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”
|
|||||
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
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
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
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
|
|
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
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
|
|||
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
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
|
|
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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