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CHRISTU JYOTI INSTITUTE OF TECHNOLOGY & SCIENCE
(Affiliated to JNTU Hyderabad), Colombonagar, Janagoan :506167
2012-13 IInd Semester
LABORATORY MANUAL
of
ELECTRICAL CIRCUITS AND SIMULATION
Prepared by
G.Ranjithkumar
Assistant Professor
for
IIB.Tech EEE
DEPARTMENT OF ELECTRICAL ELECTRONICS ENGINEERING
INDEX
Page No
List of experiments as per university
3
List of experiments to be conducted for this
4
semester
Cycle indicate schedule and the batch size
8-9
Guidelines For Laboratory Notebook
9-10
Experiment Name
Sl. No
Thevinin‟s and Norton‟s and Maximum Power Transfer
1.
5-7
Laboratory Practice Safety Rules
theorems.
11-25
2.
Superposition theorem.
26-29
3.
Verification of compensation theorem.
30-35
4.
Reciprocity and Millman‟s theorems
36-39
5.
Series and Parallel resonance.
40-46
Determination of self and mutual inductances and co
6.
efficient of coupling.
47-50
7.
Z and Y Parameters.
51-54
8.
Transmission and hybrid parameters.
55-60
9.
Simulation of dc circuits
61-62
10.
DC Transient response
63-64
Additional Experiments
1.
Time response of RL & RC Circuits
Appendix
2
64-67
JAWAHARLAL NEHRU TECHNOLOGICALUNIVERSITY HYDERABAD
II Year B.Tech. EEE-II Semester
Academic year 2013-2014
L T/P/D C
0
-/3/- 2
(54603)ELECTRICAL CIRCUITS & SIMULATION LAB
PART-A: ELECTRICAL CIRCUITS
1) Thevinin‟s and Norton‟s and Maximum Power Transfer theorems.
2) Superposition theorem and RMS value of complex wave.
3) Verification of compensation theorem.
4) Reciprocity and Millman‟s theorems
5) Locus diagram of RL & RC series circuits.
6) Series and Parallel resonance.
7) Determination of self and mutual inductances and co efficient of coupling.
8) Z and Y Parameters.
9) Transmission and hybrid parameters.
10) Measurement of Active power for Star and Delta connected balanced loads
11) Measurement of Reactive power for Star and Delta connected balanced loads.
12) Measurement of 3-phase power by two watt meter method for unbalanced loads.
PART-B: PSPICE SIMULATION
1) Simulation of dc circuits
2) DC Transient response
3) Mesh analysis
4) Nodal analysis
NOTE:

PSPICE Software Package is necessary.

Eight experiments are to be conducted from PART-A and any two from PART-B
3
Academic year 2013-2014
Experiments Conducted by the Department:1) Thevinin‟s and Norton‟s and Maximum Power Transfer theorems.
2) Superposition theorem and RMS value of complex wave.
3) Verification of compensation theorem.
4) Reciprocity and Millman‟s theorems
5) Series and Parallel resonance.
6) Determination of self and mutual inductances and co efficient of coupling.
7) Z and Y Parameters.
8) Transmission and hybrid parameters.
9) Simulation of dc circuits
10) DC Transient response
Additional Experiments
1. Time response of RL & RC Circuits
4
BATCH WISE (HT.No-201 to 235) STUDENT DETAILS:
Batch No.
Size of Batch
Roll Numbers
1
5
2
5
3
5
4
5
5
5
11681A0201, 11681A0203, 11681A0205, 11681A0206
11681A0207
11681A0208, 11681A0209, 11681A0210, 11681A0211
11681A0212
11681A0213,11681A0214,11681A0215,11681A0216
11681A0217
11681A0218, 11681A0219, 11681A0220, 11681A0221
11681A0222
11681A0223, 11681A0224, 11681A0225, 11681A0226
11681A0227
6
4
11681A0228, 11681A0229, 11681A0230, 11681A0231
7
4
11681A0232, 11681A0233, 11681A0234, 11681A0235
BATCH WISE (HT.No-236 to Remaining) STUDENT DETAILS:
Batch No.
Size of Batch
1
5
Roll Numbers
11681A0236, 11681A0237, 11681A0238,
11681A0239, 11681A0240
2
5
11681A0241, 11681A0242, 11681A0243,
11681A0244, 11681A0245
3
5
11681A0246, 11681A0247, 11681A0248,
11681A0249,11681A0250
4
5
11681A0251, 11681A0252, 11681A0253,
11681A0254, 11681A0255
5
5
11681A0256, 11681A0257, 11681A0258,
11681A0259,11681A0260
6
5
7
5
10681A0245, 12685A0201, 12685A0202,
12685A0203, 12685A0204
12685A0205, 12685A0206, 12685A0207,
12685A0208,12915A0217
5
FIRST CYCLE EXPERIMENTS:
Experiment No.
Experiment Name
Thevinin‟s and Norton‟s and Maximum Power Transfer theorems.
1
2
Superposition theorem and RMS value of complex wave.
3
Verification of compensation theorem.
4
Reciprocity and Millman‟s theorems
5
Series and Parallel resonance.
BATCH/WEEK WISE EXPERIMENTS DETAILS:
WEEK No.
Experiment No. To Be Conducted By Batch Of Students
Batch-1
Batch-2
Batch-3
Batch-4
Batch-5
Batch-6
Batch-7
1
1
2
3
4
5
1
2
2
2
3
4
5
1
2
3
3
3
4
5
1
2
3
4
4
4
5
1
2
3
4
5
5
5
1
2
3
4
5
1
6
SECOND CYCLE EXPERIMENTS :
Experiment No.
Experiment Name
6
Determination of self and mutual inductances and co efficient of coupling.
7
Z and Y Parameters.
8
Transmission and hybrid parameters.
9
Simulation of dc circuits
10
DC Transient response
BATCH/WEEK WISE EXPERIMENTS DETAILS:
WEEK No.
Experiment No. To Be Conducted By Batch Of Students
Batch-1
Batch-2
Batch-3
Batch-4
Batch-5
Batch-6
Batch-7
6
6
7
8
9
10
6
7
7
7
8
9
10
6
7
8
8
8
9
10
6
7
8
9
9
9
10
6
7
8
9
10
10
10
6
7
8
9
10
6
LABORATORY PRACTICESAFETY RULES
7
SAFETY is of paramount importance in the Electrical Engineering Laboratories.
2. Electricity NEVER EXECUSES careless persons. So, exercise enough care and attentionin
handling electrical equipment and follow safety practices in the laboratory. (Electricityis a good
servant but a bad master).
3. Avoid direct contact with any voltage source and power line voltages. (Otherwise, any such
contact may subject you to electrical shock)
4. Wear rubber-soled shoes. (To insulate you from earth so that even if you accidentally contact a
live point, current will not flow through your body to earth and hence you will be protected from
electrical shock)
5. Wear laboratory-coat and avoid loose clothing. (Loose clothing may get caught on an
equipment/instrument and this may lead to an accident particularly if the equipment happens to
be a rotating machine)
6. Girl students should have their hair tucked under their coat or have it in a knot.
7.Do not wear any metallic rings, bangles, bracelets, wristwatches and neck chains. (When you
move your hand/body, such conducting items may create a short circuit or may touch a live point
and thereby subject you to electrical shock)
8. Be certain that your hands are dry and that you are not standing on wet floor. (Wet parts of the
body reduce the contact resistance thereby increasing the severity of the shock)
9. Ensure that the power is OFF before you start connecting up the circuit.(Otherwise you will be
touching the live parts in the circuit)
10. Get your circuit diagram approved by the staff member and connect up the circuit strictly as
per the approved circuit diagram.
11. Check power chords for any sign of damage and be certain that the chords use safety plugs
and do not defeat the safety feature of these plugs by using ungrounded plugs.
12. When using connection leads, check for any insulation damage in the leads and avoid such
defective leads.
13. Do not defeat any safety devices such as fuse or circuit breaker by shorting across it.Safety
devices protect YOU and your equipment.
14. Switch on the power to your circuit and equipment only after getting them checked up and
approved by the staff member.
15. Take the measurement with one hand in your pocket. (To avoid shock in case you
accidentally touch two points at different potentials with your two hands)
16.Do not make any change in the connection without the approval of the staff member.
17. In case you notice any abnormal condition in your circuit ( like insulation heating up, resistor
heating up etc ), switch off the power to your circuit immediately and inform the staff member.
18. Keep hot soldering iron in the holder when not in use.
19. After completing the experiment show your readings to the staff member and switch off the
power to your circuit after getting approval from the staff member.
20. While performing load-tests in the Electrical Machines Laboratory using the brakedrums:Avoid the brake-drum from getting too hot by putting just enough water into the brakedrum at intervals; use the plastic bottle with a nozzle (available in the laboratory ) to pour the
water.(When the drum gets too hot, it will burn out the braking belts)Do not stand in front of the
brake-drum when the supply to the load-test circuit is switched off. (Otherwise, the hot water in
the brake-drum will splash out on you)After completing the load-test, suck out the water in the
brake-drum using the plastic bottle with nozzle and then dry off the drum with a spongewhich is
available in the laboratory.(The water, if allowed to remain in the brake-drum, will corrode it)
8
21. Determine the correct rating of the fuse/s to be connected in the circuit after understanding
correctly the type of the experiment to be performed: no-load test or full-load test, the maximum
current expected in the circuit and accordingly use that fuse-rating.(While an over-rated fuse
will damage the equipment and other instruments like ammeters and watt-meters in case of over
load, an under-rated fuse may not allow one even to start the experiment)
22. At the time of starting a motor, the ammeter connected in the armature circuit overshoots, as
the starting current is around 5 times the full load rating of the motor. Moving coil ammeters
being very delicate, may get damaged due to high starting current. A switch has been provided
on such meters to disconnect the moving coil of the meter during starting. This switch should be
closed after the motor attains full speed. Moving iron ammeters and current coils of wattmeters
are not so delicate and hence these can stand short time overload due to high starting current. No
such switch is therefore provided on these meters. Moving iron meters are cheaper and more
rugged compared to moving coil meters. Moving iron meters can be used for both a.c. and d.c.
measurement. Moving coilinstruments are however more sensitive and more accurate as
compared to their moving iron counterparts and these can be used for d.c. measurements only.
Good features of moving coil instruments are not of much consequence for you as other sources
of errors in the experiments are many times more than those caused by these meters.
23. Some students have been found to damage meters by mishandling in the following
ways:Keeping unnecessary material like books, lab records, unused meters etc. causing meters to
fall down the table. Putting pressure on the meter (specially glass) while making connections or
while talking or listening somebody.
STUDENTS ARE STRICTLY WARNED THAT FULL COST OF THE METER WILL BE
RECOVERED FROM THE INDIVIDUAL WHO HAS DAMAGED IT IN SUCH A MANNER.
Copy these rules in your Lab Record. Observe these yourself and help your friends to
observe. I have read and understand these rules and procedures. I agree to abide by these rules
and procedures at all times while using these facilities. I understand that failure to follow these
rules and procedures will result in my immediate dismissal from the laboratory and additional
disciplinary action may be taken.
GUIDELINES FOR LABORATORY NOTEBOOK
The laboratory notebook is a record of all work pertaining to the experiment. This record
should be sufficiently complete so that you or anyone else of similar technical background
can duplicate the experiment and data by simply following your laboratory notebook. Record
everything directly into the notebook during the experiment. Do not use scratch paper for
recording data. Do not trust your memory to fill in the details at a later time.
Organization in your notebook is important. Descriptive headings should be used to
separate and identify the various parts of the experiment. Record data in chronological order. A
neat, organized and complete record of an experiment is just as important as the experimental
work.
1. Heading:
9
The experiment identification (number) should be at the top of each page.Your name and
date should be at the top of the first page of each day's experimental work.
2.Object:
A brief but complete statement of what you intend to find out or verify in the experiment
should be at the beginning of each experiment
3.Diagram:
A circuit diagram should be drawn and labeled so that the actual experiment circuitry
could be easily duplicated at any time in the future. Be especially careful to record all circuit
changes made during the experiment.
4.Equipment List:
List those items of equipment which have a direct effect on the accuracy of the data. It
may be necessary later to locate specific items of equipment for rechecks if discrepancies develop
in the results.
5.Procedure:
In general, lengthy explanations of procedures are unnecessary. Be brief. Short
commentaries along side the corresponding data may be used. Keep in mind the fact that the
experiment must be reproducible from the information given in your notebook.
6.Data:
Think carefully about what data is required and prepare suitable data tables. Record
instrument readings directly.Do not use calculated results in place of direct data; however,
calculated results may be recorded in the same table with the direct data. Data tables should be
clearly identified and each data column labeled and headed by the proper units of measure.
7.Calculations:
Not always necessary but equations and sample calculations are often given to illustrate
the treatment of the experimental data in obtaining the results.
8.Graphs:
Graphs are used to present large amounts of data in a concise visual form. Data to be
presented in graphical form should be plotted in the laboratory so that any questionable data
points can be checked while the experiment is still set up. The grid lines in the notebook can be
used for most graphs. If special graph paper is required, affix the graph permanently into the
notebook. Give all graphs a short descriptive title. Label and scale the axes. Use units of
measure. Label each curve if more than one on a graph.
9.Results:
The results should be presented in a form which makes the interpretation easy. Large
amounts of numerical results are generally presented in graphical form. Tables are generally
used for small amounts of results. Theoretical and experimental results should be on the same
graph or arrange in the same table in a way for easy correlation of these results.
10.Conclusion:
This is your interpretation of the results of the experiment as an engineer. Be brief and
specific. Give reasons for important discrepancies.
10
1. THEVENIN’S,NORTON’S THEOREM AND MAXIMUM POWER
TRANSFER THEOREM.
THEVENIN’S THEOREM:
Aim: To verify Thevenin‟s, theorem
i)Theoretically
ii)Practically
iii)Direct test.
Apparatus:
S.No
1
2
3
4
Name of the Equipment
Bread board
Voltmeter/Multimeter
Ammeter/Multimeter
Regulated power supply unit (RPS)
Patch chords for connections
Type
Analog/Digital
Analog/Digital
DC
Range
0-25V
0-400 MA
30v/2A
Quantity
1
1
1
1
Circuit Elements:
Resistors:
Voltage source:
Current source:
Statement:
The current flowing through an impudence connected two terminals of active linear network
is same as if the same impendence is connected to a simple equivalent consisting of a constant
voltage source whose voltage is equal to the open circuit voltage measured between the two
terminals of the original network and a series impudence which is the impendence measured
between the same two terminals.
Theoretical Procedure:
Find the current through AB using thevenin‟s theorem.
11
First terminals AB should be open circuited then find “Voc“ or ”Vth”.Using mesh analysis
Calculation of RTh:
12
Thevenin’s Equivalent Circuit:
IAB =
𝑉𝑜.𝑐
𝑅+𝑅𝑡ℎ
Practical Procedure:
1)First the terminals “AB” should be open circuited then a voltmeter is connected between A and
B terminals.
Note down the voltmeter reading say as “Voc” or “VTh”.
2) DMM is connected between A and B in resistance mode then find “RTh”.
13
3) From the above circuit variable circuit R should be short circuit and adjust the voltages V1 and
V2 ammeter is connected between A and B then note down ammeter reading say IS.C.
4) Thevenin‟s equivalent circuit is
14
Direct test:
Connect the circuit diagram as shown in figure.
Note down ammeter reading say IAB
Result:
Vo.c
Rth
Theoretically
Practically
Hence the Thevenin‟s theorem is theoretically and practically verified
15
NORTON’S THEOREM:
Aim: To verify Norton‟s theorem
i)Theoritically
ii) Practically
iii) Direct test.
Apparatus:
S.No
Name of the Equipment
Type
Range
Quantity
1
Bread board
1
2
Voltmeter/Multimeter
Analog/Digital
0-25V
1
3
Ammeter/Multimeter
Analog/Digital
0-400 MA
1
4
Regulated power supply unit (RPS)
DC
30v/2A
1
Patch chords for connections
Circuit Elements:
1. Resistors:
2. Voltage source:
3. Current source(0-25)mA.
Statement:
The current flowing through an impedence connected to two terminals of a linear, active
network is same as if the same load impedence is connected to a simple equivalent network
consisting of a constant current source whose magnitude is equal to the flowing through the same
two terminals of the original network when the two terminals are short circuited and an
admittance connected in parallel, whose value is equal to the admittance measured between the
two terminals of the original network looking back into the network, when the sources in the
network are replaced by their internal admittance.
16
Theoretical Procedure:
1)First the terminals A and B should be short circuited then find ISC.
Using mesh analysis find I1,I2.
ISC=i1+i2
=i1-i2.
(According to the direction of the currents)
Calculation of ZTh:
The terminals A and B should be open circuited find ZTh.
17
Norton‟s equivalent circuit is:
For three different values of R calculate IAB.
IAB=𝐼𝑠𝑐
𝑍𝑡ℎ
𝑍𝑡ℎ + 𝑅
Practical Procedure:
1)First the terminal A B should be short circuited and an ammeter is connected between “AB”
terminals.
Note down ammeter reading say ISC.
2)DMM is connected between A and B in resistance mode then find “RTh”.
18
3) From the above circuit variable resistor R should be open circuited and adjust the voltages V1
and V2 and a voltmeter is connected between A and B then note down the reading say Voc.
4) Norton‟s equivalent circuit is:
For 3 different values of R calculate IAB(ammeter readings)
Direct Test:
Connect the circuit as shown in figure.
19
For 3 different values of R note down ammeter readings
R:
IAB:
Result:
Isc
Zth
Theoretical
Practical
Hence the Norton‟s theorem is practically and theoretically varifyed.
20
MAXIMUM POWER TRANSFER THEOREM
Aim: To verify maximum power transfer theorem.
Apparatus:
S.No
Name of the Equipment
Type
Range
Quantity
1
Bread board
1
2
Voltmeter/Multimeter
Analog/Digital
0-25V
1
3
Ammeter/Multimeter
Analog/Digital
0-400 MA
1
4
Regulated power supply unit (RPS)
DC
0-20 V
1
Patch chords for connections
Circuit Elements:
1. Resistances.
2. Decade resistance box.
Statement:
If a load impendence is connected between two terminals of linear active network, the
amount of power transferred to the load can be maximum is by adjusting the parameters to the
load impedances. This process of adjusting the load impendence for maximum transfer is called
“Matching of load impedances”.
Theoretical Procedure:
1) Determine the value of R for maximum power transfer. Hence find the maximum power
received by „R‟.
From the above circuit
21
Variable resistor „R‟ should be open circuited and adjust the voltage „V‟ then find the open
circuited voltage between A and B in Voc or VTh.
Calculation of RTh:
22
Thevenin’s Equivalent Circuit:
I=
𝑉𝑜.𝑐
𝑅+𝑅𝑡ℎ
P = I2R
Value of „R‟ for maximum power transfer in „RTh‟.
Maximum power received by R is
𝐼2 𝑅 =
𝑉𝑜.𝑐
2𝑅𝑡ℎ
2
𝑅𝑡ℎ =
2
𝑉𝑜.𝑐
4𝑅𝑡ℎ
Practical Procedure:
Fig 1
23
1) From the above circuit variable resistor „R‟ should be open circuited and adjust the voltage
„V‟ then voltmeter is connected between A and B terminals.
2) Note down voltmeter readings sayVoc or VTh.
3) DMM is connected across A and B in resistance made then findRTh or ZTh.
4) From the above fig.1 resistor R should open circuited and adjust the voltage „V‟ and an
ammeter should be connected across A and B then note down ammeter readings say as Isc.
𝑅𝑡ℎ =
24
𝑉𝑜.𝑐
𝐼𝑠𝑐
Thevenin‟s equivalent circuit is
5) For different values of „R‟ calculate various power drawn the curve between power versus
resistance.
From graph calculate Pmax and RTh.
Observations:
Theoretical values
S.No
RL
IL
PL= IL2RL
Result:
25
Practical values
IL
PL= IL2RL
2. VERIFICATION OF SUPERPOSITION THEOREM
Aim: To verify superposition theorem
1) Theoretically
2) Practically
Apparatus:
S.No
Name of the Equipment
Type
1
Bread board
2
DMM
MC/Digital
3
Regulated power supply unit (RPS)
DC
4
Connecting wires
Range
Quantity
1
30v/2A
2
Circuit Elements:
a) Active Elements:
b) Passive Elements:
Statement:
In Superposition theorem states that "In any linear bilateral network containing two or
more sources, the response in any element is equal to the algebraic sum of the responses caused
by individual sources acting alone, while the other sources are non-operative i.e., while
considering the effect of
individual
sources, other ideal voltage sources and ideal current
sources in the network are replaced by short circuit and open circuit across their terminals”.
Theoretical Procedure:
1) First by using mesh analysis find the current through AB say as “I”.
26
2) According to superposition theorem first Vs1 acting only then Vs2 is replaced by short
circuited. (Internal resistance of voltage source is zero) then find the current through „AB‟ say it
as “I1”.
3) Similarly Vs2is acting alone, Vs1 is short circuited then find the current through „AB‟ say it as
“I2”.
27
4) Total current in the resistor connected across „AB‟ is
I=I1+I2 (if currents are in same direction).
I=I1-I2 (if currents are in opposite direction).
Verification:
The current calculated by step 1 is equal to current calculated by step 4 hence
superposition theorem is verified.
Practical Procedure:
1) Connect the circuit as shown in fig (1)
2) Current through load resistor is noted as I by applying both the voltages Vs1 and Vs2
through RPS
3) Make the supply voltage Vs2 short circuited and apply Vs1 as shown in fig (2) and note
down the current through load resistor as I1.
4) Make the supply voltage Vs1 short circuited and apply Vs2 as shown in fig (3) and note
down the current through load resistor as I2.
28
5) Now verify that I = I1 + I2 theoretically and practically which proves Superposition
theorem
Verification:
The current calculated by step 1 is equal to current calculated to step 5. Hence
superposition theorem is verified.
Result:
Theoretical
Practical
I1
I2
I = I1+I2
Hence superposition theorem is theoretically and practically verified.
29
3. Verification of Compensation Theorem
Aim: To verify compensation theorem by following circuit.
Apparatus:
S.No
Name of the Equipment
Type
1
Bread board
2
DMM
MC/Digital
3
Regulated power supply unit (RPS)
DC
4
Connecting wires
Range
Quantity
1
30v/2A
2
Circuit elements:
Resistors:
Voltage sources:
Theory:
If current is in one branch of active linear bilateral network is I and the impendence of the
branch is increased or decreased by “ΔZ” change of current or voltage that would be produced
by compensation EMF, “ΔZ” introduce in to the modify branch after introducing one voltage
source equivalent to the source placed in by spitting is introduced into branch is responsible for
“ΔI”.
When the source is alone is active, the current it produced is “ΔI”.
The basic concept is change in the impedence can be replaced by suitable voltage is known
as “compensating EMF” or “compensating voltage”.
In other way compensation theorem states that any linear bi lateral network, may be
replaced by a voltage source of magnitude equal to the current passing through the element
multiplied by the value of element provided the currents and voltages in other replaced by
voltage source „V‟, which is equal to the current „I‟ passing through „R‟, multiplied by „R‟.
The theorem is useful in finding the change in current or voltage when the value of
resistance is changed in the circuit .Consider the network containing a resistance „R‟.
A small change in resistance „R‟ that is C.R current is change in all other branches is
equal to the current produced by the voltage source of the voltage source of the voltage IR. IR
which is placed in series with altered resistances.
30
Theoretical Calculations:
By applying mesh analysis to the given ckt
In loop -1
R1(I1-I3) + R2 (I1-I2) = V
R1I1 - R1I3 + R2I1 - R2I2 = V
I1(R1 + R2) - I2R2 - I3R1 = V ...........................(1)
In loop - 2
R2 (I2 - I1) + I2R4 + R3(I2 - I3) = 0
I2R2 -I1R2 + I2R4 + I2R3 - I3R3 = 0
I1R2 - I2(R2 + R3 + R4) + I3R3 = 0 ...................(2)
In loop - 3
R1(I3 - I1) + R3(I3 - I2) + I3R5 = 0
R1I3 - R1I1 + R3I3 - I2R3 + I3R5 = 0
- R1I1 - I2R3 + I3(R1 + R3 + R5) = 0
I1R1 + I2R3 - I3(R1 + R3 + R5) = 0 ...................(3)
By solving (1),(2) and (3) we get I1,I2,I3 values.
Now R5 replaced by 𝑅5′ then current flowing through this resistor is by applying mesh
analysis
31
In loop 1
R1(I1 - 𝐼3′ ) + R2(I1 - I2) = V
R1I1 - R1𝐼3′ + R2I1 - R2I2 = V
I1(R1 + R2) - I2R2 - 𝐼3′ R1 = V ............................(4)
In loop 2
R2(I2 - I1) + I2R4 + R3 (I2 - 𝐼3′ ) = 0
I2R2 - R2I1 + I2R4 + R3(I2 - 𝐼3′ ) = 0
-I1R2 + I2(R2 + R3 + R4) - R3𝐼3′ = 0
I1R2 - I2(R2 + R3 + R4) + R3𝐼3′ = 0 ...........................(5)
In loop 3
R1(𝐼3′ - I1) + R3(𝐼3′ - I2) + 𝐼3′ 𝑅5′ = 0
R1𝐼3′ - R1I1 + R3𝐼3′ - R3I2 + 𝑅5′ 𝐼3′ = 0
- I1R1 - I2R3 + 𝐼3′ (R1 + R3 + 𝑅5′ ) = 0
I1R1 + I2R3 - I1(R1 + R3 + 𝑅5′ ) = 0 ...........................(6)
By solving (4),(5) and (6) we get values of I1,I2 and𝐼3′ .
Now according to compensation theorem the difference between 𝑅5′ - R5 = ΔR.
Now compensation voltage VC = I3 ΔR
Changing current is ΔI =𝑅3′ - I3
Now the circuit is
32
By using mesh analysis
In loop 1
R1(I1 - I2) + R2(I1 - I3) = 0
I1R1 - I2R1 + I1R2 - I3R3 = 0
I1(R1 + R2) - I2R1 - I3R2 = 0 ................................(7)
In loop 2
R2(I2 - I1) + R3(I2 - I3) + R4 I2 = 0
R2I2 - R2I1 + R3I2 - R3I3 + R4I2 = 0
- R2I1 + I2(R2 + R3 + R4) - R3I3 = 0
I1R2 - I(R2 + R3 + R4) - I3R3 = 0 ...............................(8)
In loop 3
R1(I3 - I1) + R3(I3 - I2) + ΔRI3 + VC = 0
R1I3 - R1I1 + R3I3 - I2R3 + ΔRI3 + VC = 0
- I1R1 - I2R3 + I3(R1 + R3 + ΔR) + VC = 0
I1R1 + I2R3 - I3(R1 + R3 + ΔR) = VC .............................(9)
By solving (7),(8), and (9) we get I1,I2 and I3 values
Hence Theatrically Proved
33
Practical Procedure:
Step: 1
Step: 2
Step: 3
34
Result:
Theoretical
practical
I1
I2
I3
Theoretically and practically currents are same so compensation theorem is verifyed.
35
4. VERIFICATION OF RECIPROCITY AND MILLMAN’S THEOREMS
Aim:- To verify Reciprocity and Millman‟s theorems theoretically and practically.
Apparatus:-
S.No
Name of the Equipment
Type
1
Bread board
2
DMM
MC/Digital
3
Regulated power supply unit (RPS)
DC
4
Connecting wires
Range
Quantity
1
30v/2A
2
THEORY:Reciprocity theorem:- In a linear bilateral single source network if voltage at any point in the
network produces a current at same other point in the network , the same votage at other point
produces same current at the first point in that net work.
Millman’s theorem:- Consider the N no of voltage sources (V1,V2-------Vn) having a series
impedance(Z1,Z2-------Zn) are connected parallel as shown according to Millman‟s theorem all
the voltage source of the current can be represented as a single voltage can be in series with the
impedance .
Veq=(V1G1+V2G2+V3G3)/(G1+G2+G3)
Req=1/(G1+G2+G3)
Procedure:Reciprocity theorem1. Connect the circuit as shown in fig (1)
2. From fig (2) of Superposition theorem note down I2=IY.
3. Now interchange the source and ammeter as in fig (4).
4. Note down the ammeter reading as I1.
5. Now verify that Vs/ I1 = Vs/ I2theoretically and practically which proves reciprocity
theorem.
TABULAR COLUMN OF RECIPROCITY THEOREM:
36
Before interchanging the sources: fig (1)
Theoretical values
Vs
I2
Practical values
Vs/ I2
I2
Vs/ I2
After interchanging the sources: fig (4)
Theoretical values
Vs
I1
Practical values
Vs/ I1
I1
Vs/ I1
Millman’s theorem:Connect the circuit as in the fig (1).
Set the supply voltage as shown in circuit diagram.
Note the reading ammeter (I2).
Connect the circuit as in the fig (2). Note the reading of voltmeter (veg).
37
Connect the circuit as in the fig (3) measure the equivalent resistance as Regwith
help of multi meter.
Connect the circuit as in the fig (4), Apply (veg). From source, see Regvalue.
Note the reading of Ammeter as (I12).
38
Now verify IL= I1L Thus the Millman‟stherem is verified.
Result:- Verified Reciprocity &Millman‟s theorems theoretically and practically.
39
5. SERIES AND PARALLEL RESONANCE
Aim: To verify the resonant frequency and width Q-factor for given R-L-C circuit.
Apparatus:
S.No
1
2
3
4
5
Name of the Equipment
Function generator
Oscilloscope
Series & Parallel RLC CKT kit
Patch chords for connections
DMM
Type
Digital
Analog/Digital
Range
0-1MHZ
Quantity
1
1
1
Digital
Circuit Elements:
1. Resistance
2. Inductance
3. Capacitance
Theory:
The circuit is said to be in resonance if the current is on phase with the applied voltage on
circuit resonance can be divided into two parts
a) Series resonance
b) Parallel resonance
Series Resonance:
In a series R-L-C circuit current lags behind or leads the applied voltage depending upon the
value of XL and XC, XL causes the total current to lag.
1. If XL ˃ XC the circuit inductively dominant.
2. If XC ˃ XL the circuit capacitively dominant.
3. When XL = XC the circuit is under resonance
The impudence in a R-L-C circuit is parallel resistance at resonant frequency the voltage
across capacitance are equal M magnitude and 1800 out of phase with voltage across inductance
hence they cancel each other and zero voltage appear across the LC combination.
40
Condition for resonance frequency:
At resonance XL = XC
1
ωrL =
𝜔𝑟 𝐶
1
ωr2L =
𝐶
1
𝜔𝑟 =
𝐿𝐶
1
Fr =
2𝜋 𝐿𝐶
Fr =
𝜔𝑟
2𝜋
Parallel Resonance:
The parallel resonance circuit is generally called a tank circuit because of fact that circuit
stores energy on the magnetic field of coil and in the electric field of capacitor the stored energy
is transfer back and front between the capacitor and coil and vice versa. The circuit is said to be
substance of admittance is zero.
Condition for resonance frequency:
1
1
Y=
−
𝑅+𝑗 𝑋 𝐿
𝑗 𝑋𝐶
=
=
𝑅−𝑗 𝑋 𝐿
𝑅2
+ 𝑋𝐿2
𝑅−𝑗 𝑋 𝐿
𝑅2
+ 𝑋𝐿2
+
𝑗
𝑋𝐶
− 𝑗
𝑋𝐿
𝑅2
+ 𝑋𝐿2
−
1
𝑋𝐶
At Resonance
𝑋𝐿
𝑅 2 + 𝑋𝐿2
=
1
𝑋𝐶
XL = ωL,
1
𝑋𝐶
41
= 𝜔𝑐
𝜔𝐿
= ωc
𝑅 2 +𝜔 2 𝐿2
𝐿
𝐶
𝑅 2 + 𝜔2 𝐿2 =
𝜔2 +
𝑅2
1
=
𝐿2
𝐿𝐶
1
𝑅2
𝜔 =
− 2
𝐿𝐶
𝐿
2
1
−
𝐿𝐶
ω=
𝑅2
𝐿2
1
𝐹𝑟 =
2𝜋
𝑅2
1
−
𝐿𝐶
𝐿2
Theoretical Procedure:
a) Series Resonance:
1
𝐹𝑟 =
2𝜋
1
𝐿𝐶
Band width = F2 – F1
Band width =
𝐹𝑟
𝑄
XL – XC = -R
𝜔1 −
1
= −𝑅
𝜔1 𝐶
42
𝜔12 𝐿𝐶 − 1
+ 𝑅=0
𝜔1 𝐶
𝜔12 𝐿𝐶 − 1 + 𝑅𝜔1 𝐶 = 0
𝜔12 +
𝜔1 𝑅
1
−
=0
𝐿
𝐿𝐶
𝑅
𝜔1 =
−𝐿 ±
𝑅 2
𝐿
−4
1
𝐿𝐶
1
2
XL – XC = R
𝜔2 −
1
= 𝑅
𝜔2 𝐶
𝜔22 𝐿𝐶 − 1
− 𝑅=0
𝜔2 𝐶
𝜔22 𝐿𝐶 − 1 − 𝑅𝜔2 𝐶 = 0
𝜔22 −
𝑅
𝜔2 =
𝜔2 𝑅
1
−
=0
𝐿
𝐿𝐶
−𝐿 ±
𝐹1 =
𝑅 2
𝐿
+4
1
𝐿𝐶
2
𝜔1
𝜔2
𝐹2 =
2𝜋
2𝜋
Frequency at which VLmax FL =
Frequency at which VCmax FC =
Parallel Resonance:
43
1
Resonance Frequency
1
1. 𝐹𝑟 =
1
2𝜋
−
𝐿𝐶
2. Q – Factor =
=
=
Q=
𝑅2
𝐿2
𝜔𝑟 𝐿
𝑅
2𝜋𝐹𝑟2
𝑅
1
2𝜋𝐹𝑟2 𝐶𝑅
𝐹𝑟
𝐵𝑎𝑛𝑑 𝑤𝑖𝑑𝑡 ℎ
Band width =
𝐹𝑟
𝑄
Model Graphs:
Series Resonance:
44
f1= lower cut off frequency
f2 = upper cut off frequency
fr= Resonating Frequency
Practical Procedure:
a) Series Resonance:
Connect the circuit as shown in figure for series resonance circuit note down the voltage across
inductor and capacitor at different frequency.
b) Parallel Resonance:
45
Connect the circuit as shown in figure for Parallel resonance circuit note down the Current
through the coil and capacitor by varying the frequency.
Result:
Series Resonance:
Theoretical
Practical
Resonance frequency
Q Factor
Band width
Parallel Resonance:
46
Theoretical
Practical
Resonance frequency
Q Factor
Band width
The resonant frequency, Q factor and Band width for given R – L – C is verified.
6. Self and Mutual Inductance and Coefficient of Coupling
Aim:To determine self, mutual inductance of coils a, b, c and coupling co-efficient between
„a‟ and „b‟ and „a‟ and „c‟.
Apparatus Required:S.No
Meter
Type
Range
Quantity
1
Voltmeter
MI
0-300V
1
2
Voltmeter
MI
0-150V
1
3
Voltmeter
MI
0-75V
1
47
4
Ammeter
MI
0-1A
Circuit Diagram:-
1)When coil A is excited
2) When coil B is excited
3) When coil C is excited
48
1
Procedure:1. Connections are made as per the circuit diagram
2. Ensure that the Auto Transformer at 0V position before giving supply to the circuit.
3. Switch ON the supply and apply Va =90V and note down Vb, Vcand the ammeter
readings.
4. Similarly apply Va=195 and Va=200V and note down Vb, Vc and ammeter readings at
„V‟ excitation of coil „A‟.
5. Above steps are repeated by exciting coil B (95,100,105) and C (45, 50, 55).
Precautions:1. Before switching a coil which should be kept at „0‟ position.
2. While exciting a coil should be ensure that the applied voltage does not exceed its
reading.
Observation and Calculation:1) When coil A is excited
S.No Ex of CA
Va
Ia
Vb
Vc
Laa=(Va/wIa)
49
Mba=(Vb/wIa)
Mca=(Vb/wIa)
Average of Laa=
Average of Mba=
Average of Mca=
2) When coil B is excited
S.No
Ex of CB
Vb
Ib
Va
Vc
Va
Vb
Lbb=(Vb/wIb) Mab=(Va/wIb)
Mcb=(Vc/wIb)
Average of Lbb=
Average of Mab=
Average of Mcb=
3) When coil C excited
S.No
Ex of CC
Vc
Ic
Lcc=(Vc/wIc)
Average of Lcc=
Average of Mac=
50
Mac=(Va/wIc)
Mbc=(Vb/wIc)
Average of Mbc=
Coupling Coefficient:Kab= (Mab+Mba)/2 𝐿𝑎𝑎. 𝐿𝑏𝑏
Kca= (Mca+Mac)/2 𝐿𝑎𝑎. 𝐿𝑐𝑐
Kbc= (Mbc+Mcb)/2 𝐿𝑏𝑏. 𝐿𝑐𝑐
Result:The self inductance, mutual inductance of a, b, c and coefficient of coupling between „a‟ and „b‟
and „a‟ and „c‟ is determined.
Coupling Coefficient between „a‟ and „b‟ is Kab=
Coupling Coefficient between „b‟ and „c‟ is Kbc=
Coupling Coefficient between „c‟ and „a‟ is Kca=
7. Z and Y PARAMETERS
AIM: To obtain experimentally Z parameters and Y parameters of a given two port network.
APPARATUS:
S.No
Name of the Equipment
Type
1
Bread board
2
DMM
MC/Digital
3
Regulated power supply unit
DC
Range
Quantity
1
51
30v/2A
2
(RPS)
4
Connecting wires
PROCEDURE:
1. Open Circuiting Output Terminals (I2 = 0):
Connections are made as per the circuit diagram shown in fig (2). Output terminals are kept
Open via a voltmeter. Supply is given to input port. Note the readings of ammeter as I1 and
Voltmeter as V2.
2. Short circuiting output terminals (V2 = 0):
Connections are made as per the circuit diagram shown in fig (4). Output terminals are short
circuited via an ammeter. Supply is given to input port. Note the readings of ammeters as I1 and
I2.
3. Open circuiting input terminals (I1 = 0):
Connections are made as per the circuit diagram shown in fig (3). Input terminals are kept
open via an voltmeter. Supply is given to output terminals. Note the readings of ammeter as I2
and voltmeter as V1.
4. Short circuiting input terminals (V1=0):
Connections are made as per the circuit diagram shown in fig (5). Input terminals are short
circuited via an ammeter. Supply is given to output port. Note the readings of ammeters as I1 and
I2.
5. Calculate Z, Y Parameters values.
Circuit Diagram Z and Y PARAMETERS
CIRCUIT DIAGRAM:_
52
CALCULATION OF Z11AND Z21:-
CALCULATION OF Z22AND Z12 :-
CALCULATION OF Y11AND Y21 :-
53
CALCULATION OF Y22AND Y12 :-
OBSERVATIONS:
When I1=0
S.No.
V1
I2
V2
V1
I2
V2
When I2=0
S.No.
54
When V1=0
S.No.
I2
I1
V2
I2
I1
V2
When V2=0
S.No.
RESULT TABLE:
Z Parameters
Z11
Z12
Y Parameters
Z21
Z22
Y11
Y12
Theoretical
Practical
PRECAUTIONS:
1. Avoid making loose connections.
2. Readings should be taken carefully without parallax error.
3. Avoid series connection of voltmeters and parallel connection ammeters.
RESULT: Experimentally Determined Z and Y Parameters of Two Port Networks
55
Y21
Y22
8. Two Port network parameters
ABCD and h-Parameters
Aim:-To determine ABCD and h - parameters
i)
Theoretically
ii)
Practically
Apparatus:S.No
Name of the Equipment
Type
1
Bread board
2
DMM
MC/Digital
3
Regulated power supply unit
DC
Range
Quantity
1
30v/2A
2
(RPS)
4
Connecting wires
Circuit Elements:i.
Resistors:
ii.
Voltage Sources:
Theory: - - Port is defined as any pair of terminals into which energy is supplied, as from which
energy is withdrawn or where the network variables may be measured. The current entering into
the first part is taken as V1 and I1 at port-2 as V2 and I2 .Among these four variables two are
taken as dependent variables and other two are taken as independent variables and different
parameters are found.
ABCD Parameters:Theoretical Procedure:-In this V1 and I1 are taken as independent variables while V2 and I2 are
considered as dependent variables
V1=AV2+BI2
…………………… (1)
I1=CV2+DI2
…………………… (2)
𝑉1
𝐴
=
𝐼1
𝐶
56
𝐵 𝑉2
𝐷 𝐼2
Chain Matrix Method:-
From loop equations (1) & (2)
…………………. (3)
V1= (R1+R3) I1-R3I2
-V2=-R3I1+ (R2+R3) I2
…………………… (4)
From equation (4)
I1= (V2/R3) + ((R2+R3)/R2) I2
…………….. (5)
Substitute equation (5) in equation (3)
V1= (R1+R3) [(V2/R3) + (R2+R3)/R3)] I2-R3I2
= [(R1+R3)/R3] V2+ [{(R1+R3) (R2+R3)-(R3)2}/R3] I2
V1= [(R1+R3)/R3] V2+ [(R1R2+R1R3+R2R3)/R3] I2
Compare equations (1) and (6)
A= (R1+R3)/R3
C=1/R3
Compare equations (2) and (5)
B= (R1R2+R2R3+R3R1)/R3
D= (R2+R3)/R3
Analytical Verification:When port 2 is open circuited
I2=0
From equations (1) and (2)
V1=AV2
;
I1=CV2
57
…………………….. (6)
A=V1/V2 ; C=I1/V2
Req=R1+R3
V2=I1R3
V1/I1= R1+R3
A=V1/V2= (R1+R3)/R3
C=I1/V2= 1/R3
When port 2 is short circuited
From equation (1) & (2)
V1=BI2
I1= DI2
Req= [(R2R3)/ (R2+R3)] +R1
= (R1R2+R2R3+R3R1)/ (R2+R3)
V1=I1Req
I1=V1/Req
I2=I1 {R3/ (R2+R3)}
D= I1/I2= (R2+R3)/R3
Substituting I1
I2= (V1/Req) {R3/ (R2+R3)}
B= V1/I2
58
B= (R1R2+R2R3+R3R1)/R3
Practical Procedure for ABCD Parameters:
V1=
I1=
V2=
I1=
I2=
V1=
H-Parameters:Theoretical Procedure: - In this V2 and I1 are taken as independent variables, while V1 and I2
are taken as dependent variables.
V1=h11I1+h12V2
I2=h21I1+h22V2
Analytical Procedure:For determining h11 and h21
Thus port 2 is shorted. Therefore
59
V2=0
I1=V1/Req
Req= {R2R3/ (R2+R3)} +R1
h11=V1/I1
h21=I2/I1
I2=I1 {R2/ (R2+R3)}
For determining h12 and h22
Port 1 should be open circuited
h12=V1/V2
h22=I2/V2
Req= (R1R2+R2R3+R3R1)/ (R2+R3)
I2=V2/ (R2+R3)
V1=I2R2
60
Practical Procedure:When port 2 is short circuited
When port 1 is open circuited
Result:Therefore ABCD and h-parameters are determined for the given circuit.
Parameters
Theoretical value
Practical value
A
B
C
D
h11
h12
h21
h22
Hence we calculated ABCD and h – Parameters for the given network and verified practically as
well as theoretically.
61
SPICE Simulation of Thevinin’s DC Circuit
Aim: - A DC circuit shown in figure here SPICE to calculate and print
i. Voltage gain V(2,4)/Vin
ii. The input resistance Rin=Vin/Iin
iii. Thevenin‟s resistance
iv. Thevenin‟s voltage between nodes 2 and 4
Apparatus Required:i. P-SPICE software
ii. Computer kit
Theory:The current flowing through impedance connected to two transient of an active linear
network is same as equivalent consisting of constant voltage source whose voltage is equal
to the output circuit voltage measured between the two terminals of the original network. A
service of impedance which is the impedance between the same two terminals looking back
into the network when out the source in the network.
Circuit Diagram:1
R1=5
R2=1
0
2
3
R3=20
Vth=V(2,4)
vin=10
V
R4=40
5
0
R5=10 Vx=0
62
4
Is=2a
Program:Vin
1
0
DC
10V
Is
4
3
DC
0V
Vx
4
5
DC
0
R1
1
2
5
R2
2
3
10
R3
2
0
20
R4
3
4
40
R5
5
0
10
 TF V(2,4)
Vin
 Trans 1μs
400μs
 Probe
 end
Result:Hence node voltage is calculated .So transient response is verified.
Out Put:
63
10. Simulation of DC Circuit
Aim:-To study the DC transient response of RLC series circuit.
Apparatus Required:iii. P-SPICE software
iv. Computer kit
Theory:When a network is switched from one condition to another by change in applied voltage
or by change in anyone of the circuit elements during a period of time .Branch current and
voltage change from the initial value to new values. The time interval is called “Transient
Period”. The response or output of the network during transient period is called transient
response of the network.
Circuit Diagram:R=2Ω
1
=
2
Ω
L=50uh
C=10uf
2
=
2
Ω
3
=
2
Ω
vinDC
0
Program:RLC series circuit for step input
Vin 1 0 pwl (0 0 1ns 1v 1ms 1v)
R 1 2 2 ohm
L 2 3 50μH
C 3 0 10μF
 Tran 1μs 400μs
64
 Probe
 end
Model Graph:-
V
1
V
1ns
1ms
Time
Result:Initial
Transient
solution
Node 1
Voltages
Node 2
voltage
Nodes
Voltage
1
0.00
2
0.000
3
0.000
Voltage
Source
currents
Name
Current
Vin
0.00(- +0.00
Total power dissipation 0.00(- +00 watts
Transient response of series RLC circuit for step input is studied and verified.
65
Additional Experiments:
1. Time response of RL & RC Circuits
AIM:-To draw the time response of first order R-L & R-C Networks for periodic non sinusoidal
functions and determination of time constant.
APPARATUS:S.No
Name of the Equipment
Type
Range
Quantity
1
Function generator
Digital
0-1MHZ
1
2
Oscilloscope
Analog/Digital
4
Patch chords for connections
5
DMM
Digital
PROCEDURE:1. Make connections as per the circuit diagram.
66
1
2. Give 2V Peak to peak square wave supply through function generator with suitable
frequency.
3. Take out put across inductor in RL Circuit, across capacitor in RC Circuits.
4. Calculate the time constant from CRO.
5. For deferent values of T and V Calculate corresponding (L/R) Values.
6. Compare the time constant theoretically and practically.
OBSERVATIONS:Type
Voltage
of
Time
Time constant
Time
period
Practical
constant
circuit
theoretical
Model graph:-
67
RESULT:- Time Response of R-L and R-C Circuit was Observed.
68