Download 2. Network theorems

EXPERIMENT NO:2
OBJECTIVE: VERIFICATION OF NETWORK THEOREM
i)
ii)
iii)
SUPERPOSITION THEOREM
THEVENIN THEOREM
MAXIMAM POWER TRANSFER THEOREM
APPARATUS REQUIRED:
Sl Instrument
no.
type
Range/specification
Qty.
1.
Supply
Dc
0-12V
1
2.
Experimental board
Kit or
Breadboard
-
1
3.
voltmeter
MC
(0-15)V
1
4.
ammeter
MC
(0-10)mA
1
5.
resistance
450Ω
1
6.
resistance
350 Ω
1
7.
resistance
250Ω
1
THEORY: In a linear network containing more than one energy sources, the current flow in any
branch is the algebraic sum of currents due to each individual energy source. At the of
consideration of one energy source, rest of the energy sources will have to be inactivated.
To inactivate voltage source, voltage source will be replaced by internal resistance and if
internal resistance is not given then voltage source will be short- circuited.
To inactivate current source, current source will be replaced by internal resistance and if
internal resistance is not given then current source will be open- circuited.
CIRCUIT DIAGRAM:
Figure(a)
Figure(b)
OBSERVATION TABLE:
Sl
no.
Current “I”
Current “I1”
Current “I2”
I=I1 + I2
Practically
Practically
Practically
(Algebric Sum)
Circuit diagram
Fig (a)
Fig (b)
PROCEDURE:
i) Short circuit the terminals E &F.
ii) Connect the 9V supply with terminal DC.
iii) Connect the ammeter in series with branch DC.
iv) Observe the reading of ammeter “I1”
v) Again Short circuit the terminals DC having an ammeter in series
vi) Connect the 5V supply with terminal EF.
vii) Observe the reading of ammeter “I2”.
RESULT:
The net current I is the algebraic sum of I1 & I2 due to the individual voltage source taking one at
a time I=I1 + I2
PRECAUTION:
i) Do not make interconnection on the board with mains switched ON.
ii) As soon as mains is ON .the reading in the meters must be zero. If the reading in the
meters is not zero, check the meters.
iii) Keep the hands away from the mains transformer.
iv) Both the power supplies are short circuit protected.
ii) THEORY OF THEVENIN THEOREM:
This theorem provides a mathematical technique for replacing a linear two terminal network by
a voltage source in series with resistance Rth.
According to Thevenin’s theorem “Any linear two terminal network, containing energy source
and resistances, can be replaced by an equivalent circuit consisting of a voltage source Vth in
series with resistance Rth”. The value of Vth is the open circuit voltage between the load
terminals of the network and Rth is the equivalent resistance between the load terminals with
all energy sources replaced by their internal resistance
if internal resistances are not given then voltage
source will be short circuit, while current source will
be open circuit.
Load current (IL) across the load resistance (RL) is
given by the equation
IL 
Vth
( Rth  RL )
Where Vth=open ckt voltage across the terminals.
Rth=equivalent resistance across the terminals.
RL= the load resistance
CIRCUIT DIAGRAM:
To find Rth:
To find Vth:
Figure(a)
To find IL:
Figure(b)
IL 
Vth
( Rth  RL )
OBSERVATION TABLE:
Sl
no.
VOC
Vth
Rth
IL
IL = Vth / Rth+ RL
practically
theortically
computed
measured
calculated
CALCULATION:
IL 
Vth
( Rth  RL )
; RL=150Ω
Vth=
Rth=
PROCEDURE:
i)
Connect the circuit. According to the fig (a) and find
VOC
ii)
Connect the circuit. According to the fig(b);observe IL
PRECAUTION:
i) Do not make interconnection on the board with mains switched ON.
ii) As soon as mains is ON .the reading in the meters must br zero. If the reading in the
meters is not zero, check the meters .
iii) Keep the hands away from the mains transformer.
iv)
Both the power supply are short ckt. Protected
RESULT:
We find that the calculated value of load curent “IL” is equal to the measured “IL”
IL(calculated)=
IL(measured)
iii) MAXIMUM POWER TRANSFER THEOREM:
THEORY: According to the maximum power transfer theorem as applied to DC network a
resistance load will abstract maximum power from a network when the load resistance of the is
equal
To the resistance of the network as viewed from the output terminals with all energy source
are replaced by their internal resistance. In the case of AC network load impedance should
Be complex conjugate of source impedance.
Po = Pmax. When RL=RT=RTH
Pmax.= V2TH/ 4 RL
And power delivered to the load resistance
Po = I2L RL
CIRCUIT DIAGRAM:
CALCULATION:
IL = Vth / Rth+ RL
Vth=
Rth=
Pmax.= V2TH/ 4 RL
OBSERVATION TABLE:
Po = I2L RL in watt
sl no. Vth
Rth
Pmax.= V2TH/ 4 RL
For variable load
theoritically computed theoritically
RL=50Ω RL=100Ω
RL=150Ω
RL=200Ω
PROCEDURE:
i)Connect the ckt. According to the fig (a)
ii) Find the load current IL1, IL2, IL1, ....... for the load resistance RL=50Ω,100Ω, 150Ω,...........
PRECAUTION:
i) Do not make interconnection on the board with mains switched ON.
ii) As soon as mains is ON .the reading in the meters must br zero. if the reading in the
meters is not zero,check the meters .
iii) Keep the hands away from the mains transformer.
iv) Both the power supply is short ckt. Protected
RESULT:
From the observation table we can observed that power delivered is maximum when the load
resistance
RL=RTH