VERIFICATION OF SUPER
POSITION THEOREM
Circuit Diagram:
VERIFICATION OF SUPER-POSITION THEOREM
Aim : To verify Superposition theorem for a given network.
Apparatus:
Theory:
Procedure:
1.
2.
3.
4.
5.
6.
7.
Connect the circuit as shown in circuit diagram.
Close the switch S3 to 11’ side and close switch S4 to 44’ side and close switch S1
Note down the reading of ammeters.
Close the switch S3 to 22’ side and close the switch S4 to 33’ side.
Note down the reading of ammeters. let this be I11 and the earlier be Il.
Close the switch S3 to 11’ and switch S4 to 33’ and note down the reading of
ammeter across AB. Let this be I.
If I = I’ + I” Super Position theorem is verified.
Precautions:
1.
2.
3.
All the connections must be made properly.
All the readings must be taken without an parallax error.
The current should not exceed the rated value.
Results: Since I = I’ + I” ; Super Position theorem is verified..
VERIFICATION OF RECIPROCITY
THEOREM
Circuit Diagram:
VERIFICATION OF RECIPROCITY THEOREM
Aim : To verify Reciprocity theorem.
Apparatus:
Theory:
Procedure:
1.
2.
Connect the circuit as per circuit diagram.
Close S1, S2 to 11’ and S3 to 44’ . Note down the readings of voltmeter and
ammeter.
3.
Close S2 to 22’ , S3 to 33’ and close S4. Note down reading of voltmeter and
ammetre.
Precautions:
1.
2.
Take the readings of voltmeter and ammeter without parallax error.
The current through a particular element should be maintained below its current
rating.
Results: .
Hence, Reciprocity theorem is verified.
Viva Questions:
1)
2)
3)
4)
5)
What is the statement of the above theorem?
What is a linear network?
Where the above theorem is used practically?
What is the practical application of reciprocity theorem?
What is a bilateral network? Give one example.
DETERMINATION OF Z AND Y
PARMETRES OF A TWO PORT
NETWORK
Circuit Diagram:
DETERMINATION OF Z AND Y PARMETRES OF A TWO PORT
NETWORK
Aim : To determine Z, Y and ABCD parameters of a given two port Network.
Apparatus:
Theory:
Procedure:
1.
2.
3.
4.
5.
Connect the circuit as per circuit diagram.
Close switch S1, close S2 to 11’ and open switch S3 note down readings of
voltmeter and ammeter . from these readings calculate Z11 and Z21.
Close S4, close S3 to 33’ and open S1 not down the readings of voltmeter and
ammeter. From these readings calculate Z12 and Z22.
Close S1, S2 to 11’ and S3 to 44’. Note down the readings of voltmeter and
ammeter. From these values calculate Y11 and Y22.
Close S2 to 22’, S3 to 33’ and S4 close. Note down the readings of voltmeter
and ammeter. From these values calculate Y12 and and 22.
Precautions:
1.
2.
Take the readings of voltmeter and ammeter without parallax error.
The current through a particular element should be maintained below its current
raing..
Results: Z, Y and ABCD parameters are determined.
Viva questions:
1)
2)
3)
4)
5)
6)
7)
what is the significance of the two port parameters?
How you know the admittance parameters from impedance parameters?
What is the application of ABCD parameters?
What is the condition for reciprocal network?
What is the condition for symmetrical network?
What is a Lattice network?
What is a ladder network?
VERIFICATION OF THEVENIN’S
THEOREM
Circuit Diagram:
VERIFICATION OF THEVENIN’S THEOREM
Aim : To verify the Thevenin’s theorem.
Apparatus:
Theory:
Procedure:
1.
2.
3.
4.
5.
6.
7.
8.
Connect the circuit as per the circuit diagram..
Open switch S2 and close switch S1 to 11’. This gives supply to the circuit across
AB.
Open switch S3 and note the voltmeter reading(Voc).
Close the switch S3 and note the ammeter reading IL.
Close the switch S1 to 22’ (shorting AB) and open switch S3 (removing RL)
Close the switch S2 (giving supply across CD)
Note the voltmeter reading (Voc) and ammeter reading (IL) gives Zth.
V
Verify Zth = oc
IL
Precautions:
1.
2.
All the connection must be tight.
The readings of voltmeter and ammeter should be taken without any parallax
error.
Results:
Compare the direct value of load current and load current by calculation.
Hence
thevenin’s theorm is verified.
Viva Questions:
1) What is the statement of the above theorem?
2) What is a linear network?
3) How do you calculate Voc?
4) How do you calculate Rth?
VERIFICATION OF
MAXIMUM POWER TRANSFER
THEOREM
Circuit Diagram:
VERIFICATION OF MAXIMUM POWER TRANSFER THEOREM
Aim : To verify Maximum Power transfer theorem.
Apparatus:
Theory:
Procedure:
1.
2.
3.
4.
Connect the circuit as per the circuit diagram.
Initially the resistance should be kept in maximum position. The load resistance
RL is varied such that the voltmeter reading is varied and the corresponding
ammeter reading is noted down. Correspondingly calculate the power and load
resistance.
A graph is plotted between power delivered and load current with power taken on
Y axis and current on X axis.
The maximum power delivered is observed when RL = Rth where Rth is calculated
from the circuit.
Graph:
power
I
Precautions:
1.
2.
Loose connections should be avoided..
There should not be any parallax error while taking ammeter and voltmeter
reading.
OBSERVATION:
Rth (practical )
=
Rth (theoretical) =
Results:
Thus Maximum power transfer theorem is verified.
Viva questions :
1) What is the statement of maximum power transfer theorem?
2) What is the linear network?
3) what is a bilateral network?
4) what is the application of the above theorem?
5) what are the advantages & disadvantages of the above theoram?
SERIES AND PARALLEL
RESONANCE CIRCUITS
Circuit Diagram:
series resonance:
Graph:
Vo
4K ohm
10V (P-P) +
Vi
DRB
IR
4.05 mH
DLB
+
DCB
-
1u F
-
f
fo
parallel resonance:
IR
10V (P-P) +
Vi
DRB
100 ohm
VR
+
1u F
DCB
-
2.026 mH
DLB
fo
f
SERIES AND PARALLEL RESONANCE CIRCUITS
Aim : To study the series and parallel resonance for the given R-L-C circuit.
Apparatus:
Theory:
Procedure:
1.
2.
3.
4.
5.
6.
Connect the circuit as shown in figure..
Apply 10V P-P sinusoidal i/p to the circuit.
Tabulate the output voltage ( V0), I, for frequencies f by changing frequency
from 50 Hz to 1 KHz in steps of 50Hz.
The frequency corresponding to maximum output is called resonant frequency..
Repeat steps 2,3,4 the values corresponding to the main minimum voltage is
resonance frequency.
Compare with theoretical value.
Graph:
I
Imax
Imax/√2
fl
fh
F
Precautions:
1.
2.
All the connections should be made properly.
There should be no parallax error in noting the readings from CRO.
Results: The characteristics of RLC series and parallel circuits are studied.
Band width in case of series resonance = 300Hz.
Viva Questions:
1)
2)
3)
4)
What is the condition for the resonance?
What are the features for the resonance?
Where we can use resonance circuit?
What is the condition for resonance in parallel circuit?
DETERMINATION OF
FORMFACTOR OF A NONSINUSOIDAL WAEFORM
Circuit Diagram:
DETERMINATION OF FORMFACTOR OF A NON-SINUSOIDAL
WAEFORM
Aim : To determine the form factor of a non-sinusoidal waveform.
Apparatus:
Theory:
Procedure:
1.
2.
3.
4.
Connect the circuit as per circuit diagram.
Plot the graph that appear on the CRO connected to the resistor (i.e) a non
sinusoidal waveform.
Divide the waveform into n parts.
Calculate the VRMS value by the formula
V1 + V2 + ...... + Vn
VRMS =
n
Calculate the average by using the formula
V + V2 + V3 + ..... + Vn
Vavg = 1
n
V
Calculate the form factor as = RMS
Vavg
2
5.
6.
2
2
Precautions:
1.
2.
Plot the graph from CRO with out parallax error.
The current through a particular element should not exceed its current rating
value.
Results: The form factor of the given Non-sinusoidal waveform is 1.14.
Viva Questions:
1)
2)
3)
4)
5)
what is the definition of average value?
What is rms value?
What is form factor?
What is peak factor?
Why we get magnetization current in transformer under no – load condition?
CURRENT LOCUS DIAGRAMS
FOR R-L & R-C CIRCUITS
Circuit Diagram:
CURRENT LOCUS DIAGRAMS FOR R-L & R-C CIRCUITS
Aim : To draw the current Locus diagram of RL and RC circuits.
Apparatus:
Theory:
Procedure:
1.
2.
3.
4.
5.
Connect the circuit as per circuit diagram.
Vary the inductance value in steps.
Note the readings of voltmeter, ammeter and waltmetre.
W 
Calculate φ from the formula φ = Cos +   and plot the graph between I
 VI 
and φ .
Similarly for RC circuit repeat the above steps by replacing inductor by capacitor
and by varying R.
Precautions:
1.
2.
The reading of ammeter, voltmeter should be taken without parallax error.
The current through any element should not exceed its rated value.
Results: .
The locus diagrams of RL and RC circuits are drawn and enclosed.
Viva questions:
1)
2)
3)
4)
what is the significance of current locus?
Give the various locus diagrams for different impedances?
What is active power?
What is the significance of improved power factor?
TIME RESPONSE OF 1st ORDER
SYSTEMS
Circuit Diagram:
TIME RESPONSE OF 1st ORDER SYSTEMS
Aim : To study the response of first order systems [RL and RC systems]
Apparatus:
Theory:
Procedure:
1.
While doing the experiment single stand wires only should be used for
connections.
2.
The values of voltage & time from CRO should be taken without parallax error.
Precautions:
1.
2.
Theoritical value of Time constant T for both RC and RL circuit is 2 m sec.
Practical value of T for RC circuit is 2-3 m sec and for RL circuit is 2 m sec.
Result:
Viva Questions:
1) what is the time constant for an RL circuit?
2) What is time constant for RC circuit?
3) What is the significance of time constant?
DETERMINATION OF SELF AND
MUTUAL INDUCTANCE
Circuit Diagram:
DETERMINATION OF SELF AND MUTUAL INDUCTANCE
Aim : To determine the self and mutual inductance of a given transformer.
Apparatus:
Theory:
Procedure:
Self Inductance:-
1.
2.
3.
4.
5.
To calculate I, V, I2, V2 and Z1, Z2.
Connect the circuit as per the circuit diagram, and give the supply and connect
switch to 1 – 11 and note down the readings of V1, I1 which give Z.
Again connect switch to Z – Z1 and note down V2, I2 which gives Z2.
By using multimeter calculate the resistance of primary and secondary.
Using the formula Z = R + j XL calculate L1 and L2.
Mutual Inductance:-
1.
2.
Connect the circuit as per circuit diagram.
Adjust the variac voltage 230 v and note reading of voltmeter and ammeter and
find mutual inductance.
Precautions:
1.
Note down the readings from voltmeter and ammeter without parallax error.
Results: The coefficient of coupling of given transformer is K = 0.944.
Viva Questions:
1)
2)
3)
4)
5)
What is inductance?
What is mutual inductance?
Define coefficient of coupling?
What is the range for lc?
Can you increase the coupling coefficient between two coils?
VERIFICATION OF
COMPENSATION AND
MILLIMAN’S THEOREMS
Circuit Diagram:
1K ohm
+
A
-
4.7K ohm
20V
1K ohm
+
A
3.3K ohm
3.3K ohm
4.7K ohm
1K ohm
VC
(compensating voltage)
circuit diagram for compensation theorem
1K ohm
+
A
3.3K ohm
4.7K ohm
20V
1K ohm
]
VERIFICATION OF COMPENSATION AND MILLIMAN’S THEOREMS
AIM:- To verify compensation and Milliman’s theorem.
APPARATUS
S.NO.
Name
Rating
Quantity
THEORY
Statement of Compensation Theorem: In a linear time-in variant network if the
impedance Z of an un coupled branch carrying a current I1 is changed to (Z + ∆ Z). Then
the currents in all the branches of the network are changed. The change in the current in
any branch may calculated by assuming that an ideal voltage source of voltage VC = I
∆ Z has been connected in series with (Z + ∆ Z) when all other sources in the network
are replaced by their internal impedances. The source voltage VC opposes the original
current.
Proof:
Consider a linear time – invariant network as shown in fig (1). Suppose that we are
interested in determining the change of current in the Kth branch due to a small change
∆Z in the impedance Z of the uncoupled Kth branch as the load as shown in figure (2)
The current through branch K is given by
Vth
(1)
ZTH + Z
Set the impedance Z of the branch K be changed to (Z + ∆ Z) as shown in fig (3)
I =
Since the rest of the circuit remains un changed. The Thevenin equivalent network
remains the same as before. The current in branch K is given by
Vth
I1 =
(2)
ZTH + (Z + ∆Z )
Hence the change in current in branch K is given from (1) & (2) as
∆I
= I1 – I
=
=
∆I
=
Vth
Z + Z th + ∆Z
Vth
Z + Z th
Vth [Z th + Z − (Z th + Z + ∆Z )]
(Z + Z th )(Z th + Z + ∆Z )
I (− ∆Z )
− ∆Z
×
(Z + Z th ) Z + ∆Z + Z th
Vth
Z + Z th
From eqn (1)
-
∆I =
(3)
= I substitute I in eqn (2)
I (− ∆Z )
− VC
=
(Z + ∆Z + Z th )
Z th + Z + ∆Z
(4)
Where VC = I∆Z
The voltage VC is called the “Compensating Voltage” by using equation (4). We can
calculate the change in current in any branch. The equation (4) shows that the change in
current in branch K can be calculated by assuming that an ideal voltage source of voltage
VC = I∆Z has been connected in series with (∆Z + S) when all the sources in the
network are replaced by their internal impedances shown in fig.(4). The source voltage V
opposes the original current. Hence the compensation theorem is proved.
Uses (of compensation theorem):
1.
In finding the corresponding changes in various voltages and currents of a
network subjected to a change in one of its branches. For example we may be
interested in finding the effect of using a resistor in a network which is not of the
exact value due to component tolerance. The compensation theorem provides a
convenient method for determining such effects.
2.
The compensation theorem is particularly useful in calculating the incremental
changes in voltages and currents in all the branches of a network when one or
more of the branch impedances are changed.
Milliman’s Theorem:
Statement: When a number of voltage sources (V1, V2, . . . . Vn) are in parallel having
internal resistances (R1, R2, . . . . Rn) respecting the arrangement can be replaced by a
single equivalent voltage source V in series with an equivalent series resistance R.
Where R =
1
1
=
G
G1 + G2 + G3 ........ + Gn
(G = Conductance)
V1G1 + V2G2 + ..... + VN GN
G1 + G2 + .... + GN
Proof : Let us consider n voltage sources with internal resistances R1, R2 . . . . Rn as
shown in the fig. (6).
V =
By using source transformation method replacing all voltage sources with series
resistance as current sources in parallel with internal resistance as show n in fig.(7).
The current sources in parallel can be replaced by a single current source which is
obtained by summing individual sources as shown in fig. (8)
I =
V1 V2 V3
V
+
+
+−−−−+ n
R1 R2 R3
Rn
I = V1G1 + V2G2 + V3G3 + - - - - - - - + VnGN
1
1
1
1
=
+
+−−−−+
REQ R1 R2
RN
Geq =
1
= G1 + G2 + − − − − +Gn
Req
Req =
1
1
=
Geq G1 + G2 + − − − − +Gn
Hence Millimens theorem is proved.
Duel of Millimons Theorem:
In ‘n’ current sources I1, I2, - - - - -In having internal resistance (shunted) R1, R2 . . . . Rn
respectively connected in series then these sources may be replaced by a single current
source with shunt resistance.
Im =
I1R1 + I 2 R2 + − − − − − − + I n Rn
R1 + R2 + R3 − − − − Rn
Rm = R1 +R2 - - - - - - - +Rn
(Im1 Rm are equivalent current and equivalent resistances)
Proof: Let us consider n current sources with internal resistance are connected in series
as shown in fig. (9).
By using source transformation method convert all ‘n’ current sources to voltage sources
in series with resistance it reduces the circuit as shown in fig.(10).
Since all the voltage sources are connected in series so the total voltage is equal to sum of
all the voltages. So
Veq = I1R1 + I2R2 + - - - - - + InRn
Rm = R1 +R2 + R3 + - - - - - - - +Rn
By source transformation method transforming equivalent V source to current source we
get the network fig. (11)
Hence dual of Milliman’s theorem is proved.
PROCEDURE: To verify compensation theorem.
Step-1: Connect the circuit as per the circuit diagram shown in fig.(1).
Step-2: Now applying a voltage of 20V form the R.P.S. note down the readings applying
compensating voltage of V volts to circuit of ammeter.
Step-3: Now connect the circuit as shown in fig.(2) and note down the readings applying
compensating voltage of ‘V’ volts to circuit.
Step-4: Now add the currents obtained in step 2 and step 3.
Step-5: Again connect the circuit as shown in fig.(3) with applied voltage of 20 V and
measure
the reading of ammeter.
Step-6: Currents obtained in step 4 and step 2 should be the same.
Step-7: To Millimom’s theorem
To verify Milliman’s theorem connect the circuit as shown in fig (4)
Step-8: By applying V1 = 5V, V2 = 10V , V3 = 15V, Vn = 20V note down the load
voltage VL.
Step-9: Again connect the circuit as shown in fig (1) with V volts and R1N1s.
Step-10: Note down the voltage VL. The load voltage VL obtained in step 9 and step 10
should be the same.
PRECAUTIONS:
1.
2.
Note down the readings with out any parallel error.
All connections must be tight.
RESULT: