EC & S Lab Manual 2010

DEPARTMENT OF EEE EC&S LAB

LENDI INSTITUTE OF ENGINEERING & TECHNOLOGY 1

VERIFICATION OFSUPERPOSITION AND

RECIPROCITY THEOREMS



Experiment no: Batch no: Date:

VERIFICATION OF SUPERPOSITION& RECIPROCITY THEOREMS

AIM : To verify Superposition & Reciprocity theorems for the given network.

APPARATUS :

THEORY:-

I. Superposition Theorem Statement:

In a linear network with several independent sources which includeequivalent sources due to initial conditions and linear dependent sources, the overallresponse in any part of the network is equal to the sum of the individual responses dueto each independent source, considered separately, with all other independent sourcesreduced to zero.

Note: 1. The sources which are considered one at a time making all other sources zero,are the independent sources including sources due to initial conditions only. Thedependent sources are retained as they are in the network. 2. When one independent source is considered & all other independent sourcesare reduced to zero means that all the other independent voltage source are replaced withshort circuit and all the other independent current sources are replaced with open circuit.If the sources contain internal impedances, that sources are replaced by their internalimpedances.

II. Reciprocity Theorem Statement:

The Reciprocity theorem states that the ratio of response to excitation isinvariant to an interchange of the position of the excitation and response in a singlesource network. However if the excitation is a voltage source, the response should be acurrent and vice versa.

S. No Name of Apparatus Type Range Quantity1 Voltmeter PMMC 0-300V 2

2 Ammeter PMMC 0-2.5A 1

3 RheostatWWWWWWWW

50 /5A110 /2A

300 /1.7A300 /2A

2112

4. Fuse TCC 5A 4



PROCEDURE:-

I. SUPERPOSITION THEOREM:

1. Connect the circuit as per the Circuit diagram.2. Close Switch S1 on to the Supply mains & remain Switches S2 & S3 open and

Switch S4 closed.3. Note down the Voltmeter readings V1 ,V2 & Ammeter reading as I' in the S.No1 of Table14. Now close Switch S2 on to the Supply mains & remain Switches S1 & S4 open and

Switch S3 closed.5. Note down the Voltmeter readings V1 ,V2 & Ammeter reading as I" in the S.No2 of Table16. Now Close Switches S1 & S2 on to the Supply mains & remain Switches S3 & S4 open. 7. Note down the Voltmeter readings V1 ,V2 & Ammeter reading as I in the S.No3 of Table18. Finally disconnect the circuit from the Supply mains by open all the Switches.

II. RECIPROCITY THEOREM:

CASE : I

1. Connect the circuit as per the Circuit diagram.2. Close Switch S1 on to the Supply mains3. Note down the Voltmeter V1& Ammeter A1 readings in S. No. 1 of Table 24. Disconnect the circuit from the Supply mains by opening the Switch S1.

CASE : II

1. Connect the circuit as per the Circuit diagram.2. Close Switch S2 on to the Supply mains3. Note down the Voltmeter V2 Ammeter A2 readings in S. No. 2 of Table 24. Disconnect the circuit from the Supply mains by opening the Switch S2.

OBSERVATION TABLE:-

TABLE 1

S.No. Voltmeter Reading Voltmeter Reading Ammeter Reading

1. V1 = V2 = I' =

2. V1 = V2 = I" =

3. V1 = V2 = I =



TABLE 2

S.No. Voltmeter Reading Ammeter Reading1. V1 = I1 =2. V2 = I2 =

PRECAUTIONS:

1. Avoid Loose Connections.2. Readings must be taken without parallax error.3. Before switching on the supply for the circuit, ensure that all rheostats are at maximumposition and during the experiment these should not be disturbed.

RESULTS:

I. SUPERPOSITION THEOREM: Theoretical Practical

1. I' =

2. I" =

3. I =

II. RECIPROCITY THEOREM: Theoretical Practical 1. V1/ I1 =

2. V2/ I2 =

CONCLUSIONS:

VIVA QUESTIONS:

1) What are the Statements of the above theorems?2) What is a linear network?3) Where the above theorems are used practically?4) What are the practical applications of the above theorems?5) What is a bilateral network? Give examples.6) What are the limitations of above theorems?



VERIFICATION OF THEVENIN’SNORTON’S &MAXIMUM POWER

TRANSFER THEOREMS




A) VERIFICATION OF THEVENIN S& NORTON S THEOREMS

AIM : To verify Thevenin’s & Norton’s theorems for the given circuit.

APPARATUS:

S. No Name of Apparatus Range Type Quantity1 Voltmeters 0-300V MI 22 Ammeter 0-2A MI 2

3 Rheostats50 , 5A

110 , 2A200 , 2A

WWWWWW

211

4 1- Variac 230V / (0-270)V,15A ---- 1

5. SPST ---- ---- 26. Fuse 5A TCC 2

THEORY:-

I) Thevenin s Theorem Statement:

Any combination of linear bilateral circuit elements and active sources,regardless of the connection or complexity, connected to a given load RL, may bereplaced by a simple two terminal network consisting of a single voltage source of Vthvolts and single resistance Rth in series with the voltage source, across the twoterminals of the load RL . The Vth is the open circuit voltage measured at the twoterminals of interest, with load resistance RL removed. This voltage is also calledThevenin s equivalent voltage. The Rth is the Thevenin s equivalent resistance of thegiven network as viewed through the open terminals with RL removed and all the activesources are replaced by their internal resistances. If the internal resistances are notknown then independent voltage sources are to be replaced by the short circuit whilethe independent current sources must be replaced by open circuit.



II) Norton s Theorem Statement :

Any combination of linear bilateral circuit elements and active sources,regardless of the connection or complexity, connected to a given load RL, can bereplaced by a simple two terminal network, consisting of a single current source of INamperes and a single resistance RN in parallel with it, across the two terminals of theRL. The IN is the short circuit current flowing through the short circuited path, replacedinstead of RL. It is also called Norton s current. The RN is the equivalent resistance ofthe given network as viewed through the load terminals, with RL removed and all theactive sources are replaced by their internal resistances. If the internal resistances areunknown then the independent voltage sources must be replaced by short circuit whilethe independent current sources must be replaced by open circuit.

PROCEDURE:-

I) FOR CIRCUIT 1:

1. Connect the circuit as per the circuit diagram.2. Apply 230 V AC Supply to the Variac (with its variable position at 3C) by closing the DPST Switch.3. Gradually vary the variable position of the Variac until the Voltmeter1 reads 200 V.4. Note down the corresponding readings of Ammeter & Voltmeter2 in Table 1 with the conditions i) SPST 1 Closed & SPST 2 Open ii) SPST 1 Open & SPST 2 Open iii) SPST 1 Closed & SPST 2 Closed5. Gradually vary the variable position of the Variac until the Voltmeter1 reads 0 volts6. Disconnect the Variac from the supply by opening the DPST Switch.

II) FOR CIRCUIT 2:

1. Connect the circuit as per the circuit diagram.2. Apply 230 V AC Supply to the Variac (with its variable position at C ) by closing the DPST Switch.3. Gradually vary the variable position of the Variac until the Voltmeter reads 150 V & note down the corresponding reading of Ammeter in Table 2.4. Gradually vary the variable position of the Variac until the Voltmeter reads 0 volts5. Disconnect the Variac from the supply by opening the DPST Switch



III) FOR CIRCUIT 3:

1. Connect the circuit as per the circuit diagram.2. Apply 230 V AC Supply to the Variac (with its variable position at C ) by closing the DPST Switch.3. Gradually vary the variable position of the Variac until the Voltmeter reads Vth , as obtained in Table 14. Close the SPST Switch & vary the rheostat until the Ammeter reads current I for which Vth / I gives Rth , the value as obtained in Table 2 .5. Once the Rheostat set to Rth , open the SPST Switch & note down the reading of the Ammeter in Table 36. Gradually vary the variable position of the Variac until the Voltmeter reads 0 volts7. Disconnect the Variac from the supply by opening the DPST Switch

IV) FOR CIRCUIT 4:

1. Connect the circuit as per the circuit diagram.2. Use the same Rheostat which set to Rth as in the Circuit 33. Apply 230 V AC Supply to the Variac (with its variable position at C) by closing the DPST Switch.4. After closing the SPST switch gradually vary the variable position of the Variac until

the Ammeter1 reads current IN as obtained in Table 1 & note down the correspondingreading of the Ammeter2 in Table 4.

5. Gradually vary the variable position of the Variac until the Voltmeter reads 0 volts6. Disconnect the Variac from the supply by opening the DPST Switch

OBSERVATION TABLE:-

TABLE 1 (For Circuit 1)

S.No Switch conditions Voltmeter V1 Voltmeter V2 Ammeter1. SPST 1 Closed

SPST 2 Open VS = VL = IL =2. SPST 1 Open

SPST 2 Open VS = Vth = IL = 03. SPST 1 Closed

SPST 2 Closed VS = VL = 0 IN =


S.No Voltmeter Ammeter Rth = VS / IS

1. VS = IS = Rth =




S.No Voltmeter Ammeter1. Vth = IL =


S.No Ammeter I1 Ammeter I21. IN = IL =

PRECAUTIONS:-

1. Avoid loose connections.2. Avoid Parallax error.3. Before switching on the supply for each circuit, ensure that all rheostats are atmaximum position and during the experiment these should not be disturbed.4. Variable position of the Variac (auto transformer) should be at minimum positionbefore switching on the power supply.

RESULTS:- Theoretical Practical

1. IL from the Main circuit =

2. IL from the Thevenin’s Equivalent Circuit =

3. IL from the Norton’s Equivalent circuit =

CONCLUSIONS:-

VIVA QUESTIONS:-

1) What is the Statement of Thevenin’s theorem?2) What is a linear network?3) What is a bilateral network?4) What are Active & Passive elements?5) What are the applications of the above theorem?6) What are the limitations of application of this theorem?



B) VERIFICATION OF MAXIMUM POWERTRANSFER THEOREM

AIM : To verify Maximum Power transfer theorem for the given circuit.

APPARATUS:

S. No Name of Apparatus Type Range Quantity

1 Voltmeter MC MC

0-300V0-150V

11

2 Ammeter MC 0-2A 1

3 RheostatWWWWWW

100 /5A50 /5A200 /2A

211

4. Fuse TCC 5A 2

THEORY:

Statement: The Maximum Power transfer theorem states that A Resistance load RL,

being connected to a DC network, receives maximum power when it is

equal to the internal resistance of the source network as seen from the

load terminals i.e. Rth”



With reference to Fig (B)

Lth

thL RR

VI+

=

While the power delivered to the resistive load is

( )( ) L

Lth

thLLL R

RRVRIP ×+

== 2

22

PL can be maximized by varying R and hence, maximum power can be delivered when(dPL/dRL) = 0

( ) ( ) ( )

( )04

2222

=+

+−+⇒

Lth

LthL

LthLthL

Lth

RR

RRdRdRVRV

dRdRR

( ) ( ) ( )( )

02

4

222

=+

+⋅⋅−+⇒

Lth

LthLththLth

RRRRRVVRR

( ) 02 =⋅−+⇒ LLth RRR

thL RR =⇒

Hence it has been proved that power transfer from a dc source network to a resistivenetwork is maximum when the load resistance of the network is equal to the internalresistance of the dc source

Again with RL=Rth, the system being perfectly matched for load and source,power transfer becomes maximum and this amount of power (Pmax) can be obtained as

( ) th

th

thth

thth

RV

RRRVP

4

2

2

2

max =+

=

The total power supplied is thus

th

th

th

thin R

VR

VP24

222

=⋅=

During maximum power transfer the efficiency of the circuit becomes,.

%50100max =×=inP

Pη



PROCEDURE:-

I) TO FIND POWER VARIATIONS WITH RL

1. Connect the circuit as per the Circuit diagram 1.2. Apply 220 V DC Supply to the circuit by closing the DPST Switch.3. Note down the readings of Ammeter & Voltmeter in Table 1 which are connected across the load after keeping the load rheostat, RL at its minimum value.4. Increase the load resistance in steps and for each step, note down the corresponding Ammeter and Voltmeter readings in Table 1.5. Disconnect the circuit from the supply by opening the DPST Switch.

II) TO FIND Rth

1. Connect the circuit as per the Circuit diagram 2.2. Apply 220 V DC Supply to the circuit by closing the DPST Switch.3. Note down the readings of Ammeter & Voltmeter in Table 2.4. Disconnect the circuit from the supply by opening the DPST Switch.

OBSERVATION TABLE:-

TABLE 1

S No VL (volts) IL (amps) RL = VL/ IL ( ) PL = IL2RL

1.

2.

3.

4.

5.

6.

7.

8.

9.

10.



TABLE 2

S No VS (volts) IS (amps) Rth = VS/IS

1.

MODEL GRAPH:-

PRECAUTIONS:-

1. Avoid loose connections.2. Avoid Parallax error.3. Take more number of readings for a better plot

RESULTS:-

1. Pmax = ----------2. RL = ---------3. Rth = ---------4. = ---------

CONCLUSIONS:-

VIVA QUESTIONS:-

1) What is the Statement of Maximum Power Transfer theorem?2) What is a linear network?3) What is a bilateral network?4) What are the applications of the above theorem?5) What are the advantages & disadvantages of the above theorem?



DETERMINATION OF TWOPORT NETWORK PARAMETERS




DETERMINATION OF TWO PORT NETWORK PARAMETERS

AIM: To determine Z, Y, ABCD and H parameters of a given two port Network.

APPARATUS:

S.No Specification Range Type Quantity1 Voltmeter (0-300)V PMMC 22 Ammeter (0-5)A PMMC 2

3 Rheostat (50 , 5A) Wire Wound 34 Switches ------ DPDT 2

5 Fuses 5A Tin CoatedCopper 2

6 Connecting Wires 1 Square mm Insulatedcopper

As perRequirement

THEORY:

A network containing two pairs of terminals is called as two port network.Normally one pair of terminals coming together to supply power or to withdraw power orto measure the parameters, are called as port. To achieve simplicity, the whole network isshown with a single block.

A typical two port network is as shown below in fig (a)



OPEN CIRCUIT IMPEDANCE PARAMETERS (Z-parameters):

Z-parameters can be defined by the following equations

V1 = Z11I1 + Z12I2 …………………… (1)

V2 = Z21I1 + Z22I2 …………………… (2)

Matrix form:

( )3...............................2

1

2221

1211

2

1

∗

=

II

ZZZZ

VV

If port 2-21 is open circuited, i.e. I2 = 0 then

Z11 = V1/I1 & Z21 = V2/I1

If port 1-11 is open circuited, i.e. I1 = 0, then

Z12 = V1/I2 & Z22 = V2/I2.

Here,

Z11 is the driving point impedance at port 1-11 with 2-21 open circuited. It canalso be called as open circuit input impedance.

Z21 is the transfer impedance at port 1-11 with 2-21 open circuited. It can also becalled as open circuit forward transfer impedance.

Z12 is the transfer impedance at port 2-21 with 1-11 open circuited. It can also becalled as open circuit reverse transfer impedance and

Z22 is the driving point impedance at port 2-21 with 1-11 open circuited. It can alsobe called as open circuit output impedance.

Z-parameter representation for a two port network, shown above, will be asshown below in fig (b)



If the

Network is

a) Reciprocal then V1/I2 (where I1 = 0) = V2/I1 (where I2 = 0) i.e. Z12 = Z21

b) Symmetrical then V1/I1 (where I2 = 0) = V2/I2 (where I1 = 0) i.e. Z11 = Z22

SHORT CIRCUIT ADMITTANCE PARAMETERS (Y-parameters):

Y-parameters can be defined by the following equations

I1 = Y11V1 + Y12V2 ………………. (1)

I2 = Y21V1 + Y22V2 ………………. (2)In matrix form

( )3...............................2

1

2221

1211

2

1

∗

=

VV

YYYY

II

If port 2-21 is short circuited, i.e. V2 = 0 then

Y11 = I1/V1 & Y21 = I2/V1


Y12 = I1/V2 & Y22 = I2/V2

1

21

I2I1

Z11

+_

Z22

Z12I2 Z21I1

2

11

V2V1

Fig (b) Open circuit impedance parametric representation of a two port net work.

+_



Here, Y11 is the short circuit driving point admittance at port 1-11 with 2-21

short circuited. It will also be called as short circuit input admittance.

Y21 is the Transfer admittance at port 1-11 with 2-21 short circuited. It willalso be called as short circuit forward transfer admittance.

Y12 is the Transfer admittance at port 2-21 with 1-11 short circuited. It willalso be called as short circuit reverse transfer admittance and

Y22 is the driving point admittance at port 2-21 with 1-11 short circuited. Itcan also be called as short circuit output admittance.

Y-parameter representation for a two port network, shown above, will be asshown below

If the network is

a) Reciprocal then I2/V1 (where V2 = 0) = I1/V2 (where V1 = 0) i.e. Y21 = Y12

b) Symmetrical then I1/ V1 (where V2 = 0) = I2/ V2 (where V1 = 0) i.e. Y11 = Y22

Hybrid Parameters (h-Parameters):

h-parameters can be defined by the following equations

)2.....(..............................)1......(..............................

2221212

2121111

VhIhIVhIhV

+=+=

1

21

I2I1

Y11 Y22Y12V2 Y21V1

2

11

V2V1

Fig(c) Short circuit admittance parameter representation of a two port net work.



In matrix form

)3(..............................2

1

2221

1211

2

1

⋅

=

VI

hhhh

IV


1

221

1

111 &

IIh

Ivh ==

h11 is called input impedance and h21 is called forward current gain.

If port 1-11 is open circuited, i.e., I1=0 then

2

222

2

112 &

vIh

vvh ==

h22 is called output admittance and h12 is called reverse voltage gain.

ABCD Parameters:

ABCD parameters can be defined by the following equations

)2..(....................).........()1.(....................).........(

221

221

IDCVIIBAVV

−+=−+=

In matrix form

)3.........(....................2

2

1

1

−

=

I

VDCBA

IV

h22

1

I1

h11

+-h12V2

11

V1

Fig (d) Hybrid parametric representation of a two port net work.

21

I2

h21I1

2

V2



If port 2-21 is open circuited i.e., I2=0 then

2

1

2

1 &VIC

VVA ==

A is called reverse voltage ratio and C is known as transfer admittance.

If port 2-21 is short circuited i.e., V2=0 then

2

1

2

1 &I

IDI

VB−

=−

=

B is called transfer impedance and D is called reverse current ratio.

PROCEDURE:-

1. Connect the circuit as per circuit diagram.2. With the Switches S2 open, S3 close to 11' and S4 open, note down the

corresponding readings of voltmeter and ammeter in S.No 1 in Tabular form afterclosing the Switch S1 to supply mains

3. With the Switches S1 open, S4 close to 33' and S3 open, note down thecorresponding readings of voltmeter and ammeter in S.No 2 in Tabular afterclosing the Switch S2 to supply mains

4. With the Switches S2 open, S3 close to 11' and S4 close to 44', note down thecorresponding readings of voltmeter and ammeter in S.No 3 in Tabular afterclosing the Switch S1 to supply mains

5. With the Switches S1 open, S3 close to 22' and S4 close to 33 ', note down thecorresponding readings of voltmeter and ammeter in S.No 4 in Tabular afterclosing the Switch S2 to supply mains

OBSERVATION TABLE:-

S.NO Test Condition V1 (V) I1 (A) V2 (V) I2 (A)

1Port 2 Open(I2 = 0) and

Port-1 Active

2Port 1 Open(I1=0) and

Port-2 Active

3Port 2 Short (4 - 4’)

(V2=0) andport-1 active

4Port 1 Short (2 - 2’)

(V1=0) andPort-2 active



PRECAUTIONS:

1. Note down the readings of voltmeter and ammeter without parallax error.2. The current through a particular element should be maintained below its current

rating.3. The conditions of switches should be thoroughly checked before making the

circuit live

RESULTS:

Name of theParameter Theor Pract Theor Pract Theor Pract Theor Pract

Z-parameter Z11= Z12= Z21= Z22=

Y-parameter Y11= Y12= Y21= Y22

h-parameter h11= h12= h21= h22

ABCD-parameters A= B= C= D=

CONCLUSIONS:

VIVA QUESTIONS:

1) What is the significance of the two port parameters?2) How you know the admittance parameters from impedance parameters?3) What are the application of Z& Y parameters?4) What is the condition for reciprocal network?5) What is the condition for symmetrical network?6) What is a Lattice network?7) What is a Ladder network?



DETERMINATION OFSELF, MUTUAL

INDUCTANCES ANDCOEFFICIENT OF

COUPLING




DETERMINATION OF SELF, MUTUAL ANDCOEFFICIENT OF COUPLING

AIM:To determine the self inductance of a given transformer windings.To determine the mutual inductance and coefficient of coupling of a given transformer.

APPARATUS:

S.NO COMPONENTSREQUIRED RATING TYPE QUANTITY

1. Voltmeter (0-300)V PMMI 2

2. Ammeter (0-5)A PMMI 2

3. Switches ---- DPST 2

4. Fuse 10A Tin coated copper 2

5. Connecting wires 1mm2 ---- As per required

THEORY:

The property of the coil which opposes any change in the current passingthrough it is called self inductance or only inductance. It is analogous to electrical inertiaor electromagnetic inertia.

MAGNITUDE OF SELF INDUCED EMF: From Faradays law of electromagneticinduction, self induced emf can be expressed as

E= - Nd /dt

Negative sign indicate the direction of emf opposing change in current due to which itexists.

The flux can be expressed as

= (flux/ampere)*ampere = ( /I)*I



Now as long as permeability is constant, ratio of flux to current remains constant.

Rate of change of flux= ( /I)*rate of change of current

d /dt= ( /I)*(dI/dt)

e= (-N /I)*(dI/dt)

e= - (N /I) dI/dt

The constant N /I in this expression is nothing but the quantitative measure of theproperty due to which coil opposes any change in current. So this constant is calledcoefficient of self inductance and denoted by L.

L= N /I where its units are henry (H)

MUTUAL INDUCTANCE: The mutual inductance between the two circuits isdefined as the flux linkage of one circuit to the current in the other circuit. Thus theinductance M12 is given by

M12=flux linkage in circuit 1/current in circuit 2= (N1 21)/I2

Similarly mutual inductance M21 is given by M21=flux linkage in circuit 2/current incircuit 1= (N2 12)/I1

If the medium surrounding two circuits in linear without ferromagnetic material, thenmutual inductance represented in equation are equal, thus for linear medium around, twocircuits we can write

M12=M21=M where units are Henry (H)

COEFFICIENT OF COUPLING: When two magnetic circuits kept closed to eachother interact with each other magnetically through flux linkage in the circuit, due tocurrent in other circuit then the circuits are called magnetically coupled circuits.

M=K*[ (L1*L2)]Where K is called coefficient of coupling between two coils.

When two magnetic circuits are coupled together in series aiding and if M is the mutualinductance between them, then effective inductance of system is given by

Leq= (L1+L2+2M) H

Similarly two magnetic circuits with inductance L1 and L2 are magnetically coupled inseries opposing then effective inductance is given by

Leq= (L1+L2-2M) H



APPLICATIONS:

Transformer being a static with full load efficiency around 98% areextensively used in various applications. The various applications may cause under anyone of the following categories.

(1)Steeping up of voltage: Electrical energy in generating like hydro power stations,situated fart away from consumers, is generating at a voltage around 11kv.Fortransmitting the power from generating stations to the place of use by long transmissionlines, it is more economical to raise the level of voltage of transmission of 230kv or400kv’s.This steeping up of voltage is carried by installing transformer.

(2) Steeping down of voltage: High tension consumers are provided with electrc powersat 11kv or 6.6kv, 3-phase.The consumers at his/her cost has to install transformer to stepdown the voltage to 415v,3-phase to shift their requirement.

(3)Instrument extension: To measure high current in the order of several hundreds ampereand voltage of several kilowatt measurements transformers are used along with ammeterand voltmeter of lower range.



PROCEDURE:SELF INDUCTANCE:1. Connect the circuit as per the circuit diagram.

2. Give the supply and connect switch to 1-1 and note down the readings ofV1 and I1 which gives Z1.

3. Connect switch to z-z1 and note down the readings of V2 and I2 which gives Z2.4. By using the multimeter calculate the resistance of primary and secondary.

5. Using the formula Z=R+jXc, calculate L1 and L2.

MUTUAL INDUCTANCE:1. Connect the circuit as per circuit diagram.2. Adjust the variac voltage 230v and note the readings of voltmeter and ammeter andfind mutual inductance.

OBSERVATION TABLE:SELF INDUCTANCE:

S.NO SWITCH ‘S’POSITION

VOLTMETERREADING(V)

AMMETERREADING(A) RESISTANCE( )

MUTUAL INDUCTANCE:

S.NO VOLTMETERREADING(V)

AMMETERREADING(A) RESISTANCE( )

PRECAUTIONS:1. Note down the readings from ammeter and voltmeter without parallax errors.

2. Care should be taken that the ammeter reading should not exceed the rated value.

RESULT:Hence the mutual inductance of a given transformer is verified.Hence the self inductance of a given transformer is verified.



DETERMINATION OFFORM FACTOR OF ANON-SINUSOIDAL

WAVEFORM




DETERMINATION OF FORM FACTOR OF NON-SINUSOIDAL WAVEFORM

AIM:To determine the form factor of a non-sinusoidal waveform.

APPARATUS:

S.NO Name of Apparatus RANGE TYPE QUANTITY1 Voltmeter (0-300)V PMMI 12 Ammeter (0-5)A PMMI 13 Rheostat 12 /5A WW 14 Fuse 5A TCC 25 CRO 20MHZ 16 Connecting wires 1mm2 As required

NAME PLATE DETAILS:

S.NO RATING TRANSFORMER AUTOTRANSFORMER

1 KVA 2 2.7

2 Voltage 115/230V (0-270)V

3 Current 17.4A/8.7A 10A

4 Frequency 50HZ 50HZ

THEORY:

AVERAGE VALUE: In a.c circuit applications we are interested in finding out value of awaveform, that wave could be sinusoidal, triangular or any other shape.DEFINITION: The value of a cycle of a waveform in the area under the waveformdivided by length of one cycle.Mathematically vavg= (1/T) 0

TVdt where T is time period

Vavg= (v1+v2+v3+………………+vn)/n

THEORITICAL VALUE: Vavg = RVm/n = 0.6366vm for sine waveform

ROOT MEAN SQUARE VALUE (RMS VALUE): In mathematics, the root mean

square also known as quadratic mean. It is a statistical measure of the magnitude of a

varying quantity especially useful when variants are positive and negative.

Eg: sinusoid



It can be calculated for a series of discrete values or continuously varying function. The

name comes from the fact that it is the square root of the mean of the square of the value.

It is a special case of power mean with the exponent, p=2.

DEFINITION: The rms or effective value of a wave is defined as that dc value which

allowed to flow through a particular resistance for a certain time would produce the same

heating effect as that produced by the wave.

Mathematically ∫==T

effrms dttVT

II0

2)(1

The rms of collection of n values is given by

nVVVV n

rms)( 22

22

1 +++=

LLL=0.707vm (sinusoidal wave)

The RMS value of a periodic function is equal to the rms of one period of one function.The RMS value of a continuous function or signal can be approximately calculated bytaking the rms of a series of equally spaced samples. It is used to get average electricpower. It is used to find RMS value of a given waveform.

FORM FACTOR: The form factor of an alternating current waveform (signal) is theratio of rms values to the average value (mathematically) mean of absolute value of allpoints on the waveform.

In case of sinusoidal waveform, the form factor is approximately equal to 1.11

Mathematically form factor = Vrms/Vavg

Theoretical value: 1107.122

=Π

∗m

m

VV



PROCEDURE:1. Connect the circuit as per circuit diagram.2. Plot the graph that appears on CRO connected to the resistor i.e., non sinusoidal waveform.3. Divide the waveform into n-parts.

4. Calculate the Vrms using the formula( )volts

nVVVV n

rms

222

21 +++

=LLLL

5. Calculate the form factor asavg

rms

VV

PRECAUTIONS:1.Note down the readings from ammeter and voltmeter without parallax errors.

2.Care should be taken that the ammeter reading should not exceed the rated value.3.Trace the waveform carefully from CRO.

RESULT:

The theoretical and practical values for form factor are

Theoretical value Practical value

CONCLUSION: Theoretical and practical values of a form factor are found to beapproximately equal.



VERIFICATION OFCOMPENSATION

THEOREM




VERIFICATION OFCOMPENSATION THEOREM

AIM:-To verify compensation theorem.

APPARATUS:-

S.No APPARATUS RANGE TYPE QUANTITY1 Voltmeter 0-300V MI 12 Ammeter 0-1A MI 1

3 Rheostats 290 /2.8A WW 155 /1.7A WW 1

4 1- Variac 230/0-270V,8A ----- 1

THEORY:- In a linear, network N, if the current in the branch is I and the impedance Zof the branch is increased by Z, then the increment of voltage and current in each branchof network is that voltage and currents that would be produced by an opposing voltagesource of value VC = I Z introduced into the altered branch after the modification.

EXPLANATION:- Consider network N in figure (A), having branch impedance Z. Let thecurrent through Z be I and its voltage be V.

Let Z be the change in Z. Then I (the new current) can be written as,

I = VOC / (Z+ Z+Zs)

I = I – I = V0C/ (Z+ Z+Zs) - VOC / (Z+ Zs) = - (VOC / (Z+ Zs)) ( Z/ (Z+ Z+Zs))



= -I Z/ (Z+ Z+Zs)

= - Vc/ (Z+ Z+Zs)

Where, Vc = I Z The equation shown above follows the shown below in which I has thesame direction as I .

This shows that the change in current I due to change in any branch in a linearnetwork can be can be calculated by determining the current in that branch in a networkobtained from the original network, by nulling all the independent sources and placing avoltage source called the compensation source in series with the branch whose value is Vc= I Z, where I is the current through the branch before its impedance is changed and Zis the change in the impedance. The direction of Vc is opposite to that of I.



CIRCUIT DIAGRAM -1:-



TABULAR FORM 1:-

S.NO. Voltage (V) Current I (Amps)

TABULAR FORM -2:-

S.No. Voltage (V) Current I (Amps)

TABULAR FORM-3:-

S.No. Voltage (V) Current I (Amps)

PROCEDURE:-1. Connections are made as per the circuit diagram.2. With the help of 1 - Variac apply 200V to the circuit.3. Note down the corresponding ammeter readings (I).4. Apply 200V to the circuit 2 and note the corresponding ammeter readings(I ).5. Apply compensating Voltage (VC) to the circuit 3 and note down the

corresponding ammeter readings ( I).

PRECAUTIONS:-1. Before switching on the supply for each circuit it should be ensured that all

rheostats at maximum position and during the experiment this should not bedisturbed.

2. It is also to be ensured that the auto transformer should be at minimum positionbefore switching on the power supply.

RESULT:-



MEASUREMENT OF 3-PHASEPOWER BY 2-WATTMETER

METHOD




Measurement of 3-phase Power by two Wattmeter MethodAIM: To measure 3-phase power by two wattmeter method for the given load.

APPARATUS :

THEORY:-

In a three phase three wire system we require 3 elements, but if we make thecommon points of the pressure coils coincide with one of the lines, then we will requireonly n-1=2 elements.

Let us consider two wattmeters connected to measure power in three phase circuitas shown in figure. The sum of the two wattmeter readings is equal to the powerconsumed by the load. This is irrespective of the load is balanced or unbalanced.

Total Active power is given by P = W1+W2

Total Reactive power is given by Q = 3 (W1-W2)

Power factor is given by

Where W1 & W2 are two wattmeter readings, they can be expressed mathematically as

W1 = VL IL cos (30- ) W2 = VL IL cos (30+ )

When power factor is unity both the wattmeter show same reading. As the powerfactor decreases, up to 0.5 both the meters read positive values but unequal. If the powerfactor decreases below 0.5 one of the wattmeter shows negative reading. In such case wehave to inter change either current coil or pressure coil connections.

S. No Name of Apparatus Type Range Quantity1 Voltmeter PMMC 0-600V 1

2 Ammeter PMMC 0-10A 13 Rheostat WW 50 /5A 34 Wattmeter -- 600V, 10A, UPF 25 Fuse TCC 10A --



0-600VMI

50 / 5A

50/ 5

A

50/5

A



0-600VMI



0-600VMI

RBY

CBY



0-600VMI

RBY



PROCEDURE:-

1. Connect the circuit as per circuit diagram.

2. Initially variac should be in minimum position.

3. Close the TPST switch and slowly vary the variac until voltmeter reads line voltage of

415 V.

4. Note down the readings of Wattmeter, Voltmeter and Ammeter and tabulate.

OBSERVATION TABLE:-

S.NO. VL (V) IL (A) W 1(watt) W2 WT=W1+W2

PRECAUTIONS:

1. Avoid Loose Connections.2. Readings must be taken without parallax error.3. Before switching on the supply for the circuit, ensure that all rheostats are at maximumposition and during the experiment these should not be disturbed.

RESULTS:

CONCLUSIONS:



VIVA QUESTIONS:

1. What is active power?2. What are the different powers available?3. What is the difference between balanced load & un balanced load?4. Draw the Phasor diagram.5. What is the active power consumed for a purely inductive and capacitive loads.6. What is the apparent power for a resistive load.

EC & S Lab Manual 2010

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Transcript of EC & S Lab Manual 2010