204--E & EC Experiments Prof. R.S.Pukale

Experiment no. 1

Object
 Verification of Superposition theorem.
Objectives
1.      To understand the Superposition theorem.
2.      To know the application of Superposition theorem.
Apparatus
Sr. No
Name of Apparatus
Range
Quantity
1
D.C Power supply (V1)
                  Volt

2
D.C Power supply (V2
                  volt

3
Resistance (R1)
                   Ω

4
Resistance (R2)
                   Ω

5
Resistance (R3)
                   Ω

6
Digital ammeter/ Multimeter
                   A

7
Digital Voltmeter/ Multimeter
                   V         

8
Bread board



Circuit Diagram
   
Fig(a)
Fig(b)

              
Fig (c)
Theory
If  a number of voltage or current source are acting simultaneously in a line network, the resultant current in any branch is the algebraic sum of the current that would be produced in it, when each source acts alone replacing all other independent sources by their internal resistances.

In above fig (a), to apply superposition theorem, let us first take the voltage V1 alone at first replacing V2 by short circuit as shown in fig (b).
Here,                                                    
Next, removing V1 by short circuit let the circuit be energized by V2 only as shown in fig (c)
Here,                                                    
As per superposition theorem,



Procedure
1.      Take only one independent source of voltage / current and deactivate the other independent voltage/current sources.(for voltage source, remove the source and short circuit the respective circuit terminals and for current source, just delete the source keeping the respective circuit terminal open). Obtain branch current.
2.      Repeat the above step for each of the independent sources.
3.      To determine the net branch current utilizing superposition theorem, just add the current obtained in step 1 and step 2 for each branch. If the currents obtained in step 1 and step 2 are in same direction, just add them; on the other hand ,if the respective currents are directed opposite in each step, assume the direction of the clockwise current to be positive and subtract the current obtained in next step from the original current.
4.      Apply the superposition theorem and net current in each branch is obtained.












































































Observation Table

Voltage
(Volt)
Observed values
I1’+I1”
I2=
I2’+I2”
I3=
I3’+I3”
I1’
I2’
I3’
I1”
I2”
I3”
1
V1=









V2=









2
V1=









V2=









3
V1=









V2=










Sr. No
Voltage
(Volt)
Calculated values
I1=
I1’+I1”
I2=
I2’+I2”
I3=
I3’+I3”
I1’
I2’
I3’
I1”
I2”
I3”
1
V1=









V2=









2
V1=









V2=









3
V1=









V2=









Sample Calculation










Questions
1.         State the superposition theorem?
2.         What men by bilateral circuit?
3.         What mean by linear circuit?


  

Experiment no. 2

Object
 Verification of Thevenin’s theorem.
Objectives
1.     To understand the Thevenin’s theorem.
2.     To know the application of Thevenin’s theorem.
Apparatus

Sr. No
Name of Apparatus
Range
Quantity
1
D.C Power supply (V1)
                   V

2
Resistance (R1)
                   Ω

3
Resistance (R2)
                   Ω

4
                   Ω

5
Resistance (R4)
                   Ω

6
Load resistance (RL)
                   Ω

7
Digital ammeter/ Multimeter
                   A

8
Digital Voltmeter/ Multimeter
                   V         

9
Bread board



Circuit Diagram
Fig (a)

I1

I2
   
Fig (b)
Fig (c)
Theory
Any two terminal bilateral linear D.C. circuits can be represented by an equivalent circuit consisting of a voltage source and a series resistance.
Let us consider a simple D.C. circuit as shown in fig (a). We are to find IL by Thevenin’s theorem.
In order to find the equivalent voltage source, RL is removed as shown in fig (b) and VTh is calculated.
Next, to find the Thevenin’s resistance of the network in series with VTh, the voltage source removed by a short circuit as shown in fig (c).
RTh={(R1II R3)+R2IIR4}
As per the Thevenin’s theorem, the equivalent circuit as shown in fig (d)


IL
Fig (d)





Procedure
1)      First we select the values of resistance R1, R2, R3, R4, RL and   applied voltage V1.              
2)      Connect the resistance R1, R2, R3, R4, RL and applied voltage V1 as shown in fig.(a)
3)      Remove the load resistance RL and find the Thevenin’s voltage VTh across the open circuited load terminals.
4)      eactivate the constant source and find the Thevenin’s resistance of the source side looking through the open circuited load terminals.
5)      Obtain the Thevenin’s equivalent circuit by placing RTh in series with VTh, as shown in fig (d)
6)      Reconnect RL across the load terminal as shown in fig (d) and find IL

Observation Table


Sr. No
Voltage
(Volt)
Observed values
Calculated Values
RTh
VTh
IL
RTh
VTh
IL
1
V1=






2
V1=






3
V1=






4
V1=






5
V1=







Sample Calculation













Questions
1.      State and explain the Thevenin’s theorem.


  

Experiment no. 3

Object
 Verification of Norton’s theorem
Objectives
1.      To understand the Norton’s theorem.
2.      To know the application of Norton’s theorem.
Apparatus

Sr. No
Name of Apparatus
Range
Quantity
1
D.C Power supply (V1)
                   V

2
Resistance (R1)
                   Ω

3
Resistance (R2)
                   Ω

4
Resistance (R3)
                   Ω

5
Resistance (R4)
                   Ω

6
Load resistance (RL)
                   Ω

7
Digital ammeter/ Multimeter
                   A      

9
Digital Voltmeter/ Multimeter
                  V

10
Bread board



Circuit Diagram
Fig (a)
Theory
Any two terminal linear networks with current source, voltage source and resistance can be replaced by an equivalent circuit consisting of a current source in parallel with a resistance.
In order to find the current through RL, the load resistance fig (a), by Norton’s theorem, let us replace RL by short circuit as shown in fig (b).
Fig (b)
Next, the short circuit is removed and the independent source is deactivated as done in Thevenin’s theorem as shown in fig (c).
Fig (c)
RN =={(R1II R2)+R3IIR4}
As per the Norton’s theorem, the equivalent source circuit would contain a current source in parallel to the internal resistance, the current source being the short circuited current across the shorted terminal of the load resistance.
Fig (d)
Obviously



Procedure
1. First we select the values of resistance R1, R2, R3, R4, RL and   applied voltage V1.              
2.   Connect the resistance R1, R2, R3, R4, RL and applied voltage V1 as shown in fig.(a)
3.   Short the load resistance and find the short circuit current or Norton’s current (IN) flowing through the short circuited load terminals as shown in fig (b).
4.   Next removing the load résistance RL find the Norton’s resistance (RN) by deactivating the constant voltage source as shown in fig (c).
5.   Norton’s equivalent circuit is drawn by keeping resistance Norton’s (RN) in parallel with Norton’s current (IN).
6.   Reconnect the load resistance (RL) across the load terminal as shown in fig (d)and the current through it (IL) is given by

Observation Table


Voltage
(Volt)
Observed values
Calculated Values
RN
IN
IL
RN
IN
IL
1
V1=






2
V1=






3
V1=






4
V1=







Sample Calculation











Questions
1.      State and explain the Norton’s theorem.



Experiment no. 4

Object
 Verification of Maximum power transfer theorem.
Objectives
 To verify the Maximum power transfer theorem.
Apparatus

Sr. No
Name of Apparatus
Range
Quantity
1
D.C Power supply (V1)
                 V

2
Resistance (R1)
                  Ω

3
Resistance (R2)
                  Ω

4
Resistance (R3)
                  Ω

5
Load resistance (RL)
                  Ω

6
Digital ammeter/ Multimeter
                   A

6
Digital Voltmeter/ Multimeter
                   V         

7
Bread board



Circuit Diagram
Fig (a)
Theory
A resistance load, being connected to a dc network, receives maximum power when the load resistance is equal to the source resistance.
A variable resistance RL is connected to a dc source network as shown in fig (a) while fig (b) represents the thevenin voltage VTh and thevenin resistance RTh of the source network. The aim is to determine the value of RL such that it receives maximum power from the dc source.
Fig (b)
Procedure
1. First we select the values of resistance R1, R2, R3, R4, RL and   applied voltage V1.
2. Connect the resistance R1, R2, R3, R4, RL and applied voltage V1 as shown in fig.(a)
3. Remove the load resistance and find Thevenin’s resistance (RTh) of the source network looking through the open circuited load terminals.
4. as per maximum power transfer theorem, this RTh is the load resistance of the network i.e, RL=RTh that allows maximum power transfer.
5. Find the Thevenin’s voltage (VTh) across the open circuited load terminals.
6. Maximum power transfer is given by


Observation Table
Observed Values
Resistance
VTh
1





2
RTh> RL





3
RTh= RL









Calculated Values
Sr.no
Resistance
RTh
RL
VTh
IL
1
RTh< RL





2
RTh> RL





3
RTh= RL






Sample Calculation
























Questions
1.      State and explain the Maximum power transfer theorem.

Experiment no. 5

Object
 Verification of Reciprocity theorem.
Objectives
 To verify the Reciprocity theorem.
Apparatus

Sr. No
Name of Apparatus
Range
Quantity
1
D.C Power supply (V1)
                   V

2
Resistance (R1)
                   Ω

3
Resistance (R2)
                   Ω

4
Resistance (R3)
                   Ω

5
Resistance (R4)
                   Ω

6
Digital ammeter/ Multimeter
                   A

7
Digital Voltmeter/ Multimeter
                   V         

8
Bread board



Circuit Diagram

Theory
In any linear bilateral network, if a single voltage source Va in branch ‘a’ produce a current Ib in branch ‘b’, then if the voltage source Va is removed and inserted in branch ‘b’ will produce a current Ib in branch ‘a’. The ratio of response to excitation is same for the two condition mentioned above. This is called the reciprocity theorem.
Consider the network shown in above fig. AA’ denotes input terminal and BB’ denotes output terminals.
The application of voltage V across AA’ produce current I at BB’. Now if the positions of the source and responses are interchanged, by connecting the voltage source BB’ the resultant current I will be at terminal AA’. According to the reciprocity theorem, the ratio of response to excitation is the same in both cases.
Procedure
1        First we select the values of resistance R1, R2, R3, R4, and applied voltage V1.              
2.      Connect the resistance R1, R2, R3, R4 as shown in fig1.
3.      The applied voltage V1 connect to branch AA’ as shown in fig1.
4.      Apply the voltage V1 and measure the current Ib flowing through branch BB’ as shown in fig 1.
5.      The applied voltage V1 in branch AA’ removed and connect to branch BB’ in series with R4 resistance as shown in fig 2.
6.      Now apply the same value of voltage V1 in branch BB’ and measure the current Ia flowing through branch AA’.
7.      The value of both current Ia and Ib is same

Observation Table


Sr. No
Voltage
(Volt)
Observed Values
Calculated Values
Ia
Ib
Ia
Ib
1
V1=




2
V1=




3
V1=




4
V1=





Sample Calculation





Questions
1.      State and explain the reciprocity theorem.




Experiment no. 6

Object
 Verification of Millman’s theorem.
Objectives
 To verify the Millman’s theorem.
Apparatus

Sr. No
Name of Apparatus
Range
Quantity
1
                Volt

2
D.C Power supply (V2)
               Volt

3
D.C Power supply (V3)
               Volt

2
Resistance (R1)
              Ω

3
Resistance (R2)
              Ω

4
Resistance (R3)
              Ω

6
Ammeter
               A


Circuit Diagram


                                      
fig (a)                                                 Fig (b)
Theory
Millman’s theorem sates that in any network, if the voltage sources V1, V2, V3……..Vn in series with internal resistance R1, R2, R3………Rn, respectively are in parallel, then these sources may be replaced by a single voltage source V’ in series with R’ as shown in fig (b),



Where Gn is the conductance of the nth branch,


Procedure
1.      First select value of R1, R2 , R3 and applied voltage V1, V2, V3.
2.      Connect the circuit as in the fig (1).
3.       Set the supply voltage as shown in circuit diagram.
4.      Note the reading ammeter (I2).
5.       Connect the circuit as in the fig (2). Note the reading of voltmeter (veg).
6.       Connect the circuit as in the fig (3) measure the equivalent resistance as Reg with
help of multi meter.
7.       Connect the circuit as in the fig (4), Apply (veg). From source, see Reg value.
8.       Note the reading of Ammeter as (I1).
9.       Now verifies IL= I1 Thus the Millman’s theorem is verified.


Observation Table


Sr. No
Observed Values
Calculated Values
V
R
V
R
1




2




3





Sample Calculation






Questions
1.      State and explain Millman’s theorem.
…………………………………………………………………………………………………………




Experiment no. 7

Object
 Verification of Compensation theorem.
Objectives
 To verify the Compensation theorem.
Apparatus

Sr. No
Name of Apparatus
Range
Quantity
1
D.C Power supply (V1)
                Volt

2
D.C Power supply (V2)
               Volt

3
D.C Power supply (V3)
               Volt

2
Resistance (R1)
              Ω

3
Resistance (R2)
              Ω

4
Resistance (R3)
              Ω

6
Ammeter
               A


Circuit Diagram

fig a.
Theory
Fig b
The compensation theorem states that any element in the linear, bilateral network may be replaced by a voltage source of magnitude equal to the current passing through the element multiplied by the value of the element, provided the current and voltage in other parts of the circuit remain unaltered. Consider the circuit shown in fig.b. The element R can be replaced by voltage source V, which is equal to the current I passing through R multiplied by R as shown in fig.b.
Procedure
1.      Connect the circuit as in the fig (a).
2.       Switch on the power supply and note down the readings of ammeter (I1).
3.       Connect the circuit as in the fig (2.b) with increase value of resistance.
4.       Switch on the power supply and note down the readings of ammeter (I2).
5.       Connect the circuit as in the fig (2.c)
6.      Switch on the power supply and note apply compensated voltage Vc=-I2 ΔR and note down the readings of ammeter (I3 ).

Observation Table

Sr. No
Observed values
Calculated Values
Vm
Rm
IL
Vm
Rm
IL
1






2






3







Sample Calculation












Questions
1. State and explain the Compensation theorem.



Experiment no. 8

Object

Objectives
 To verify the self mutual induction of coupled circuit and to find coefficient coupling.
Apparatus

Sr. No
Name of Apparatus
Range
Quantity
1
Single phase AC supply
                Volt

2
Auto-transformer
               Volt

3
AC voltmeter
               Volt

4
AC voltmeter
               Volt

5
AC Ammeter
              A

6
Wattmeter
              Ω

7
Single phase transformer
             


Circuit Diagram

fig a.
Procedure
1. To find the inductance of coil-1:
a) All the connections are made as per the circuit diagram.
b) To determine L, the resistance R1 of coil is neglected.
c) The Supply voltage is given and the reading of the voltmeter and ammeter are noted
L1= x/2 Πf when X1=V1/I1.
2. To find Self inductance of coil – 2:
a) The determine L2 remove the connections by interchanging the windings as per the circuit diagram
b). The voltage given and by varying dimmer stat required voltage is applied to coil and the readings of ammeter and voltmeter are noted.
L2 = X2 / 2 Πf, X2 = V2/I2


3. To find mutual inductance:
a) All the connections are made as per the circuit diagram.
b) The supply voltage is given by varying the dimmer stat and the reading of a ammeter and
Voltmeter is noted.
M = -1/2[X3/2 Πf – (L1+L2)]
Where X3 = V3 / I3
Coefficient of coupling K= M/sqrt(L1L2)


Observation Table

S.No
V1
V2
Io
Wi
COSФ= Wi/ V1* Io
Iμ=IoSINФo
1






2






3






4







Sample Calculation





Questions
1. What is mean by efficient of coupling.

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