
 
 
 
 
Delta to start conversion 
?
??
bc
1
a b c
RR
R
R R R
 
?
??
ac
2
a b c
RR
R
R R R
 
?
??
ab
3
a b c
RR
R
R R R
 
 
Sources 
Independent Voltage Source 
An ideal independent voltage source maintains a specified voltage across its terminals. The 
voltage is independent of current flowing through it. 
 
Independent current source 
An ideal independent current source maintains a specified current to flow through it. The current 
through this is independent of voltage across it. 
Dependent Source 
Voltage controlled voltage source (VCVS) ; 
X
V AV ? 
Current controlled voltage source (CCVS) ; 
X
V Ai ? 
Voltage controlled current source (VCCS) ; ?
x
i AV 
Current controlled current source (CCCS) ; 
x
i Ai ? 
 
Capacitor 
A capacitor is a combination of a two conducting plates separated by a non-conducting material. 
Capacitance is donated by ‘C’ 
 
 
?= Permittivity of medium 
A = Area of Plates 
D = distance between the plates. 
Charge on Plates,    Q = CV 
V = Potential difference between the plates. 
 
?
?
A
C
d
 
 
 
 
Voltage Current relationship 
 
? ?
? ? dq t
it
dt
?
 
 
? ?
? ?
?
dv t
i t C
dt
 
Sign Convention 
Energy Stored in a capacitor 
? ?
? ? ? ?
? ? ? ?
? ? ?
2
2
Qt
11
E cv t Q t v t
2 2C 2
 
Properties of ideal capacitor 
? If voltage across capacitor is constant (dc) then current through capacitor is zero & it acts as open 
circuit. 
? The voltage across capacitor must be continuous, if it as discontinuous, then 
? ? dv t
iC
dt
? is infinite, 
so voltage across capacitor cannot change instantaneously. 
 
? A capacitor never dissipates energy, it only stores energy. 
 
Capacitor in series & parallel 
? In ‘n’ capacitors are connected in series 
1 2 n
C ,C ,.............C 
?
??
eq
1 2 n
1
C
1 1 1
.................
C C C
 
 
? If ‘n’ capacitors are connected in parallel, 
1 2 n
C ,C ,..........................C 
eq 1 2 n
C C C ....................... C ? ? ? ?
 
 
In series connection, charge is same whereas in parallel connection voltage is same.