1(a). VERIFICATION OF THEVENIN’S THEOREMsmec.ac.in/sites/default/files/lab1/ELECTRICAL...

Electrical circuits and simulation lab manual

1 Dept. of EEE

1. THEVENIN’S AND NORTON’S THEOREMS

1(a). VERIFICATION OF THEVENIN’S THEOREM

1.1. OBJECTIVE: To verify Thevenin’s & Norton’s theorems for the given circuit. 15v

1.2. RESOURCES:

S. No Name of the apparatus Range Type Quantity

1 Regulated power supply (0 – 30)V/2A Digital 01

2 Voltmeter (0-30)V MC 01

3 Ammeter (0-200m)A MC 01

4 Resistors100Ω150Ω200Ω

CarbonComposition

020101

5 D.R.B 0-10k Ω --- 01

6 Connecting wires --- ---- Required number

1.3. PRECAUTIONS:

1. Initially keep the RPS output voltage knob in zero volt position.

2. Set the ammeter pointer at zero position.

3. Take the readings without parallax error.

4. Avoid loose connections.

5. Avoid short circuit of RPS output terminals.

Exp - 1


2 Dept. of EEE

1.4. PROCEDURE:

1. Connect the circuit as per fig (1)

2. Adjust the output voltage of the regulated power supply to an appropriate value (Say 30V).

3. Note down the response (current, IL) through the branch of interest i.e. AB (ammeter reading).

4. Reduce the output voltage of the regulated power supply to 0V and switch-off the supply.

5. Disconnect the circuit and connect as per the fig (2).

6. Adjust the output voltage of the regulated power supply to 30V.

7. Note down the voltage across the load terminals AB (Voltmeter reading) that gives Vth.



10. Adjust the output voltage of the regulated power supply to an appropriate value (Say V = 30V).

11. Note down the current (I) supplied by the source (ammeter reading).

12. The ratio of V and I gives the Rth.



15. Adjust the output voltage of the regulated power supply to 30V

16. Note down the response (current, IN) through the branch AB (ammeter reading).


18. Disconnect the circuit.

1.5. GIVEN CIRCUIT:

STATEMENTS:

Thevenin’s Theorem

It states that any linear, active network with two open terminals can be replaced by an equivalent circuit

consisting of Thevenin’s equivalent voltage source Vth in series with Thevenin’s equivalent resistance Rth. Where

Vth is the open circuit voltage across the two terminals and Rth is the resistance seen from the same two terminals.


3 Dept. of EEE

1.7. CIRCUIT DIAGRAMS:-

EXP.SETUP TO FIND IL:

FIG(1)

EXP.SETUP TO FIND VTH:

FIG(2) TO FIND Rth:

EXP. SET UP TO FIND RTH AND RN


4 Dept. of EEE

TO FIND IN:

Fig(4)

1.8. THEORY:

Thevenin’s Theorem:

Statement:

The values of VTh and RTh are determined as mentioned in thevenin’s theorem.

Once the thevenin’s equivalent circuit is obtained, then current through any load resistance

RL connected across AB is given by, I =

Thevenin’s theorem is applied to d.c. circuits as stated below.

Any network having terminals A and B can be replaced by a single source of

e.m.f. VTh in series with a source resistance RRh.

(i) The e.m.f the voltage obtained across the terminals A and B with load, if any removed i.e., it

is open circuited voltage between terminals A and B.

(ii) The resistance RTh is the resistance of the network measured between the terminals A and B

with load removed and sources of e.m.f replaced by their internal resistances. Ideal voltage sources

are replaced with short circuits and ideal current sources are replaced with open circuits.

To find VTh, the load resistor ‘RL’ is disconnected, then VTh = Χ R3

To find RTh,

RTh = R2 + , Thevenin’s theorem is also called as “Helmoltz theorem”


5 Dept. of EEE

Norton’s Theorem:

Statement:

It states that any linear, active network with two open terminals can be replaced by an

equivalent circuit consisting of Norton’s equivalent current source IN in parallel with Norton’s

equivalent resistance RN. where IN is the short circuit current through the two terminals and RN is the

resistance seen from the same two terminals.

Nortom’s theorem is applied to d.c circuits may be stated as below.

Any linear network having two terminals ‘A’ and ‘B’ can be replaced by a current

source of current output IN in parallel with a resistance RN.

(i) The output IN of the current source is equal to the current that would flow through AB when

A&B are short circuited.

(ii) The resistance RN is the resistance of network measured b/wn A and B with load

removed and the sources of e.m.f replaced by their internal resistances.

Ideal voltage source are replaced with short circuits and ideal current sources are replaced with

open circuits.Norton’s theorem is converse of thevenin’s theorem in that Norton equivalent circuit

uses a current generator instead of voltage generator and the resistance RN is parallel with

generator instead of being series with it.

for source current,

II = =

for short-circuit current,

IN = Χ =


6 Dept. of EEE

1.9. TABULATION FOR THEVINEN’S THEOREM:

THEORITICAL VALUES PRACTICAL VALUES

RTH=RL=

IL=

Vth=

RTH=RL=

IL=

Vth=

1.10. TABULATION FOR NORTON’S THEOREM:

THEORITICAL VALUES PRACTICAL VALUES

RN=RL=

IL=

IN=

RN=RL=

IL=

IN=

1.11. RESULT:-


7 Dept. of EEE

1.12. PRE LAB QUESTIONS:-

1) The internal resistance of a source is 2 Ohms and is connected with an External load of 10 Ohms resistance. What is Rth ?

2) In the above question if the voltage is 10 volts and the load is of 50Ω. What is the load current and Vth? Verify IL?

3) If the internal resistance of a source is 5 Ω and is connected with an External load of 25 Ohms resistance. What is Rth?

4) In the above question if the voltage is 20V and the load is of 50 Ohms, What is the load current and IN ? Verify IL ?

1.13. LAB ASSIGNMENT QUESTION:

Calculate the current in 200Ω branch by using thevenin’s & norton’s theorem.

1.14. POST LAB QUESTIONS:1) Show that Thevenin’s Theorem and Norton’s Theorems are dual to each other.

ParameterThevenin’s theorem Norton’s theorem

Theoretical Values

PracticalValues

Theoretical Values

PracticalValues

IL in given circuit

Thevenins voltage(vTH)

Thevenins resistance(RTH)/nortons resistance(RN)

Nortons current IN

IL in Thevinens equi. ckt

IL in Nortonsequi. ckt


8 Dept. of EEE

SUPERPOSITION AND MAXIMUM POWER TRANSFER THEOREM

2. (a) VERIFICATION OF SUPERPOSITION THEOREM

2.1. OBJECTIVE: To verify the superposition theorem

2.2. RESOURCES:


1Dual channel regulated power supply

(0 – 30) V/2A

digital 01No

2 Ammeter (0 – 200m) A MC 01No

3 Resistors

100

150200

CarbonComposition

01No01No01No

4 Experi mental board - - 01No

5 Connecting wires - - Required number

2.3. PRECAUTIONS:





5. Avoid short circuit of RPS output terminals

Exp - 2


9 Dept. of EEE

2.4. PROCEDURE: 1. Connect the circuit as per the fig (1).

2. Adjust the output voltage of sources X and Y to appropriate values (Say 30V and20V

respectively).

3. Note down the response (current, IL) through the branch of interest i.e. AB ammeter reading.

4. Now set the source Y (20V) to 0V.

5. Note down the response (current, ILl) through the branch AB (ammeter reading).

6. Now set the source X (20V) to 0V and source Y to 20V.

7. Note down the response (current, ILll) through the branch AB (ammeter reading).

8. Reduce the output voltage of the sources X and Y to 0V and switch off the supply.


GIVEN CIRCUIT:

STATEMENT:

Super Position Theorem:

In any linear, bilateral, multi source network the response in any element is equal to the algebraic sum of the responses obtained by each source acting separately while all other sources are set equal to zero.


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2.5. CIRCUIT DIAGRAM:

WhenV1&V2 source acting(To find I):-

WhenV1 Source Acting (To Find I1):-

Whenv2 Source Acting(To Find I2):-


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2.6. THEORY:

Superposition theorem:

The superposition theorem states that in a linear bilateral network consisting N number of

sources each branch current is the algebraic sum of N currents through ( branch voltage), each of

which is determined by considering one source at a time and removing all other sources. In

removing the sources, voltage sources are short circuited or replaced by resistances equal to their

internal resistances for no ideal sources, while the ideal current sources are open circuited.

2.7. TABULAR FORMS:Tabular Column:

Theoretical values

Practical values

When v1 and v2 acting (20v,10v) current (I)

when v1 acting (20v)current (I1)

When v2 acting (10v) current (I11)

.

2.8.RESULT:

Theoretical values

Practical values

When v1 and v2 acting (20v,10v) current (I)

when v1 acting (20v)current (I1)

When v2 acting (10v) current (I11)


12 Dept. of EEE


1) What do you mean by Unilateral and Bilateral network? Give the limitations of Superposition theorem.

2) What are the equivalent internal impedances for an ideal voltage source and for a Current source?

3) Transform a physical voltage source into its equivalent current source.

4) If all the 3 star connected impedance are identical and equal to ZA,then what is the Delta connected resistors?

2.10. LAB ASSIGNMENT:

Calculate the current in 200Ω branch by using superposition theorem at 30V & 20V.

2.11. POST LAB QUESTIONS:

Why super position theorem is not applicable for power calculation?


13 Dept. of EEE

2(b) VERIFICATION OF MAXIMUM POWER TRANSFER THEOREM

2b.1. OBJECTIVE:

To verify maximum power transfer theorem on D.C circuit.

2b.2. RESOURCES:


1 Regulated power supply (0 – 30)V/2A digital 01No

2 Voltmeter (0-30) V MC 01No

3 Ammeter (0-1) A MC 01No

4 Rheostats100 /5A50/5A

Wound Wire01No01No


2b.3. PRECAUTIONS:

→ Avoid loose connections

→ Ammeter should always connected in series with the circuit.

2b.4MODEL GRAPH FOR MAXIMUM POWER TRANSFER THEOREM:


14 Dept. of EEE

2B.5. PROCEDURE:

1. Connect the circuit as per the circuit diagram fig(1).


3. Vary the load rheostat. in steps, and note down the response (current) through the load for

each step (ammeter reading) & load voltage.



6. Calculate the power absorbed by the load, PL for each step using the formula PL=IL2 RL.

7. Plot the graph by taking ‘RL’ on X-axis and PL on Y-axis.

8. Get the practical value of the load resistance for which it will gain the maximum power from

the source.

STATEMENT:

It states that, maximum power will be transferred from source to load when the load

resistance is the complex conjugate of source resistance.


15 Dept. of EEE

2B.6. CIRCUIT DIAGRAM:

Fig(1)

THEORY:

The statement of maximum power transfer is “ In d.c circuits, maximum power

is transferred from a source to load when the load resistance is made equal to the internal

resistance of the source as viewed from the load terminal with load removed and all e.m.f

sources replaced by their internal resistance.

Consider a voltage source of V of internal resistance R delivering power to aload

RL. We shall prove that when RL = RS the power transferred is maximum.

Circuit current =

Power delivered P = I2 RL

RL

=0

RL+Ri cannot be zero,

Ri – RL = 0

RS ==RL


16 Dept. of EEE

2b.7. TABULATION FOR MAXIMUM POWER TRANSFER THEOREM:

SNO.

LOAD

RESISTENCE

In ohms

VOLTAGE

VL (in Volts)

CURRENT

IL (in amps)

POWER

P=VL*IL(watt)

1

2

…….

2b.8. THEORETICAL CALCULATIONS:

Total current I =

P = I2 RL

= 2. RL

Power is maximum dp/dRL =0

→ = 0

→ =0

→ =0

Rs=RL


17 Dept. of EEE

2b.9. RESULT:-

2b.10. PRE LAB QUESTIONS:-

1. Derive the condition for maximum power transfer theorem.2. Where and why maximum power transfer theorem is applied?3. What is the efficiency of the circuit at the maximum power transfer condition & why?

2b.11. LAB ASSIGNMENT:

Prove the maximum power transfer theorem for the given circuit at 30V.

2b.12. POST LAB QUESTIONS:

1. Derive the condition for maximum power transfer theorem for a.c. Circuits.2. Define a dependent source.


18 Dept. of EEE

3. COMPENSATION THEORM

4.1. OBJECTIVE:

To verify compensation theorem for the given circuit.

4.2. RESOURCES:


1 Regulated power supply (0 – 30)V/2A digital 01No

2 Ammeter (0-200)mA MC 2No

3 Resistors

100 150K200100

CarbonComposition

01No01No01No01No

4 Connecting Wires ---- ---- Required number

5 Experimental Board ---- ----- 01No

4.3. PRECAUTIONS:

→ Avoid loose connections

→ Ammeter should always connected in series with the circuit.

4.4. PROCEDURE:1. Connect the circuit as per the fig (1).

2. Adjust the output voltage of source X to an appropriate value (say 30V).

3. Note down I1 and I2 by using ammeters A1 & A2. Now set the source X(30V) to 0V.

4. And connect the circuit as per the fig (2). If 100Ω resistance is charged to 150Ω then find the

charge in 200Ω connect the circuit as shown in fig.

5. By applying ΔE = I2ΔR using R.P.S find the current in 200Ω.

6. Note down the response (current, I200) through AB branch (ammeter reading).


Exp -4


19 Dept. of EEE

GIVEN CIRCUIT:

STATEMENT:

It states that in a linear bilateral network any element may be replaced by a voltage source of

a magnitude equal to the current passing through the element multiplied by the value of its resistance

(provided that the current and voltage in the other parts of the circuit remain unaltered).

4.5. CIRCUIT DIAGRAMS:

To find I100 Ω and I200Ω:


20 Dept. of EEE

To find I200Ω:

To find current in 200 when 100 changed to 150:

4.6. THEORY:

The compensation theorem states that any element in the linear, bilateral network,

may be replaced by a voltage through the element multiplied by the value of the element, provided

the currents and voltages in other parts of the circuit remain unallered. Consider the circuit shown.

The element R can be replaced by voltage source V, which is equal to the current I passing through

R Multiplied by R.

This theorem is useful in finding the changes in current of voltage when the value of

Resistance R is changed M the circuit consider the network containing a resistance R. A small

change in resistance R, that is (R+ΔR) causes a change in current in all branches. This current

increment in other branches is equal to the current produced by the voltage source of voltage I.ΔR

which is placed in series with altered resistance.


21 Dept. of EEE

4.7. TABULATIONS:

THEORITICAL VALUES

PRACTICAL VALUES

Current in 100 and 200 I and I200

Current in 200 when 100changed to 150 I1

200Current in 200 when

ΔE = ΔRI applied I11200

Change in current I200-I1200

4.8. MODEL CALCULATIONS:-

From compensation theorem:-

I =

I2 =

I = I1 + I2

I1 = I-I2

I =

I =

I200 =

From the figure (b)ΔE = ΔR I1

ΔE =

4.9. RESULT:


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1. State the compensation theorem?2. Application of compensation theorem?

4.11. LAB ASSIGNMENT QUESTIONS:

Verify compensation theorem for the given circuit at 20V.


1. Advantages of compensation theorem?


23 Dept. of EEE

RECIPROCITY AND MILLMAN’S THEOREMS

5. (a) VERIFICATION OF RECIPROCITY THEOREM

5a.1. OBJECTIVE:To verify reciprocity theorem for the given circuit.

5a.2. RESOURCES:


1 Regulated power supply(0 – 30) V/2A

digital 01No

2 Ammeter(0 – 200m)

AMC 01No

3 Resistors100150200

CarbonComposition

01 No01No01No


5 Connecting wires - -Required number

5a.3. PRECAUTIONS:





5.Avoid short circuit of RPS output terminals.

6.If voltmeter gives (-) ve reading then interchange the terminals connections of a voltmeter.

Exp - 5


24 Dept. of EEE

5a.4. PROCEDURE:

Reciprocity Theorem:

1. Connect the circuit as per the fig (1).


3. Note down the response (current, IL) through 150 resistor (ammeter reading).

4. Reduce the output voltage of the signal generator to 0V and switch-off the supply.

5. Disconnect the circuit and connect the circuit as per the fig (2).


7. Note down the response (current, IL1) through 100 resistor (ammeter reading).

8. Reduce the output voltage of the signal generator to 0V and switch-off the supply.


CIRCUIT:

STATEMENT:

Reciprocity theorem:

In any linear, bilateral, single source network, the ratio of excitation to the response is same even

though the positions of excitation and response are interchanged.


25 Dept. of EEE

5a.5. CIRCUIT DIAGRAMS:-

CIRCUIT – 1(Before Interchanging source and Response):

CIRCUIT -2(After Interchanging source and Response)

5a.6. THEORY:

RECIPROCITY THEOREM:Statement:

This theorem permits in to transfer source from one position in the circuit to another and may

be stated as under.

In any linear bilateral network, if an e.m.f E acting in a branch causes a current ‘I’ in branch

‘Y’ then the same e.m.f E located in branch ‘Y’ will cause a current I in branch. However, currents

in other branches will not change.


26 Dept. of EEE

5a.7. TABULAR FORM:

For Circuit-1

S. NoApplied voltage

(V1) Volt

CurrentIL

(mA)

For Circuit-2

S. NoApplied voltage

(V2) Volt

CurrentIL

1

(mA)

5a.8. RESULT:

Theoretical Value Practical Value

V/I(Before inter change source & excitation)

V/I (After inter change source & excitation)


27 Dept. of EEE

5a.9. PRE LAB QUESTIONS:-

1. State the reciprocity theorem?2. Application of reciprocity theorem?3. Advantages of reciprocity theorem?

5a.10. LAB ASSIGNMENT:

Calculate the current in 150Ω branch by using reciprocity theorem at 30V supply.

5a.11. POST LAB QUESTIONS:

1. Prove that the given circuit is reciprocal?


28 Dept. of EEE

5. (b) MILLMAN’S THEOREM

5B.1. OBJECTIVE: To verify Millman’s theorem for the given circuit.

5b.2. RESOURCES:


1Dual channelRegulated power supply

(0 – 30)V/2A digital 02No

2 Ammeter(0-200)mA

(0-0.5)AMCMC

01No01No

3 Resistors100150200

CarbonComposition

01No01No01No



6. Voltmeter 0-30V MC 01No

5b.3. PRECAUTIONS:





5. Avoid short circuit of RPS output terminals.

5b.4. PROCEDURE:

1. Connect the circuit as per the fig (1).

2. Adjust the output voltage of sources X,andY to appropriate values. (Say 30Vand 25V

respectively).

3. Note down the response (current, IL) through the branch of interest (AB)(ammeter reading).

4. Disconnect the circuit and connect the circuit as per the fig (2).

5. Adjust the output voltage of sources X,andY to appropriate values. (Say 30Vand 25V

respectively).


29 Dept. of EEE

6. Find the voltage across open circuit terminals

7. Connect the circuit as shown in fig

8. Find the current in 200Ω.

GIVEN CIRCUIT:

STATEMENT:

Millman’s theorem:Statement:

It states that in a linear active network, if number of voltage sources V1,V2,……….Vn with

internal resistances R1,R2,……….Rn are connected in parallel, then this network can be replaced by

a single voltage source V1 in series with single resistance R1.

Where V1 = n21

nn2211

GGG

GVGVGV

R1 = n21 GGG

1


30 Dept. of EEE

5b.5. CURCUIT DIAGRAMS:

To find I200Ω:

To find’V’

To find’R’


31 Dept. of EEE

To find’I200’

To find I200Ω

5b.6. THEORY:

Millman’s theorem slates that in any network, if the voltage sources V1,V2, --------Vn in

series with internal resistances R1,R2---------RN, respectively, are in parallel, then these sources may

be replaced by a single voltage sources V in series with R as

shown.

where

V =

Here Gn is the conduction of the nth branch , R1=


32 Dept. of EEE

Similar theorem can be stated for n current sources having internal conductances which can

be replaced by a single current source I’ in parallel with an equivalent conductance.

where

G1 =

5b.7. TABULATIONS :

TABLE-1(FIG(1):

V (V) I (Amp) R1=V/I

Theoretical

Practical

Table-2(fig(2):

V1(V) V2(V) VI (V)

Theoretical

practical


33 Dept. of EEE

Table-3(fig(3):

V1 I200 V1 V2

Theoretical

practical

5b.8. RESULT:

Theoretical values Practical values

Current in 200 Actual

given circuit

Millimans resistance(R1)

Millimans voltage(V1)

Current in 200 (Millimans

Circuit )

5b.9. PRE LAB QUESTIONS:-

1. State the Millman’s theorem?2. Advantages of Millman’s theorem?

5b.10. LAB ASSIGNMENT:

Prove Millman’s theorem for the given circuit for load resistance of 300Ω

5b.11. POST LAB QUESTIONS:

1. Application of the Millman’s Theorem?


34 Dept. of EEE

LOCUS DIAGRAMS OF SERIES RL AND RC CIRCUITS

6.1. OBJECTIVE: To draw the current locus diagrams for series RL and RC circuits by varying resistance and

for series RC circuit by varying capacitance.

6.2. RESOURCES:


1 Signal generator (0 – 3M) Hz, (0-20) VPP - 1No

2 Decade Resistance Box (0-111.11K) - 1No

3 Decade inductance Box (0-1.11)H - 1No

4 Decade Capacitance Box (0-1.11)F - 1No

5 Ammeter (0-2000m)A MC 1No


6.3. PRECAUTIONS:





5. Avoid short circuit of Function Generator output terminals.

Exp - 6


35 Dept. of EEE

6.4. MODEL GRAPHS:

6.5. PROCEDURE:

Series RL circuit (varying resistance):

1. Set the signal generator to be in sine wave mode and adjust the output voltage to 20V peak-

to-peak, frequency to 200 Hzs.

2. Connect the circuit as per fig (7.1).

3. Vary the resistance in the circuit using DRB in steps and note down the current through the

circuit for each step (ammeter reading).

4. Calculate phase angle using to formula = tan-1

R

XL for each step.


6. Plot the current locus diagram by taking current on x axis and voltage on Y – axis.


36 Dept. of EEE

Series RC circuit( varying resistance ):

1. Set the signal generator to be in sine wave mode and adjust the output voltage to 20V peak

to peak,frequency to 200 Hzs.

2. Connect the circuit as per fig(7.2).

3. Vary the resistance in the circuit using DRB in steps and note down the current through the

circuit for each step(ammeter reading).


R

XC for each step.


6. Plot the current locus diagram by taking current on Y axis and voltage on X – axis.

Series RC circuit (varying capacitance):

1. Set the signal generator to be in sine wave mode and adjust the output voltage to 20V peak-

to-peak, frequency to 200 Hzs.

2. Connect the circuit as per fig (7.3).

3. Vary the Capacitance in the circuit using DCB in steps and note down the current through the

circuit for each step (ammeter reading).


R

XC for each step.


6. Plot the current locus diagram by taking current on Y-axis and voltage on X – axis.


37 Dept. of EEE

6.6. CIRCUIT DIAGRAMS:

Series RL circuit (R Varying):

Series RC circuit (RVarying):

Set up for series R-L circuit:


38 Dept. of EEE

Set up for series R-c circuit:`

6.7. THEORY:A phasor diagram may be drawn and is expanded to develop a curve; known as a

locus. Locus diagrams are useful in determining the behavior or response of an RLC circuit when one of its parameters is varied while the frequency and voltage kept constant. The magnitude and

phase of he current vector in the circuit depends upon the values of R,L, and C and frequency at the

fixed source voltage. The path traced by the terminus of the current vector when the parameters R<L

or of are varied while f and V are kept constant is called the current locus.

The term circle diagram identifies locus plots that are either circular or semi circular loci of

the terminus ( the tip of the arrow) of a current phasor or voltage phasor. Circle diagrams are often

employed as aids in analyzing the operating characteristics of circuits like equivalent circuit of

transmission lines and some types of AC machines.


39 Dept. of EEE

6.8. TABULATIONS:

6.9. RESULT:


1. What is RC circuit

2. What is the Q factor of series circuit

3. What is RL circuits

6.11. LAB ASSIGNMENT:

1. Draw the locus diagram for the given circuit at 30V peak-to-peak, frequency to 150 Hzs.


What is meant by Effective value of an alternating quantity.

S.NO Current in circuit (mA)

Voltage across rheostat(v)

resistance=

R

Xl1tan

S.NO Current in circuit (mA)

Voltage across rheostat(v)

resistance=

R

XC1tan

SERIES AND PAREALLEL RESONANCE

7.1. OBJECTIVE: To determine the performance of the series and parallel circuit at resonance.

7.2. RESOURCES:


1 Signal generator (0 – 1M)Hz,(0-20) VPP

digital 01No

2 Decade inductance Box (0-40mH) ---- 01No

3 - 01No

4 Capacitor 0.1uf 01No

5 Resistors 30 Carbon

Composition01No

6 Ammeter (0-200m) A MI 01No

7 Experimental board - - 1No

8 C.R.O 30 MHz - 1No

9 Connecting wires - -Required Number

7.3. PRECAUTIONS:

1. Meter reading should be taken without parallax error.

2. Connection should be made tight.

Exp - 7

Electrical circuits and simulation lab

Dept. of EEE

SERIES RESONANCE

7.4. MODEL GRAPH:

PARALLEL RESONANCE

7.5. PROCEDURE:

1. Connections are made as per the circuit diagram.

2. By varying the frequency note down the corresponding values of current in both cases and

note down f, VC, VL and VR.

3. At a particular value of frequency the current reaches its Maximum /minimum in

Series/Parallel resonance. That instant of frequency VC = VL and VR = VS in series Resonance

circuit.


Dept. of EEE

7.6. GIVEN CIRCUIT:

SERIES RESONANCE

PARALLEL RESONANCE

FOR PARALLEL RESONANCE


Dept. of EEE

7.7. THEORY:

Resonance is a particular type of phenomenon inherently found normally in every

kind of system, electrical, mechanical, optical, Acoustical and even atomic. There are several

definitions of resonance. But, the most frequently used definition of resonance in electrical

system is studied state operation of a circuit or system at that frequency for which the

resultant response is in time phase with the forcing function.

Series resonance:

A circuit is said to be under resonance, when the applied voltage ‘V’ and current are

in phase. Thus a series RLC circuit, under resonance behaves like a pure resistance network

and the reactance of the circuit should be zero. Since V & I are in phase, the power factor is

unity at resonance.

The frequency at which the resonance will occur is known as resonant frequency.

Resonant frequency, fr =

Thus at resonance the impedance Z is minimum. Since I = V/Z. The current is maximum. So

that current amplification takes place.

The parallel circuit consisting branches with single pure elements R,L & C is an ideal

circuit. How ever the performance of such a circuit is of interest in the general subject of

resonance. This ideal parallel circuit is of interest in the general subject of resonance.

Lower cut-off frequency is above the resonant frequency at which the current is

reduced to times of it’s minimum value. Upper cut-off frequency is above.

Quality factor is the ratio of reactance power inductor (or) capacitor to its resistance.

Selectivity is the reciprocal of the quality factor.


Dept. of EEE

7.8. TABULAR FORMS:

FOR SERIES RESONANCE

S.NO FREQUNCY V(L) V(C) V(R) I(mA)

1

2

...

7.9. THEORITICAL CALCULATIONS:

For Series Resonance circuit:

1. Resonant frequency fr =

2. Lower cut-off frequency fl = +

3. Upper cut-off frequency f2 = +

4. Band width = f2-f1

5. Quality factor Q = =

6. Current at Resonance Io = VRo/R TABULAR FORMS:

FOR PARALLEL RESONANCE

S.NO FREQUNCY V(L) V(C) V(R) I(mA)

1

2


Dept. of EEE

For parallel Resonance circuit:

1. Resonant frequency fr =

2. Lower cut-off frequency fl

3. Upper cut-off frequency f2 =

4. Band width =

5. Quality factor Q = =

6. Current at resonance Io

7.10. RESULT:


1. Definition of resonance?

2. Define the series resonance?

3. Define the parallel resonance?

4. Applications of resonance?

5. What is the condition of voltage &current at the resonance condition?

7.12. LAB ASSIGNMENT:Design the circuit for resonance frequency, f = 10,000 Hz


What is meant by bandwidth?

S.No ParameterSeries Resonant circuit Parallel Resonant circuit

Theoretical Values

PracticalValues

Theoretical Values

PracticalValues

1Resonant Frequency (fo)

2Lower cut off frequency(f1)

3Upper cut off frequency(f2)

4 Band width(f2- f1)

5 Quality factor


Dept. of EEE

DETERMINATION OF SELF, MUTUAL INDUCTNCES ANDCOEFFICIENT OF COUPLING

OBJECTIVE

To determine the self-inductance, mutual inductance and coefficient of coupling of

the given 1- transformer.

RESOURCES:


1 Single phase transformer 230V / 115V, 3KVA - 01No

2 1- auto transformer 230V / 0-270V,10A, Induction 01No

3 Ammeter (0-2) A MI 01 No

4 Voltmeter (0-600) / (0-300) V MI 01No

5 Ammeter (0-2) A MC 01No


7 Voltmeter 0-1V MC 01No

PRECAUTIONS:

1. Ensure the minimum position of autotransformer during power on and off.




PROCEDURE:

To find Z1:

Apply rated voltage (V1) i.e 115 to primary winding and note down corresponding

ammeter reading. Then find out Z given . We use auto transformer to vary voltage.

Exp - 8


Dept. of EEE

To find Z2:

Apply rated voltage i.e 230 to primary winding and note down corresponding

ammeter reading. Then find out Z2 using the formula .

To find Rdc1:

Apply low voltage to primary winding i.e 115 V and note down corresponding

ammeter readings. Then find Rdc given by and from this Rac1 = 1.0 Rdc.

To find Rdc2 :

Apply a low voltage to primary i.e 230V winding and note down corresponding

ammeter readings. Then find Rdc2 given by and from this Rac2 = 1.6 Rdc2.

To find M :

Apply voltage of primary winding till the voltmeter in secondary reads 115V and note

down corresponding ammeter reading in primary.

CRICUIT FOR FINDING ‘ M’ VALUE:


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CIRCUIT FOR SELF INDUCTANCE (L1):

CIRCUIT FOR SELF INDUCTANCE (L2):

CIRCUIT FOR RDC1:

CIRCUIT FOR RDC2:


Dept. of EEE

THEORY:

A voltage is induced in a coil when there is a time rate of charge of current

through it. The inductance parameter L, is defined in terms of the voltage across it and the

time rate of change of current through it V(t) = Where V(t) is the voltage across the

coil. I(t) is the current through the coil, L is the inductance of the coil, Strictly speaking, this

definition is of self-inductance and this is considered as a circuit element with a pair of

terminals. Whereas circuit element “mutual inductor” does not exist mutual inductance is a

property associated with two or more coils or inductors which are in close proximity and the

presence of common magnetic flux which links the coils? A transformer is such a device

whose operation is based on mutual inductance. The two coils, or circuits are said to be

inductively coupled, because of this property they are called “

coupled elements “ , are coupled circuits and the induced voltage or emf is called voltage (or)

emf of mutual induction and is given by V2(t) = volts. Where V2 is the voltage

induced in coil L2 And M1 is the co-efficient of proportionality and is called the co-efficient

of mutual inductance or simple mutual inductance.

The amount of coupling b/wn the inductively coupled coils is expressed in terms of

the co-efficient of coupling which is defined as

K = where M= mutual inductance b/wn the coils,

L1 = self inductance of first coil,

L2 = self inductance of second coil.

Co-efficient of coupling is always less than unity, and has a maximum value of

1(or100%).

This case, for which K=1 is called perfect coupling when the entire flux of one coil

links the other. The greater the co-efficient of coupling b/wn the two coils, the greater the

mutual inductance between them, and vice-versa. It can be expressed as the fraction of the

magnetic flux produced by the current in one coil that links the other coil.

The co-efficient of coupling k is a non magnetic number and is independent of the

reference directions of the currents in the coils. If the two coils are a great distance apart in

space, and K is also very small. For iron core coupled circuits, the value of K may be as high

as 0.999, for air-core coupled ckts, K varied between 0.4 to 0.8.


Dept. of EEE

TABULAR FORMS:

To find Z1:

S.NoV1

(Volts)I1

(amp)Ω

I

VZ

1

11

1

To find Z2:

S.NoV2

(Volts)I2

(amp)Ω

I

VZ

2

22

1

To find M :

S.NoV

(Volts)I

(amp)M=V/I

1

To find Rdc1:

S.NoV1

(Volts)I1

(amp)Ω

I

V

1

11 R

1

To find Rdc2 :

S.NoV2

(Volts)I2

(amp)Ω

I

V

2

22 R

1


Dept. of EEE

CALCULATIONS:

XL1 = =

XL2 = = XL1 = 2 fL1 L1 = XL2 = 2 fL2 L2 =

Co-efficient of coupling K= =

Where M = =

RESULT:

PRE LAB QUESTIONS:-

1. Derive an expression for Mutual coupling coefficient.

2. Explain series aiding & series opposing in coupled circuit.

3. Explain parallel aiding& parallel opposing in a coupled Circuit

LAB ASSIGNMENT:

Calculate the self-inductance, mutual inductance and coefficient of coupling of the given 220V/220V , 3KVA 1- transformer

DETERMINATION OF Z AND Y PARAMETERS

OBJECTIVE:

To determine open circuit impedance parameters (Z) and short circuit admittance

parameters (Y) of the given two port network.

.

Exp - 8


Dept. of EEE

RESOURCES:


1 Regulated power supply (0 – 30) V/2A digital 01

2 Voltmeters (0-30) V MC 01

3 Ammeters (0-200m) A MC 01

4 Resistors 330 470630

CarbonComposition

010101

5 Experi mental board - - 01

6 Connecting wires - -RequiredNumber

PRECAUTIONS:


2. Set the ammeter pointer to zero position.


4. Avoid loose connections

5. Do not short-circuit the RPS output terminals.

PROCEDURE:


2. Open the port – I i.e, I1=0 find the values of I1,I2, V1.

3.Short circuits the port V2 =0 find the values of V2,I1, I2.

4. Repeat steps 2,3 for port – II and find the values of V1,I1,I2 and V2,I1,I2 respectively.

5. Find all the parameters of two port networks I,e, Z,Y, ABCD, AI BI CI DI, h, g

parameters from the above data

GIVEN CIRCUIT:


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CIRCUIT DIAGRAMS:

Exp set up When V1=0:

Exp set up When I1=0:



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WHEN I2=0:

THEORY:

A port is normally referred to a pair of terminals of a network though which we can

have access to network of calculating current in any part of network. Frequently the problem

is move restried in nature and may be that of calculating the response at a terminal pair

designated an input when excitation is applied at another terminal pair designated as input

terminals. It is a problem of terminal through which it is accessible, is called “Two Port

Network.“

If we relate the voltage of one port to the current of the same port, we get driving

point immitance. On the other hand, if we relate the voltage of one port to the current at

another port, we get transfer immittance. Immitance is a general term used to represent either

the impudance or the admittance of a network.

We will consider a general two-port network composed of linear, bilateral elements

and no independent sources. Dependent sources are permitted. It is represented as a black box

with two accessible terminals pairs as shown in. The voltage and current at port -1 are V1 and

I1 and at port =II are V2 and I2. The position of V1 and V2 and the directions of I1 and I2 are

customarily selected. out of four variables, I1I1V2 and I2 only two are independent. The other

two are expressed in terms of the independent variable of network parameters.


Dept. of EEE

TABULAR FORMS:

THEORATICAL VALUES

V1

(volts)I1

(mA)V2

(mA)I2

(mA)V1=0

I1=0

V2=0

I2=0

PRACTICAL VALUES

V1

(volts)I1

(mA)V2

(mA)I2

(mA)V1=0

I1=0

V2=0

I2=0

THEORETICAL CALCULATIONS:

1. When I1 = 0 (i.e.,) When port is open circuited:RL = V2 =I2= =

V1 = I2.R =2. When port -2 is open circuited (I2=0):V1 =Rt =I1 = =

V2 =3. When port -1 is short circuited ( V1=0):V2 =Rt =I2 = =


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I1 = I2

4. When port –II is short – circuited (V2 = 0 ) :V1 =Rt =I1 = V1/Rt =I2 =

THEORETICAL CALCULATIONS FOR PARAMETERS:

Z-parameters:Z11 = / I2=0 =

Z12 = / I1=0 =

Z21 = / I2=0 =

Z22 = / I1=0 =

Y – ParametersY11 = / V2=0 =

Y12 = / V1=0 =

Y21 = / V2= 0 =

Y22 = / V1= 0 =

.RESULT:

S. No Parameter Theoretical Values Practical Values

1 Z11

2 Z12

3 Z21

4 Z22

5 Y11

6 Y12

7 Y21

8 Y22


Dept. of EEE

PRE LAB QUESTIONS:-

1. Write the 2-port network equations in terms of hybrid parameter?

2. Define image impedance?

3. What is Z- parameter?

4. Write the network equations of Y- parameter

LAB ASSIGNMENT:

Determine open circuit impedance parameters (Z) and short circuit admittance

parameters (Y) of the 25Ω, 50Ω, 10Ω T network circuit.

POST LAB QUESTIONS:

Write Y parameters in terms of Z parameters.


Dept. of EEE

DETERMINATION OF TRANSMISSION AND HYBRID PARAMETERS

OBJECTIVE:

To determine transmission parameters and hybrid parameters of the given two port

network.

. RESOURCES:


1 Regulated power supply (0 – 30) V/2A digital 01

2 Voltmeters (0-30) V MC 01

3 Ammeters (0-200m) A MC 01

4 Resistors 330 470630

CarbonComposition

010101

5 Experi mental board - - 01

6 Connecting wires - -RequiredNumber

PRECAUTIONS:


2. Set the ammeter pointer to zero position.



5. Do not short-circuit the RPS output terminals

PROCEDURE:


2. Open the port – I i.e, I1=0 find the values of I1,I2, V1.

3. Short circuits the port V2 =0 find the values of V2,I1, I2.

4. Repeat steps 2,3 for port – II and find the values of V1,I1,I2 and V2,I1,I2 respectively.

5. Find all the parameters of two port networks I,e, Z,Y, ABCD, AI BI CI DI, h, g

parameters from the above data.

Exp - 9


Dept. of EEE

GIVEN CIRCUIT:

CIRCUIT DIAGRAMS:


Exp set up When I1=0:



Dept. of EEE

WHEN I2=0:

THEORY:

A port is normally referred to a pair of terminals of a network though which we can

have access to network of calculating current in any part of network. Frequently the problem

is move restried in nature and may be that of calculating the response at a terminal pair

designated an input when excitation is applied at another terminal pair designated as input

terminals. It is a problem of terminal through which it is accessible, is called “Two Port

Network.

If we relate the voltage of one port to the current of the same port, we get driving

point immitance. On the other hand, if we relate the voltage of one port to the current at

another port, we get transfer immittance. Immitance is a general term used to represent either

the impedance or the admittance of a network.

We will consider a general two-port network composed of linear, bilateral elements

and no independent sources. Dependent sources are permitted. It is represented as a black box

with two accessible terminals pairs as shown in. The voltage and current at port -1 are V1 and

I1 and at port =II are V2 and I2. The position of V1 and V2 and the directions of I1 and I2 are

customarily selected. out of four variables, I1I1V2 and I2 only two are independent. The other

two are expressed in terms of the independent variable of network parameters.


Dept. of EEE

.TABULAR FORMS:

THEORETICAL VALUES

V1

(volts)I1

(mA)V2

(mA)I2

(mA)V1=0

I1=0

V2=0

I2=0

PRACTICAL VALUES

V1

(volts)I1

(mA)V2

(mA)I2

(mA)V1=0

I1=0

V2=0

I2=0

THEORETICAL CALCULATIONS:

1. When I1 = 0 (i.e.,) When port is open circuited:RL = V2 =I2= =

V1 = I2.R =2. When port -2 is open circuited (I2=0):V1 =Rt =I1 = =

V2 =


Dept. of EEE

3. When port -1 is short circuited ( V1=0):V2 =Rt =I2 = =

I1 = I2

4. When port –II is short – circuited (V2 = 0 ) :V1 =Rt =I1 = V1/Rt =I2 =

THEORETICAL CALCULATIONS FOR PARAMETERS:

ABCD parameters:A = / I2= 0 =

B = / V2= 0 =

C= / I2= 0 =

D = / V1=0 =

H – Parameters:h11 = / V2 =0 =

h12 = / I1=0 =

h21 = / V2 =0 =

h22 = / I1 =0 =

RESULT:

S. No Parameter Theoretical Values Practical Values

1 A

2 B

3 C

4 D

5 H11

6 H12

7 H21

8 H22


Dept. of EEE

PRE LAB QUESTIONS:-

1. Write the 2-port network equations in terms of hybrid parameter?

2. Define image impedance?

3. What are Transmission parameters?

4. Write the network equations of Hybrid parameters.

LAB ASSIGNMENT:

Determine transmission parameters and hybrid parameters of the given two port network of

25Ω, 50Ω, 10Ω T network ciruit.

POST LAB QUESTIONS:

Obtain the condition for symmetry in ABCD parameters.


Dept. of EEE

MEASUREMENT OF 3-PHASE REACTIVE POWER USING SINGLE PHASE WATTMETER

OBJECTIVE : To measure reactive power in a three-phase circuit using single phase wattmeter.

RESOURCES :

Sl.No Apparatus Range Type Qty1 Voltmeter (0-600V) M I 1 no.2 Wattmeter 1,600V,10A,

LPFD.M.T 1 no.

3 Ammeter 0-10A, M I 1 no.4 3 autotransformer 415/0-470V,

10A, 8.14KVA1no.

5 3 loading inductor 10A, 415V 1 no.

PRECAUTIONS:

1. Ensure the minimum position of Three phase autotransformer during power on and off.




MODEL GRAPH:

Exp - 10


Dept. of EEE

PROCEDURE:

1. Connect the circuit as per the circuit diagram.

2. Keep the variac of the auto-transformer in minimum position.

3. Close supply TPST switch and vary the auto-transformer slowly and apply rated

voltage i.e.230V.

4. Vary the load gradually and at different loads, note down readings of ammeter,

Voltmeter and Wattmeter.

5. Draw the phasor diagram

CIRCUIT DIAGRAM:


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IR

VYB

VY

VBN

VR

THEORY:

Reactive power measurement in 3- circuits using 1- wattmeter can be done only for

balanced 3- loads. By connecting the current coil of the wattmeter in one line and the

pressure coil across the other two lines of 3- circuit, current through the current coil and

voltage across the pressure coil are determined. Now as the current in the current coil lags the

voltage by an angle of 90,the wattmeter reads a value proportional to the reactive power of

the circuit.

PHASOR DIAGRAM:

OBSERVATIONS:

For ideal inductive load = 900 --> Sin= 1

S.

No

Voltage

VL volts

Current

IL amp

Wattmet

er

reading

(W)

Reactive power

(measured

value)Qm=

)(3 VARW

Reactive power

(actualvalue)

Qa=

)VAR(

sinLILV3

%err

or =

(Qm-

Qa)/

Qa*1

00

1

2

3

4

5


Dept. of EEE

SAMPLE CALCULATIONS:

Load voltage VL = Load current IL =Watt meter reading W =

Reactive power (measured value) = W3 =

Reactive power (actual value) = sinLILV3 =

% error = 100 valueactual

valueactual- valuemeasuredx

RESULT:

PRE LAB QUESTIONS:-

1. What is meant by Reactive power?2. What is the difference between balanced and unbalanced loads?3. What is meant by complex power?

LAB ASSIGNMENT:

Calculate the active & apparent power for the given circuit


Dept. of EEE

MEASUREMENT OF 3-PHASE POWER BYTWO WATTMETER METHOD FOR UNBALANCED LOADS

OBJECTIVE:

To measure the 3-phase active and reactive power by 2 – wattmeter method for (i) resistance load (ii) inductive load.

RESOURCES:

Sl. No. Apparatus Range Quantity1 Voltmeter (0-600V) MI 12 Ammeter (0-10A) MI 13 Wattmeter 600V, 10A, UPF 24 Wattmeter 600V, 10A, LPF 2

PRECAUTIONS:

1) THE TPST switch must be kept open initially. 2) Load must not be applied while starting.

PROCEDURE:

(i) – Resistive load

1) Give the connections as per the circuit diagram. 2) Give the supply by closing TPST switch. 3) Vary the resistance load and note down the corresponding readings.

(ii) Inductive load

1) Give the connections as per the circuit diagram. 2) Give the supply by closing the TPST switch 3) Vary the inductive load and note down the corresponding readings.

Exp - 13


Dept. of EEE

For inductive load

For resistive load


Dept. of EEE

Formulae Used:

1. Real power = w1 + w2

2. Reactive power = 3(w1w2 )

3. Tan= 3(w

1

w2

)

w1 w2

4. Power factor = cos

OBSERVATIONS:

Two Wattmeter Method: Resistive Load

MF = MF = PowerV I Wattmeter Wattmeter

(volt) (A) Reading (W1) Reading (W2) Cos OBS ACT = OBS ACT=OBS Real Reactive

(watt) OBS X (watt) x MF Power powerMF (watt) (watt) (watt)

(watt)


Dept. of EEE

Two Wattmeter Method: Inductive Load

MF = MF = PowerWattmeter Wattmeter

V I Reading (W1) Reading (W2) Cos (volt) (A) OBS ACT = OBS ACT=OBS Real Reactive

(watt) OBS x (watt) x MF Power powerMF (watt) (watt) (watt)

(watt)

RESULT:

PRE LAB QUESTIONS:

1) What are the methods to measure 3 phase power?

LAB ASSIGNMENT QUESTIONS:

1) Explain about two wattmeter method for 3 phase power measurement?

POST LAB QUESTIONS:

1) What is meant by balanced and un balanced loads?


Dept. of EEE

VERIFICATION OF RMS VALUE OF A COMPLEX WAVE

OBJECTIVE:

To calculate the RMS value of a complex wave.

RESOURCES:

Sl. No. Apparatus Range Quantity1 Function generator 0-20mhz 12 DRB 0-100K 23 DLB 0-1H 14 Multimeter 15 CRO 0-30mhz 1

PRECAUTIONS:



PROCEDURE:

1. Connect the circuit as per the circuit diagram.

2. Apply the sinusoidal wave as input from the Function Generator.

3. Observe the output waveform in the CRO. Note down the peak value of the output

wave, from the CRO.

4. Switch OFF the supply.

Exp - 03


Dept. of EEE

CIRCUIT DIAGRAM:

RESULT:

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