This document provides information about Parshva Classes, an educational institution that offers courses for engineering degrees and diplomas from various universities. It lists the contact details and addresses of the institution's main and branch offices. The bulk of the document consists of definitions and explanations of various electrical circuit and network terms like active and passive elements, nodes, branches, loops, meshes, Kirchoff's laws, Maxwell's loop theorem, Thevenin's theorem and Norton's theorem. Key concepts from circuit analysis such as superposition theorem and reciprocity theorem are also summarized.

1. 'PARSHVA CLASSES', Khatri Pole, Behind Jubilee Baug, Baroda-1, [[ 1 ]]
NETWORK THEOREMS
ELECTRICAL CIRCUITS & NETWORKS
Mob. : 9825117931
9825977394
9825017931
FATEHGUNJ BRANCH :
SB-17, EMPEROR COMPLEX,
BESIDE " GOODIES "
FATEHGUNJ,
VADODARA.
SHREE PARSHVA
JAY AMBE PRAKASH K. BHAVSAR'S
PARSHVA CLASSES
[ FOR ENGINEERING ]
DEGREE & DIPLOMA MSU & GTU
A NEW NAME OF 'GURU CLASSES'
HEAD OFFICE :
PANKIL CHAMBERS,
KHATRI POLE,
B/H. JUBILEE BAUG,
RAOPURA, VADODARA.
WAGHODIA BRANCH :
3-GAJANAND SOC.,
ABOVE INDIAN OVERSEAS
BANK, UMA CHAR RASTA,
WAGHODIA ROAD, VADODARA.
  NETWORK TERMINOLOGY :
[1] Electric Network : It is a combination of various electric elements connected
in any manner.
[2] Electric Circuit :
   A circuit is a closed conducting path through which an electric current either
flows or is intended to flow.
[3] Parameters :
   The various elements of an electric circuit are called its parameters like
resistance (R), inductance (L) and capacitance (C).
   They may be lumped or distributed.
[4] Linear circuit :
   A linear circuit is one whose parameters are constant i.e. they do not
change with voltage or current.
[5] Non-linear circuit :
   A non-linear is one whose parameters change with voltage or current.
[6] Bilateral circuit :
   A bilateral circuit is one whose properties or characteristics are the same
in either direction. A transmission line is bilateral because it can be made to
perform its function equally well in either direction.
[7] Unilateral circuit :
   A unilateral circuit is one whose properties or characteristics change with
the direction of its operation. A diode rectifier circuit is a unilateral circuit
because it cannot perform equally in either direction.
[8] Active Elements :
   The elements which are capable of delivering an average power (or energy)
greater than zero to some external device over an infinite time interval are
called an active elements.
or
E1

2. 'PARSHVA CLASSES', Khatri Pole, Behind Jubilee Baug, Baroda-1, [[ 2 ]]
OR The elements in the electrical circuit or network which supplies electrical energy
are called active elements.
 This is a source of emf or current. Source of emf gives constant electromotive
force whereas the current source supplies constant current.
 In fig., B1 is voltage source and G1 is current source.
[9] Passive Elements :
   The elements in the electrical circuit which are capable only of receiving power
(or energy) are called passive elements.
OR The elements in the electrical circuit which
receives the electrical energy and disposes the
same in their way of disposal are called passive
elements.
   In D.C. circuit, passive element is the resistance
only. While in A.C. circuit, resistance, inductance
and capacitance are the passive elements.
   In the network shown R1, R2, R3 etc., are the passive elements.
[10]Active Network :
   A network in which one or more than one sources of emf or current is known
as active network.
[11] Passive Network :
 A network in which no source of emf or current is known as passive network.
[12]Electric Network :
   A circuit made by combination or interconnection of various passive elements
or active and passive elements both (sources, resistors etc.) is called an
electric network.
[13]Node : The point in a circuit at which two or more circuit elements meet is
called node.
   In figure, A, B, C, D etc. It is shown by dot.
   In the network, node shows the voltage level. Wire connecting two elements is
assumed to have zero reistance. Point 'a' and 'b' is treated the as same node A.
[14]Junction :
   It is a point where three or more elments are connected together in the
circuit or network.
   In figure, B, F are the junction.
[15]Branch :
   A section or portion of a network or circuit which lies between two junction
points is called as branch.
   For e.g. element R5 joining nodes B and C is a branch.
[16]Loop :
   It is a close path in a circuit or network in which no element or node is
encountered more than once.
OR Any closed path in a network is called loop.
   For e.g. AFGA, ABEDFGA, ABCDFGA are loops.
[17]Mesh :
   It is a loop that contains no other loop within it.
OR It is the most elementary form of a loop and cannot be further divided into
other loops.
   For e.g. AFGA, ABEDFA, BCDEB.
   Everey mesh is a loop but every loop may not be mesh.

3. 'PARSHVA CLASSES', Khatri Pole, Behind Jubilee Baug, Baroda-1, [[ 3 ]]
 KIRCHOFF'S LAWS :
   There are two Kirchoff's law (a current & a voltage law).
   These laws are useful to solve complex network which cannot be easily
solved by Ohm's law. These laws are applicable to both AC and DC circuits.
 Kirchoff's current law (KCL) OR Point law OR Kirchoff's First law :
  It states that the algebraic sum of all the currents meeting at a
junction or a node in any electric circuit is zero.
   Consider the case of a few conductors meeting at point A as shown in
figure. The arrows indicate the direction of current flow. Assuming positive
sign for incoming currents and negative sign for outgoing current.
According to Kirchoff's law, I = 0
i.e. (+ I1) + (- I2) + (+ I3) + (-I4) + (+I5) = 0
 I1 + I3 + I5 = I2 + I4
  Iin =  Iout
i.e. incoming currents = outgoing currents
The above law can also be stated as,
   It states that the algebraic sum of the currents flowing towards a
junction is equal to the sum of all the currents flowing away from
that junction.
Note : There is no accumulation or depletion of current at any junction of network.
 Kirchoff's voltage law (KVL) OR Mesh law OR Kirchoff's Second law :
* In any closed path (mesh or loop) of an electric circuit, the algebraic
sum of product of current and resistance in each of the conductors
plus the algebraic sum of electromotive forces (emfs) in that closed
path is zero. i.e.  I R +  emf = 0
 I1 R1  E2  I2 R2 + I3 R3 + E1  I4 R4 = 0
 I1 R1  I2 R2 + I3 R3  I4 R4 = E2  E1
 I1 R1 + I2 R2  I3 R3 + I4 R4 = E1  E2
 Determination of signs :
[a] Direction of current :
   The current direction can be assumed clockwise or anticlockwise. If assumed
direction of current is not the actual, the calculated value of current will
have a negative sign. Once particular direction is assumed for current,
same should be maintained throughout the solution of network.
[b] Direction of EMFs : A rise in potential must be considered +ve and
fall in potential must be considered -ve. If we go from +ve terminal of
battery to -ve terminal, there is fall in potential and hence it must be
considered -ve. It should be noted that sign of EMF is independent of the
direction of current through that branch.
Fall in voltage Rise in voltage
[c] Direction of voltage drop : There is a volt drop across resistors due to
current flow. If we go with the current, the volt drop must be taken as
negative because the current flows from higher potential to lower one
and vice-versa.
voltage drop = I R sign  - I R voltage rise = I R sign  + I R

4. 'PARSHVA CLASSES', Khatri Pole, Behind Jubilee Baug, Baroda-1, [[ 4 ]]
 MAXWELL'S LOOP THEOREM OR MAXWELL LOOP CURRENT METHOD :
  This theorem which is particularly well-suited to coupled circuit solutions
employs a system of loop or mesh currents instead of branch currents (as
in Kirchhoff's Laws). Here the current in different meshes are assigned
continuous paths so that they do not spilt at a junction into branch currents.
   This method eliminates a great deal of tedious work involved in the branch-
current method and is best suited when energy sources are voltage equations
by kirchhoff's voltage law in terms of unknown loop current.
   Figure shows two barriers E1 and E2
connected in a network consisting of five
resistors. Let the loop currents for the
three meshes be I1, I2 and I3. It is
obvious that currents through R4 (When
considered as a part of the first loop) is
(I1  I2) and that through R5 is (I2  I3).
However, when R4 is considered part of the second loop, current through it
is (I2  I1). Similarly when R5 is considered part of the third loop, current
through it is (I3  I2).
   Applying Kirchhoff's Voltage Law (KVL) to the three loops, we get,
E1  I1 R1  R4 (I1  I2) = 0 OR I1 (R1 + R4)  I2 R4  E1 = 0 Loop (1)
 I2 R2  R5 (I2  I3)  R4 (I2  I4) = 0
I1 R4  I2 (R2 + R4 + R5) + I3 R5 = 0 Loop (2)
I3 R3  E2  R5 (I3  I2) = 0 OR I2 R5  I3 (R3 + R5)  E2 = 0 Loop (3)
   The above three equations can be solved not only to find the loop currents
but branch currents as well.
  THEVENIN'S THEOREM :
 It provides a mathematical technique for replacing a given network, as viewed
from two output terminals, by a single voltage source with a series resistance.
 Thevenin's Theorem as applied to d.c. circuits, may be stated as under.
The current flowing through a load
resistance RL connected across any
two terminals A and B of a linear,
active bilateral network is given by VOC
/(Ri + RL) where, VOC is the open-
circuit voltage (i.e voltage across the
two terminals when RL is removed) &
Ri is the internal resistance of the
network as viewed back into the open-circuited network from terminals
A & B with all voltage sources replaced by their internal resistance (if
any) & current sources by infinite resistance. (Here Ri = Rth).
   It makes the solution of complicated networks quite quick and easy.
 How to Thevenize a given circuit :
[1] Temporarily remove resistance (called load resistance RL) from the circuit terminals
A & B of fig.(a) whose current is required and redraw circuit as shown in figure (b).
[2] Find the open-circuit voltage VOC which appears across the two terminals A
& B from where resistance has been removed (i.e. when RL is removed).
Current when A & B are open I =
E
R1 + R2 + r
E1
R1 R2 R3
R4 R5 E2
I1 I2 I3
A
B
N
e
t
w
o
r
k
A
B
R
th
V
th
Original Network Thevenin's
Equivalent
Network

5. 'PARSHVA CLASSES', Khatri Pole, Behind Jubilee Baug, Baroda-1, [[ 5 ]]
r is the internal resistance of the battery.
Voltge drop across R2, VOC = I . R2 VOC =
E R2
R1 + R2 + r
It is also called Thevenin equivalent voltage Vth.
[3] Compute the resistance of the whole network as looked into from these two
terminals after all voltage sources have been removed leaving behind their
internal resistance (if any) and current sources have been replaced by open-
circuit i.e. infinite resistance as shown in figure-(c).
Equivalent resistance of the network, as viewed from these terminals is given
as
R = R2 ll (R1 + r) =
R2 (R1 + r)
R2 + (R1 + r)
It is also called Thevenin resistance Rth or Ri or Ro.
[4] Replace the entire network as viewed from terminals A & B by a single Thevenin
source, whose voltage Vth or Voc and whose resistance Rth or Ri in series as
shown in figure-(d).
[5] Connect RL back to its terminal from where it was previously removed. Fig.-(e)
[6] Finally, calculate the current flowing through RL by using the equation.
I =
Vth
OR I =
VOC
(Rth + RL) (Ri + RL)
 NORTON'S THEOREM : Norton's Theorem may be stated as follows,
   Any two-ter minal activ e network
containing voltage sources and
resistance when viewed from its output
terminals, is equivalent to a constant-
current sources and a parallel
resistance. The constant current is
equal to the current which would flow
in a short-circuit placed across the
terminals and parallel resistance is the resistance of the network when
viewed from these open-circuited terminals after all voltage and current
sources have been removed and replaced by their internal resistance.
Thevenin
Source
RL
Rth
Vth
I
A
B
r r
r
(a) Original Network
(b) Determination of Vth (c) Determination of Rth
(d) Thevenin's (e) Determination of Current
Equivalent Network
A
B
N
e
t
w
o
r
k
A
B
Req
I
sc
Original Network Norton's
Equivalent
Network

6. 'PARSHVA CLASSES', Khatri Pole, Behind Jubilee Baug, Baroda-1, [[ 6 ]]
 To nortonize Given circuit :
[1] Remove the resistance RL (if any) across two given terminals A and B as
shown in fig.-(a) and put a short-circuit across them as shown in figure-(b).
[2] Determine the current ISC through the short circuit across A & B.
ISC =
E
R1
[3] Remove all voltage sources and replace it by their internal resistance, if any.
Similarly, remove all current sources & replace them by open-circuits i.e. by
infinite resistance. Fig.-(c)
[4] Next, find the equivalent resistance Req of the network as looked into from
the given terminals A & B as shown in fig.-(c). It is exactly the same as Rth.
Req = R1 ll R2 =
R1 R2
R2 + R1
[5] The current source (ISC) joined in parallel across R between the two terminals
gives Norton's equivalent circuit. Fig.-(d).
[6] Now connect R2 back to the Norton's equivalent network as shown in figure-(e).
Calculate the current through RL using
IL = ISC
Req
(Req + RL)
 SUPER POSITION THEOREM : Super Position theorem can be stated as follows,
In a network of linear resistance containing more than one generator
(or source of e.m.f.) the current which flows at any point is the sum of
all the currents which would flow at that point if each generator were
considered separately and all the other generators replaced for the
time being by resistance equal to their internal resistance.
6 V
0.5
I1 I2
A
B
I1 I2
12 V
1 
6 
Fig. 1
I
6 V
0.5
I1' A I2'
6  I'
B
I1' I2' Fig. 2
1
I1'' A I2''
2.5 2 2.5 2 2.5 2
12 V
1 
6  I''
0.5
B
I1'' I2'' Fig. 3
(c) Determination of Req (d) Norton's (e) Determination of Current
Equivalent Network
(a) Original Network (b) Determination of Isc