NT-2 LAB MANUAL
1. VERIFICATION OF SUPERPOSITION THEOREM
1.1 Aim: To verify Superposition theorem for the given circuit both theoretically and practically.
1.2 Apparatus:
S.No
Name o the Apparatus
Range
Type
Quantity
1
Dual channel R.P.S
(0-30)V/(0-2)A
DC
2
2
Digital Multimeters
3
Resistors
1
1k Ω,2.2k Ω,3.3k
C.C
1
Ω,4.7k Ω
4
Bread Board
1
5
Connecting wires
Required Number
1.3 Circuit Diagram:
10 V
2.2 k
3.3 k
4.7 k
1k
10 V
5V
15 V
1.4 Theory:
Superposition theorem states that in any linear bilateral network containing one or more sources, the
response in any element is equal to the algebraic sum of the responses cause by individual sources,
other ideal voltage sources and ideal current sources in the network are replaced by their internal
10 V source active
resistances.
15v, 10v, 5v sources active
IT = i1 + i2 + i3
5 V source active
15 V source active
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1.5 Limitations:
1. The superposition theorem is not valid for power responses as it is applicable only for computing
voltage & current responses.
2. It is not applicable for non linear network.
3. The response in the elements depends linearly on source voltages.
1.6 Procedure:
1. Connect the circuit as per the circuit diagram.
2. Adjust the output voltage of R.P.S to 15V remaining voltage sources replaced with internal
resistances (Short circuit) and note down the response i.e.…the current (i1) through branch of interest
(3.3k).
3. Adjust the output voltage of R.P.S to 10V remaining voltage sources replaced with internal
resistances (Short circuit) and note down the response i.e.…the current (i2) through branch of interest
(3.3k).
4. Adjust the output voltage of R.P.S to 5V remaining voltage sources replaced with internal
resistances (Short circuit) and note down the response i.e.…the current (i3) through branch of interest
(3.3k).
5. Now calculate the total current IT by activating the three voltage sources simultaneously.
6. Reduce the output voltage of R.PS to 0V and switch off the supply.
7. Disconnect the circuit.
1.7 Observations:
S.No
15 VSource
i1
10 V Source
i2
5 V Source
i3
15V&10V&5V
1.8 Result:
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NT-2 LAB MANUAL
2. VERIFICATION OF THEVENIN’S THEOREM
2.1 Aim: To verify Thevenin’s theorem for the given circuit both theoretically and practically.
2.2 Apparatus:
S.No
Name o the Apparatus
Range
Type
Quantity
1
Dual channel R.P.S
(0-30)V/(0-2)A
DC
1
2
Digital Multimeters
3
Resistors
1
1k Ω,2.2k Ω,3.3k
C.C
1
Ω,4.7k Ω
4
Bread Board
1
5
Connecting wires
Required Number
2.3 Circuit Diagram:
2.2 k
1k
1k
kk
1k
3.3 k
10 V
2.4 Theory:
In any linear bilateral circuit having more than one element can be replaced by single equivalent
circuit consisting of voltage source (VTH) in series with equivalent resistance (RTH).
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2.5 Observations:
S.No
Theoretical Values
Practical Values
1
RTH
RTH
2
VTH
VTH
3
IL
IL
2.6 Procedure:
1. Connect the circuit as per the circuit diagram.
2. Adjust the output voltage of R.P.S to an approximate value say 10 V.
3. Calculate VTH (open circuit voltage) across the load terminals by replacing the load resistance
RLwith an voltmeter.
4. Calculate RTH (open circuit resistance) across the load terminals by reducing the output voltage of
the R.P.S to zero volts.
5. Now calculate the load current IL from the Thevenin’s equivalent circuit.
6. Disconnect the circuit and tabulate the theoretical & practical values.
2.7 Result:
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3. VERIFICATION OF NORTON’S THEOREM
3.1 Aim: To verify Norton’s theorem for the given circuit both theoretically and practically.
3.2 Apparatus:
S.No
Name o the Apparatus
Range
Type
Quantity
1
Dual channel R.P.S
(0-30)V/(0-2)A
DC
1
2
Digital Multimeters
3
Resistors
1
1k Ω,2.2k Ω,3.3k
C.C
1
Ω,4.7k Ω
4
Bread Board
1
5
Connecting wires
Required Number
2.3 Circuit Diagram:
2.2 k
1k
1k
kk
1k
3.3 k
10 V
2.4 Theory:
In any linear bilateral circuit having more than one element can be replaced by single equivalent
circuit consisting of current source (IN) in parallel with equivalent resistance (RTH = RN).
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2.5 Observations:
S.No
Theoretical Values
Practical Values
1
RTH = RN
RTH = RN
2
IN
IN
3
ILN
ILN
2.6 Procedure:
1. Connect the circuit as per the circuit diagram.
2. Adjust the output voltage of R.P.S to an approximate value say 10 V.
3. Calculate IN (short circuit current) across the load terminals using ammeter by replacing the load
resistance RLwith short circuit.
4. Calculate RTH = RN (Norton resistance) across the load terminals by reducing the output voltage of
the R.P.S to zero volts.
5. Now calculate the load current ILN from the Norton’s equivalent circuit.
6. Disconnect the circuit and tabulate the theoretical & practical values.
2.7 Result:
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4. VERIFICATION OF MAXIMUM POWER TRANSFER THEOREM
4.1 Aim: To verify Maximum Power Transfer theorem for the given circuit both theoretically and
practically.
4.2 Apparatus:
S.No
Name o the Apparatus
Range
Type
Quantity
1
Dual channel R.P.S
(0-30)V/(0-2)A
DC
1
2
Digital Multimeters
3
Resistors
2
1k Ω,2.2k Ω,3.3k
C.C
1
Ω,4.7k Ω
4
Bread Board
1
5
Decade Resistance
1
Box (D.R.B)
6
Connecting wires
Required Number
4.3 Circuit Diagram:
2.2 k
1k
4.7 k
3.3 k
10 V
4.4 Theory:
1. This theorem is used to find the value of load resistance for which there would be maximum
amount of power transfer from source to load.
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2. The maximum power transfer theorem can be stated as “A resistive load being connected to a DC
network receives maximum power when the load resistance is equal to the internal resistance of
source”.
3. The efficiency under maximum power transfer is very poor because
Efficiency = Power absorbed by load
× 100
Power available in source
= V2/4RL × 100
V2/2RL
= 50 %.
I = VS/ RTH+RL
PL = I2 × RL = (VS)2 /( RTH+RL)2 × RL
d PL/d RL = 0
∴
(𝑅𝑆 + 𝑅𝐿 )2 . 𝑉𝑆 2 − 𝑉𝑆 2 𝑅𝐿 (2)(𝑅𝑆 + 𝑅𝐿 )
𝑑𝑃𝑙
𝑑
𝑉𝑠 2 𝑅𝑙
=0⟹
.
=
0
⇒
=0
(𝑅𝑆 + 𝑅𝐿 )4
𝑑𝑅𝑙
𝑑𝑅𝑙 (𝑅𝐿 + 𝑅𝑆 )2
⇒ (𝑅𝑆 + 𝑅𝐿 )2 . 𝑉𝑆 2 = 𝑉𝑆 2 (2𝑅𝐿 )(𝑅𝑆 + 𝑅𝐿 )
⇒ 𝑅𝑆 + 𝑅𝐿 = 2𝑅𝐿 ⇒ 𝑅𝐿 = 𝑅𝑆 .
∴ 𝑃𝐿(𝑀𝐴𝑋)
𝑃𝐿
𝑅𝐿
𝑉𝑆 2
2
=
=
𝑉𝑆 =
𝑅𝐿 = 𝑅𝑆
4𝑅𝐿
4𝑅𝐿 2
∴ 𝑃𝐿(𝑀𝐴𝑋)
𝑉𝑆 2
=
4𝑅𝐿
4.5 Procedure:
1. Connections are made as per the circuit diagram.
2. Adjust the output of R.P.S to Thevenin’s equivalent circuit VTH.
3. Vary the Resistance in each step and note down the Response (current) in each step.
4. Calculate the power absorbed by load for each step using the
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Formula 𝑃𝐿 = 𝐼𝐿 2 𝑅𝐿
5. Draw the graph RL on x-axis and PL on y-axis for both theoretical & practical values.
6. For practical value of load resistance it will gain maximum power from the circuit.
4.6 Theoretical Tabular Column: -
S.NO
RS
RL
𝐼=
𝑉𝑆
𝑅𝑆 + 𝑅𝐿
𝑃𝐿 = 𝐼 2 . 𝑅𝐿
RL
𝐼=
𝑉𝑆
𝑅𝑆 + 𝑅𝐿
𝑃𝐿 = 𝐼 2 . 𝑅𝐿
4.7 Practical Tabular Column: -
S.NO
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RS
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4.8 Result:
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NT-2 LAB MANUAL
5. VERIFICATION OF RECIPROCITY THEOREM
5.1 Aim: To verify Reciprocity theorem for the given circuit both theoretically and practically.
5.2 Apparatus:
S.No
Name o the Apparatus
Range
Type
Quantity
1
Dual channel R.P.S
(0-30)V/(0-2)A
DC
1
2
Digital Multimeters
3
Resistors
4
Bread Board
1
5
Connecting wires
Required Number
1
1k Ω,2.2k Ω,3.3k Ω
C.C
1
5.3 Circuit Diagram:
1k
3.3 k
1k
2.2 k
2.2 k
Figure.1
3.3 k
Figure.2
5.4 Theory:
1. The reciprocity theorem can be explained as “The ratio of response to excitation is invariant to an
interchange of the positions of the excitation and response in a single source.
2. However if the excitation is a voltage source the response should be a current and vicecersa, the
network which obeys this theorem are called as Reciprocal networks.
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5.5 Procedure:
1. Connect the circuit as per circuit diagram.
2. Adjust the output voltage of R.P.S to an appropriate voltage say 10 V in Figure 1.
3. Note down the response of I1 through 3.3 kΩ resistor and tabulate the values.
4. The circuit connections are changed as per the Figure 2,change the source to load end and replace
the source with internal resistance.
5. Note down the response of I2 through 1 kΩ resistor and tabulate the values.
6.Compare the theoretical & practical values and prove reciprocity theorem.
5.6 Observations:
Theoretical Values:
S.No
E in volts
I1
I2
V/ I1 = V/I2
I1
I2
V/ I1 = V/I2
Practical Values:
S.No
E in volts
5.7 Result:
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NT-2 LAB MANUAL
6. VERIFICATION OF MILLMAN’S THEOREM
6.1 Aim: To verify Millman’s theorem for the given circuit both theoretically and practically.
6.2 Apparatus:
S.No
Name o the Apparatus
Range
Type
Quantity
1
Dual channel R.P.S
(0-30)V/(0-2)A
DC
2
2
Digital Multimeters
3
Resistors
4
Bread Board
1
5
Connecting wires
Required Number
1
1k Ω
C.C
4
6.3 Theory:
In any network having a number of voltage sources (V1,V2,……….Vn) with internal resistances
(R1,R2………….Rn) are in parallel can be replaced by a single voltage source V in series with
resistance R.
where V =
𝑽𝟏𝑮𝟏+𝑽𝟐𝑮𝟐+⋯………………….𝑽𝒏𝑮𝒏
𝑮𝟏+𝑮𝟐+⋯………………………+𝑮𝒏
𝟏
R = 𝑮𝟏+𝑮𝟐+⋯…………………………𝑮𝒏
Figure 1
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for DC Circuits.
Figure 2
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NT-2 LAB MANUAL
6.4 Circuit Diagram:
6.5 Procedure:
1.Connect the circuit as per the figure 1 and adjust the output voltage of RPS to an appropriate value
say 5 V.
2.Note down the response I in the 1 kΩ Resistor.
3.Reduce the output voltage of RPS to zero volts and switch off the supply.
4.Now connect the circuit as per the figure 2 and note down the value of I in 1 kΩ Resistor.
5.Compare both theoretical and practical values of I ,hence Millman’s theorem is verified.
6.6 Observations:
Theoretical Value of I
Practical Value of I
Millman’s Theorem
6.7 Result:
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NT-2 LAB MANUAL
7.DETERMINATION OF Z & Y PARAMETERS
7.1Aim: Determination of Impedance (Z) & Admittance (Y) parameters of a two port network.
7.2 Apparatus Required:
S.No.
1
2
Name
Bread Board
Resistors
3
Digital
Multimeter
Regulated
Power supply
4
Range
Type
1k, 2k, 3.3k
, 4.7k
Quantity
1
1
1
DC
1
7.3 Circuit Diagram:
To determine Z parameters conduct open circuit test on either ports.
Fig.1 Open circuit test on Port1
Fig.2 Open circuit on Port2
1k
4.7 k
2.2 k
3.3 k
Two Port Network
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To determine Y parameters conduct Short circuit test on either ports.
Fig.3 Short circuit test on Port 2
Fig.4 Short circuit test on Port 1
7.4 Theory:
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7.5 Procedure:
1.Connect the circuit as shown in fig.1 note down the currents & voltages.
2.Calculate the values of Z12 & Z22.
3. Connect the circuit as shown in fig.2 note down the currents & voltages.
4.Calculate the values of Z11 & Z21.
5. Connect the circuit as shown in fig.3 note down the currents & voltages.
6.Calculate the values of Y11 & Y21.
7. Connect the circuit as shown in fig.4 note down the currents & voltages.
8.Calculate the values of Y12 & Y22.
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7.6 Observations:
7.7 Result:
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8.DETERMINATION OF ABCD & HYBRID PARAMETERS.
8.1Aim: Determination of ABCD & Hybrid (h) parameters of a two port network.
8.2 Apparatus Required:
S.No.
1
2
Name
Bread Board
Resistors
3
Digital
Multimeter
Regulated
Power supply
4
Range
Type
1k, 2k, 3.3k
, 4.7k
Quantity
1
1
1
DC
1
8.3 Circuit Diagram:
1k
3.3 k
2.2 k
4.7 k
8.4 Theory:
h-parameters:
For the two port network the input voltage (V1) & output currents (I2) are expressed in terms of input
current (I1) & output voltage V2 respectively as
V1 = h11I1+h12V2
I2 = h21I1+h22V2
When V2 =0 ⇒ h11 = V1 / I1 (Input impedance expressed in ohms).h21 = I2 /I1 (forward current gain).
When I1=0 ⇒ h12 = V1 / V2 (Reverse voltage gain).h22 =I2 / V2 (output admittance in mhos).
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Fig.1 Output is short V2=0
Fig.2 if input is open I1 = 0
ABCD-parameters:
ABCD parameters are also called as transmission parameters. ABCD parameter equations are given as
V1 = AV2 –BI2
I1 = CV2 – DI2
When I2 =0 ⇒ A = V1 / V2 (reverse voltage gain).C = I1 /V2 (Transfer admittance in mhos).
When V2 =0 ⇒ B = - V1 / I2 (Transfer impedance in ohms).D = -I1 /I2 (Reverse current gain).
Fig.3 output is open circuit I2 = 0
Fig.4 output is short V2 =0
8.5 Procedure:
1.Connect the circuit as shown in fig.1 note down the currents & voltages.
2.Calculate the values of h11 & h21.
3. Connect the circuit as shown in fig.2 note down the currents & voltages.
4.Calculate the values of h12 & h22.
5. Connect the circuit as shown in fig.3 note down the currents & voltages.
6.Calculate the values of A & C.
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7. Connect the circuit as shown in fig.4 note down the currents & voltages.
8.Calculate the values of B & D
8.6 Observations:
Short circuit on port 2:
S.No
V1
I1
I2
h11= V1 / I1
h21= I2 /I1
V2
I2
h12 = V1 / V2
h22 =I2 / V2
V2
I1
A = V1 / V2
C = I1 /V2
I1
I2
B = - V1 / I2
D = -I1 /I2
Open circuit on port 1:
S.No
V1
Open circuit on port 2:
S.No
V1
Short circuit on port 2:
S.No
V1
8.7 Result:
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