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. Connect the circuit as shown in circuit diagram. 2. Close the switch S3 to 11’ side and close switch S4 to 44’ side and close switch S1 3. Note down the reading of ammeters. 4. Close the switch S3 to 22’ side and close the switch S4 to 33’ side. 5. Note down the reading of ammeters. let this be I11 and the earlier be Il. 6. Close the switch S3 to 11’ and switch S4 to 33’ and note down the reading of

ammeter across AB. Let this be I. 7. If I = I’ + I” Super Position theorem is verified. Precautions: 1. All the connections must be made properly. 2. All the readings must be taken without an parallax error. 3. 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. Connect the circuit as per circuit diagram. 2. 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. Take the readings of voltmeter and ammeter without parallax error. 2. The current through a particular element should be maintained below its current

rating. Results: . Hence, Reciprocity theorem is verified. Viva Questions:

1) What is the statement of the above theorem? 2) What is a linear network? 3) Where the above theorem is used practically? 4) What is the practical application of reciprocity theorem? 5) 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. Connect the circuit as per circuit diagram. 2. 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. 3. Close S4, close S3 to 33’ and open S1 not down the readings of voltmeter and

ammeter. From these readings calculate Z12 and Z22. 4. Close S1, S2 to 11’ and S3 to 44’. Note down the readings of voltmeter and

ammeter. From these values calculate Y11 and Y22. 5. 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. Take the readings of voltmeter and ammeter without parallax error. 2. The current through a particular element should be maintained below its current

raing.. Results: Z, Y and ABCD parameters are determined.

Viva questions:

1) what is the significance of the two port parameters? 2) How you know the admittance parameters from impedance parameters? 3) What is the application of ABCD 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?

VERIFICATION OF THEVENIN’S THEOREM

Circuit Diagram:

VERIFICATION OF THEVENIN’S THEOREM Aim : To verify the Thevenin’s theorem. Apparatus: Theory: Procedure: 1. Connect the circuit as per the circuit diagram.. 2. Open switch S2 and close switch S1 to 11’. This gives supply to the circuit across

AB. 3. Open switch S3 and note the voltmeter reading(Voc). 4. Close the switch S3 and note the ammeter reading IL. 5. Close the switch S1 to 22’ (shorting AB) and open switch S3 (removing RL) 6. Close the switch S2 (giving supply across CD) 7. Note the voltmeter reading (Voc) and ammeter reading (IL) gives Zth.

8. Verify Zth = L

oc

I

V

Precautions: 1. All the connection must be tight. 2. 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. Connect the circuit as per the circuit diagram. 2. 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.

3. A graph is plotted between power delivered and load current with power taken on Y axis and current on X axis.

4. The maximum power delivered is observed when RL = Rth where Rth is calculated from the circuit.

Graph:

Precautions: 1. Loose connections should be avoided.. 2. 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.

power

I

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:

4K ohm

1u F10V (P-P)

Vi

+

-

Vo

DRB

4.05 mH

DLB

DCB

100 ohm

1u F10V (P-P)

Vi

+

-

VR

DRB

2.026 mH

DLB

DCB+

-

+

-

IR

fof

IR

fof

series resonance:

parallel resonance:

Graph:

SERIES AND PARALLEL RESONANCE CIRCUITS

Aim : To study the series and parallel resonance for the given R-L-C circuit. Apparatus: Theory: Procedure: 1. Connect the circuit as shown in figure.. 2. Apply 10V P-P sinusoidal i/p to the circuit. 3. Tabulate the output voltage ( V0), I, for frequencies f by changing frequency

from 50 Hz to 1 KHz in steps of 50Hz. 4. The frequency corresponding to maximum output is called resonant frequency.. 5. Repeat steps 2,3,4 the values corresponding to the main minimum voltage is

resonance frequency. 6. Compare with theoretical value. Graph:

Precautions: 1. All the connections should be made properly. 2. 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.

I

Imax

Ffl fh

Imax/√2

Viva Questions:

1) What is the condition for the resonance? 2) What are the features for the resonance? 3) Where we can use resonance circuit? 4) What is the condition for resonance in parallel circuit?

DETERMIN ATION OF FORMFACTOR OF A NON -SINUSOIDAL 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. Connect the circuit as per circuit diagram. 2. Plot the graph that appear on the CRO connected to the resistor (i.e) a non

sinusoidal waveform. 3. Divide the waveform into n parts. 4. Calculate the VRMS value by the formula

VRMS = n

VVV n22

22

1 ......+++

5. Calculate the average by using the formula

Vavg =n

VVVV n++++ .....321

6. Calculate the form factor as = avg

RMS

V

V

Precautions: 1. Plot the graph from CRO with out parallax error. 2. 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) what is the definition of average value? 2) What is rms value? 3) What is form factor? 4) What is peak factor? 5) 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. Connect the circuit as per circuit diagram. 2. Vary the inductance value in steps. 3. Note the readings of voltmeter, ammeter and waltmetre.

4. Calculate φ from the formula φ =

+VI

WCos and plot the graph between I

and φ . 5. Similarly for RC circuit repeat the above steps by replacing inductor by capacitor

and by varying R. Precautions: 1. The reading of ammeter, voltmeter should be taken without parallax error. 2. 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) what is the significance of current locus? 2) Give the various locus diagrams for different impedances? 3) What is active power? 4) 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. Theoritical value of Time constant T for both RC and RL circuit is 2 m sec. 2. 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. To calculate I, V, I2, V2 and Z1, Z2. 2. 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. 3. Again connect switch to Z – Z1 and note down V2, I2 which gives Z2. 4. By using multimeter calculate the resistance of primary and secondary. 5. Using the formula Z = R + j XL calculate L1 and L2. Mutual Inductance:- 1. Connect the circuit as per circuit diagram. 2. 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) What is inductance? 2) What is mutual inductance? 3) Define coefficient of coupling? 4) What is the range for lc? 5) Can you increase the coupling coefficient between two coils?

VERIFICATION OF COMPENSATION AND

MILLIMAN’S THEOREMS

Circuit Diagram:

A+ -1K ohm

4.7K ohm 3.3K ohm20V

A+ -1K ohm

4.7K ohm

3.3K ohm

1K ohm

(compensating voltage)VC

A+ -1K ohm

4.7K ohm

3.3K ohm

1K ohm20V

circuit diagram for compensation theorem

]

VERIFICATION OF COMPENSATION AND MILLIMAN’S THEOREM S 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

I = ZZ

V

TH

th

+ (1)

Set the impedance Z of the branch K be changed to (Z + ∆ Z) as shown in fig (3)

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

I1 = ( )ZZZ

V

TH

th

∆++ (2)

Hence the change in current in branch K is given from (1) & (2) as

I∆ = I1 – I

=ZZZ

V

th

th

∆++ -

th

th

ZZ

V

+

= ( )[ ]

( )( )ZZZZZ

ZZZZZV

thth

ththth

∆+++∆++−+

∆I = ( )

( )thZZ

ZI

+∆−

× thZZZ

Z

+∆+∆−

(3)

From eqn (1) th

th

ZZ

V

+ = I substitute I in eqn (2)

∆I = ( )

( )thZZZ

ZI

+∆+∆−

= ZZZ

V

th

C

∆++−

(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 = nGGGGG +++

=........

11

321

(G = Conductance)

V = N

NN

GGG

GVGVGV

++++++

....

.....

21

2211

Proof : Let us consider n voltage sources with internal resistances R1, R2 . . . . Rn as shown in the fig. (6). 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 = n

n

R

V

R

V

R

V

R

V +−−−−+++3

3

2

2

1

1

I = V1G1 + V2G2 + V3G3 + - - - - - - - + VnGN

NEQ RRRR

1111

21

+−−−−++=

Geq = neq

GGGR

+−−−−++= 21

1

Req = neq GGGG +−−−−++

=21

11

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 = n

nn

RRRR

RIRIRI

−−−−+++−−−−−−++

321

2211

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. Note down the readings with out any parallel error. 2. All connections must be tight. RESULT: