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Basic Electricity And Network Theorems 1
il.com
OHM’S LAW
Ohm’s law statesthis relationshipin simple words ‘‘the current flowing circuit (I)
is directly proportional to applied voltage (V) provided resistance in the circuit
is constant ’’
IαV or VαI
Voltage V
1.Resistance= OR R=
Current I
2.Voltage=Current×Resistance OR V=I×R
Voltage V
3.Current OR
Resistance
I
R
 
VOLTAGE
Voltage is necessary to set up the current flow. Voltage is also known as
'' '', '' ''potential difference EMF
In actual practice voltage source is of two types
1. AC Voltage (Alternating Current type)
2. DC voltage (Direct Current type)
CURRENT
An electric current through a conductor is a flow of electrons; actually electriccharge
in motion is called as current.
 Conventional Current
The electron flow is always from-Ve terminal to +Ve terminal of the battery but
theoretically it is assumed to be from positive to negative, because as a
convention, electric current direction a conventional current from positive to
negative.
BASIC ELECTRICITY AND
NETWORK THEOREMS

Electron Flow & conventional current
SOURCES OF ELECTRICITY
i) AC Source and
ii) DC Source
i) AC Source
a) Signal generator
If can generate AC supply with variable voltage and variable frequency,
sometimes, they are capable of generating different AC signal with different
waveforms like square wave, triangular wave, sawtooth etc.
b) Alternator
It is a sort of generator can generate AC supply converting mechanical energy
into electrical energy.E.g. in auditorium when MSEB fails they start generators
or while in festivals or Circus owner they use their self-generators.

DC SOURCES
We get AC supply from main electric power station but most of the electronic circuits
work on DC supply, user has to take DC supply from the following sources
i) Batteries ii) DC generators
iii) Rectifiers iv) solar cell
The battery is a very common DC source because of its high current capacity and
recharging facility. It can be recharged for many times; now a day in automobile
applications it is continuously charged by electronic circuits when engine starts. A
battery is a unit in which no. of cell are arranged in series and parallel arrangement.
The DC generator is a dynamic engine it generates DC energy by means of
rotating shaft it generates electrical energy by converting mechanical energy.
A rectifier is an electronicinstrument which converts mains AC supply into DC
there is no rotating part.
IDEAL AND PRACTICAL VOLTAGE SOURCE
Ideal voltage source is not possible; the source cannot maintain source voltage at its
terminals it would mean that it could supply an infinite power to a load even if the
circuit is a short circuit.
A practical voltage source is the true source it is a source with small internal
impedance as indicated by fig. There I-V characteristics show that as load current
increasesits terminal voltage decreases due to drop across its internal impedance.

IDEAL AND PRACTICAL CURRENT SOURCE
A current source can be a source, which can deliver constant current even if load
varies from low to high value.
It is a quite similar concept of ideal current source, where it
supplies constant current (I) even current through load
varies. It means that evenif the circuit is an open circuit
practically current flow is not possible. On the other hand a
practical current source is represented by a current source
with internal impedance in parallel with source. It can be
stated that a good current source has high internal
impedance so that very small current is passed through it
and almost constant current flows through the load. As
shown in the fig LZ=Ziparallel Z
L LZ=Z when Z =0 or Zi=
 Comparison
Voltage source Current source
It is voltage with minimum internal
impedance.
It is voltage with maximum internal
impedance.
It is a voltage source in series with Zi It is a voltage source in parallel with Zi
It works when ZL>>Zi It works when Zi>>ZL
IMPORTANT FORMULAE
1. Rt=R1+R2+R3+……….Series circuit
2.
1 2 3
1 1 1 1
TR R R R
  
……..Parallel circuit
3. When R1 and R2 are in series across a supply V then voltage across R2
By voltage divider formula

2
2
1 2
R
R X V
V
R R


4. When R1 and R2 are in parallel then the current through R2 by current divider
formula
1 2
2 1
1 2 1 2
 
 
T TR X I R X I
I I
R R R R
POWER
Power is defined, as ‘‘it is the rate of doing electric work ‘’.
Now we can make one more relation by substituting (I=V/R) in equation (1)
2
2
2
( / )
...........(3)
Formulae:
(1) (2) (3)
P V V R
V
P
R
V
P V I P I R P
R
  

   
2
/
But / / /
Substituting these two
/
............(1)
(Watts Volts Amp)
Substituting in equation (1)
( )
.............(2)
P W t
V W Q W V Q and I Q t Q I
V Q
P V I
Q I
P V I
V IR
P IR I
P I R

     

  
 
 

 
 


KIRCHHOFF’S LAWS
(1) Kirchhoff’s current law (KCL)
It states that ‘‘The algebraic sum of currents at any junction or node is
always zero’’. Where currentscoming towards node are considered with positive
sign and currents leaving the node are considered with negative sign.
As shown in fig. the equation for node will be
1 2 3 4 0I I I I   
(2) Kirchhoff’s voltage law (KVL)
It states that ‘‘The algebraic sum of voltages around any closed loop is always
zero.’’ Here loop means a closed circuit path. Kirchhoff’s equation can be written
as 1 2 3 1 2 3.V V V V or V V V V     
SUPERPOSITION THEOREM
Statement
‘‘In a network containing two or more sources, the current or voltage for any
component is the algebraic of the results produced by each source acting
individual source’’.
Example 1 : Find the P.D. between point A and B
Solution:
Step-I Make V2 short and find VAB across R2 say (V1)
By Voltage divider formula

2
1
1 2
a
R
V V
R R
 

6
24 16
9
a
K
V V
K
  
Step-II Now make V1 short and find VAB across R1 say (V2)
1
2
1 2
b
R
V V
R R
 

3
9 3
9
bV V   
Example 2
Find current through 3R if 3 1R K 
 Step-I Make 2V short & find voltage across
2R (say aV )
12 30
20
18
a
x
V V 
 Step- II Make 1V short and find voltage across 1R (Say bV )
2 1
1 2
30 6
18
b
V x R x
V
R R
 

10 V
 Step-III Apply Superposition
AB a bV V V 
= 20+10
=30V
The current through 3
3 3
3
30
30 10 30
1 10
ABV
R mA
R

    

Drawback of superposition theorem: it is suitable only when the network contains
linear components.

THEVENIN’S THEOREM
Statement
Any linear active, resistive complex network containing one or more sources
can be replaced by an equivalent voltage source (Veq) and a series equivalent
resistance (Req).
Where (Veq) or ( THV ) = The venin’s equivalent voltage source
And (Re ) ( )THq or R = Thevenin’s Equivalent resistance
NORTON’S THEOREM
Statement
Any linear active, resistive complex network containing one or more sources
can be replaced by an equivalent current source (Ieq) and a parallel equivalent
resistance (Req).
Where ( ) ( )NIeq or I = Norton’s equivalent current source
And (Re ) ( )Nq or R = Norton’s Equivalent resistance

COMPARISON OF THEVENIN’S WITH NORTON’S THEOREM
Thevenin’s Theorem Norton’s Theorem
1. It is used when a complex
network containsone or many
voltage sources.
1. It is used when a complex
network containsone or many
current sources
2. Mostly used in analysisvoltage. 2. Mostly used in analysisof current
3. It has a single equivalent voltage
source (Veq) when terminalsare
open circuited.
3. It has a single equivalent current
source (Ieq) when terminals are
short circuited.
4. The Theveninsequivalent
resistace (Req) is in series with
Veq.
4. Req is in parallel with Ieq.
5. Thevenin’s Equivalent circuit
5. Norton’s Equivalent circuit
 Example 1 Draw Thevenin’s equivalent circuit and find voltage across ‘RL’.
Step (I) Step (II)
Make terminal AB open and find Veq Make terminal AB open and find Veq
2 2
2 2
1 2 1 2
   
 
R eq R eq
VxR VxR
V V V V
R R R R

6 12 6 10
4 6.66
18 9
   
x x
V V
(Note that R3 is open hence VR2 is Veq)
Step (II) Find Req by making source short
1 2 1 2
3
1 2 1 2
Re Re  
 
R x R R x R
q q R
R R R R ,
6 12 6 3
4 3 5
18 9
      
x x
Step (III) Step (III)
Draw Thevenine’s equivalent circuit Draw Thevenine’s equivalent circuit
& find VL & find VL
2 2
Re Re
4 6 6.6 3
2.4 2.4975
10 8
L L
R R
L L
Veq x R Veq x R
V V
q R q R
x x
V V
 
 
   
 Example 2 Find Current through the load and voltage across the load by
Norton’s theorem in the given circuit.

Solution: Step (I) Make output terminals short and find short find short circuit
current Ieq.
Note: that 20 Ω resistance becomes short or 0 Ω J
Step (II) Make voltage source short and find Req.
Step (III) Draw Norton’s equivalent circuit and find IL and VL.
It can be verified by Thevenin’s equivalent circuit.
Step (I) Find Veq by making AB open
Step (II) Find Req or use Req from Norton’s method and find VL by voltage divider
formula.

Example 3: Find VL and IL by Norton’s & Thevenin’s Theorem.
Solution Applying Norton’s Theorem
Step (I) Make the output terminals short and find short circuit current Ieq.
Step (II) Make source voltage short and find Req.
Step (III) Draw Norton’s equivalent circuit and find IL and VL
Step (I) Find Veq by making AB open

 Example 4 Find VL and IL by using both Norton’s & Thevenin’s Theorems.
Solution (A) Applying Norton’s Theorem
Step (I) Make the output terminals short and find short-circuit current Ieq.
Step (II) Make the source voltage short and find Req.
Step (III) Draw Norton’s equivalent circuit and find IL

(B) Applying Thevenin’s Theorem
Step (I) Find Veq by making AB open. Veq is nothing but voltage across R2
because AB is open.
MAXIMUM POWER TRANSFER THEOREM
‘’The maximum power transfer takes place when the load resistance 1( )R is
equal to the to the equivalent source resistance (Req)’’.
 Comparison Of Electric And Magnetic Field
Electric circuit Magnetic circuit
1.
Electricfield resultsin electron flow
1.
Magnetic system results in flux.
2. Flow of electron is current. 2. Flow of flux.
3. The cause of current is E.M.F.
(Voltage)
3. The cause of flux is M.M.F
Magneto Motive Force.
4. Opposition to the flow of electron is
known as resistance (R)
4. Opposition to the flow is known as
reluctance (R)
5. Resistance is given by
R=σ1 A
where
 is the conductivity.
5. Reluctance is given by
R=1 μ
where
 is the permeability.
6. Conductance =
1 R 6. Permanence=
1 R
7. Ohms law =
V I 7. Reluctance R=MMF/


8. Current in an electriccircuit is due to
electron flow.
8. Flux in magnetic circuit does not
actually flow.
9. Magnetic field is generated when
curre3nt flows through a conductor.
9. Electricity can be generated by
magnetic field.
10.Energy is required to maintain the
current in the
10. Energy is required only to create
flux but not no maintain it.
ELECTROMAGNETISM
Magnetic field is always produced around the conductor, when electric current flows
through it. This phenomenon can be observed by performing simple experiment as
shown in fig….
Shown that when current flows through the conductor iron filings are aligned in
concentric ringsaround the conductor; this shows that magnetic field is developed in
circular orbits around the conductor. Another important conclusion is, iron filings
are dense near to the conductor that is magnetic field is strongest neat the
conductor and it decreases withincrease in distance. Third conclusion is- higher is
the current flow higher is the magnetic field. Magnetic force of lines is known as
‘‘ ( )’’magnetic flux  and the number of magnetic lines of force that pass through the
unit area of a section perpendicular to the direction of the magneticflux is known as
‘‘ ’’.fluxdensity

ELECTROMAGNETIC INDUCTION
Electrons in motion (current) produce a
magneticfield, similarly when magneticflux
moves, it forces free electrons in conductor
to move, which produce an electric current.
Shows the conductor AB is placed at right
angles to the flux produced by the magnet.
When magnet is moved up and down, the
conductor cuts the lines of magnetic flux.
Therefore whenever the conductor cuts flux current is produced in the conductor.
This current is observed in micrometer as shown. When magnet is moved downward,
current flows from A to B and when it moves upward, current flows in opposite
direction.
If you move conductor AB instead of magnet then also induction can be observed
because the conductor cuts magneticflux. Hence whenever either flux is in motion
or conductor is in motion electricity is produced in the conductor by induction. Same
principle is used in an electric generator.
INDUCTANCE
It is the ability of conductor induced voltage, when current through it varies.
Induced voltage is the result of flux cutting across a conductor because when ac
current flows through it magneticflux varies its strengthand the direction, which is
equivalent to motion of magnetic flux.
 FARADAY’S LAW
When a conductor cuts the line of magnetic field (flux) an e.m.f. is generated
in the conductor or when magnetic flux is made varying across the
conductor an e.m.f. can be generated in the conductor.

The voltage induced by induction depends upon the following three factors:
1) Amount of Flux ( ) :
Higher is the number of magnetic lines of force (or magnetic flux) higher will be
the induced voltage.
2) Number of Turns (N):
The more turns in a coil the higher is induced voltage, because induced voltage is
the sum of individual voltages generated in each turn of the coil.
3) Faster the rate of cutting flux, higher is the induced voltage.
SELF INDUCTANCE AND MUTUAL INDUCTANCE
The ability of a conductor to induce voltage in itself when the current changes
through it, is known as its‘‘ Self inductance’’or simply inductance. The notation of
inductance is ‘L’ and it is measured in ‘Henry’. This induced voltage has a tendency
to oppose change in current. Therefore induced voltage is often called as ‘‘counter
emf’’ or ‘‘back emf’’.
When current through coil is AC and if voltage is induced in itself it is called as its
‘self-inductance’.
But when AC current flows through one coil and voltage is induced in other coil
placed near to it then it is known as ‘mutual inductance’.

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