II-year M.Sc. Physics Practical Experiments (DD&CE)

Laboratory Manual for Practical Courses

M.Sc. Physics

Directorate of Distance and Continuing Education

Manonmaniam Sundaranar University

Tirunelveli – 627012

November 2021

I-year M.Sc. Physics Practical Experiments (DD&CE) 2021

2

Practical I: Electronics (DKPP1)

Contents Page no.

1 Op-amp as Integrator and Differentiator 3

2 Op-amp as Adder and Subtractor 6

3 Half Adder and Full Adder 11

4 Hallf Subtractor and Full Subtractor 14

5 Verification of Demorgan’s Law 17


3

1. OP-AMP AS INTEGRATOR AND DIFFERENTIATOR

AIM

To construct an integrator and differentiator using operational amplifier and trace its

waveform.

APPARATUS REQUIRED

IC741, 10KΩ resistor, 0.01 μ F capacitor, signal generator, trainer kit, connecting wires.

THEORY

Operational amplifier:

Operational amplifiers were used for mathematical operations such as addition, subtraction,

integration and differentiation. An OP-Amp is used to amplify both alternating and direct current

signals at the input. It is fundamentally a voltage amplifying device designed to be used with

external feedback components, resistors and capacitors between its output and input terminals.

An Op-amp is basically a three terminals device which consists of two high impedance

inputs, one is called the inverting input, marked with negative sign and the other one is called non

inverting input marked with positive sign.

Offset Null:

Due to high gain provided by IC741 even slight difference in voltages at the inverting and

non-inverting inputs, caused due to reregulating in manufacturing process or external disturbance

can influence the output. To nullify this effect voltage can be applied at pin 1 and pin 5 using a

10K potentiometer.

Op- Amp integrator:

In an integrator circuit, the output voltage is integral of the signal. The output of an

integrator is given by

At low frequencies the gain becomes infinite, so the capacitor is fully charges and behaves

like an open circuit. The gain of integrator at low frequency can be limited by connecting a resistor

in shunt with capacitor.


4

Operational amplifier - Differentiator:

The circuit which produce the differentiation of the input voltage at its output is called

differentiator. The following circuit diagram, shows the differentiation using op amp. Output

voltage is nothing but time differentiation of the input signal and hence acting as differentiator here

Rc is the time constant of the differentiator.

PROCEDURE

Integrator:

Connect the circuit as shown in circuit diagram. Apply sine wave, square wave and

triangular wave, as the input in the function generator and measure the voltage and time in CRO.

Then study the output waves displayed on CRO, measure its voltage and time in CRO. Trace the

respective input and output waveforms.

Figure 1: Integrator input and output wave forms


5

Differentiator

Connect the circuit as shown in the circuit diagram. Then apply sine wave as input in CRO using function

generator. A Cosine wave will be displayed in CRO. Then measure the voltage and time of input and output wave.

Then trace the input and output waveform. Repeat the same procedure for various input wave.

RESULT

The integrator and differentiator circuit is constructed using operational amplifier IC741 and the Input and

output waveforms are traced.


6

2. OP-AMP ADDER AND SUBTRACTOR

AIM

To construct an adder and subtractor using IC741

APPARATUS REQUIRED

IC741, 10KΩ resistor, 0.01 μ F capacitor, signal generator, trainer kit, connecting wires.

FORMULA

Adder

(i) Inverting terminal

Output Vo = - ( V1 + V2)

(ii) Non Inverting terminal

Output Vo = ( V1 + V2)

Subtractor

Output Vo = ( V2 – V1)

V1 , V2 - Two input voltages (volt)

Vo - Output voltages (volt)

Theory

An adder is an electronic circuit that produces an output, which is equal to the sum of the

applied inputs. It is also called as a summing amplifier, since the output is an amplified.The non-

inverting input terminal of the op-amp is connected to ground. That means zero volts is applied at

its non-inverting input terminal

A subtractor is an electronic circuit that produces an output, which is equal to the difference

of the applied inputs. It is also called as a difference amplifier. An op-amp based subtractor

produces an output equal to the difference of the input voltages applied at its inverting and non

inverting terminals.


7

Pin Configuration

1

2

3

4

8

7

6

5

No connection

+ VCC

output

off set null

off set null

Inverting terminal

Non Inverting terminal

- VCC

ICI-741

Fig. 1. Pin Configuration

Fig. 2. Offset null

10 k

10 k

10 k

+ VCC

- VCC

o/p7

2

3

4

56

-

+


8

Procedure

Adder Inverting and Non Inverting Terminal

The adder circuit is constructed as shown in Fig. 3 and Fig. 4. The circuit diagrams shows

a two input inverting summing amplifier. It has two input voltages V1andV2, two input resistors R1,

R2 and a feedback resistor Rf. Set the voltages V1, V2 in the input terminal. Measure the output

voltages at the output terminal ( 6th

pin). Repeat the same procedure and tabulate the values. Find

the percentage error.

10 k

10 k

+ VCC

- VCC

VO

72

3

4

6

-

+10 k

V1

V2

Fig. 3. Adder - Inverting

10 k

+ VCC

- VCC

VO

72

3

4

6

-

+

10 k

V1

V2

10 k

Fig. 4. Adder – Non Inverting


9

Table. 1 Adder - Inverting terminal

S. No V1

(volts)

V2

(volts)

Calculated value

Vo = - ( V1 + V2)

(volts)

Experimental Value

Vo = - ( V1 + V2)

(volts) % Error

Table. 2 Adder – Non Inverting terminal

S. No V1

(volts)

V2

(volts)

Calculated value

Vo = ( V1 + V2)

(volts)

Experimental Value

Vo = ( V1 + V2)

(volts)

% Error

Subtractor

The subtractor circuit is constructed as shown in Fig. 5. the output voltage V0 is equal to the

voltage V1 applied to the non inverting terminal difference voltage V2 applied to inverting terminal.

Set the voltages V1, V2 in the input terminal. Measure the output voltages at the output terminal (

6th

pin). Repeat the same procedure and tabulate the values and find the percentage error.

10 k

10 k

10 k

+ VCC

- VCC

VO

72

3

4

6

-

+

10 k

V1

V2

Fig.5 Subtractor


10

Table. 3 Subtractor

S. No V1

(volts)

V2

(volts)

Calculated value

Vo = ( V2 + V1)

(volts)

Experimental Value

Vo = ( V2 + V1)

(volts) % Error

Result

The adder and subtractor circuit is constructed using IC 741. The calculated and

experimental values are verified.


11

3. HALF ADDER AND FULL ADDER

AIM

To construct half adder and full adder circuits and verify their truth tables.

APPARATUS REQUIRED

IC 7408, IC 7432, IC 7486 and digital trainer kit

Fig. 1. Pin Configuration


12

Procedure :

An half adder is a logic circuit that adds two bits and produces two outputs sum (s)and carry (c). The half-

adder does not take the carry bit from its previous stage into account. This carry bit from its previous stage is called

carry-in bit. A combinational logic circuit that adds two data bits, A and B, and a carry-in bit, Cin, is called a full-

adder. A full adder is useful to add three bits at a time but a half adder cannot.

Fig. 2. HALF ADDER

Table1. Half Adder - Truth Table

A B SUM CARRY

0 0 0 0

0 1 1 0

1 0 1 0

1 1 1 1

Table 2. Half adder - Voltage Table

A

(v)

B

(v)

SUM

(v)

CARRY

(v)


13

Fig. 3. Full Adder

Table3. Half Adder - Truth Table

A B C SUM CARRY

0 0 0 0 0

0 0 1 1 0

0 1 0 1 0

0 1 1 0 1

1 0 0 1 0

1 0 1 0 1

1 1 0 0 1

1 1 1 1 1

Table 4. Half Adder - Voltage Table

A

(v)

B

(v)

C

(v)

SUM

(v)

CARRY

(v)

Ressults

The half adder and full adder circuits are constructed using IC and their truth tables are verified.


14

4. HALF SUBTRACTOR AND FULL SUBTRACTOR

Aim :

To construct half subtractor and full subtractor circuits using logic

gates.

Apparatus required

IC 7408, IC 7432, IC 7486, IC7404 and digital trainer kit

FIG. 1 Half Subtractor

Table. 1 Half Subtractor - Truth Table

A B Difference Borrow

0 0 0 0

0 1 1 0

1 0 1 0

1 1 0 1


15

Table. 2 Half Subtractor – Voltage Table

A

(v)

B

(v)

Difference

(v)

Borrow

(v)

Fig. 1 Full Subtractor

Table. 3 Full Subtractor - Truth Table

A B C Difference Borrow

0 0 0 0 0

0 0 1 1 0

0 1 0 1 0

0 1 1 0 1

1 0 0 1 0

1 0 1 0 1

1 1 0 0 1

1 1 1 1 1


16

Table. 4 Full Subtractor - Voltage Table

A

(v)

B

(v)

C

(v)

Difference

(v)

Borrow

(v)

Results

The half and full subtractor circuits are constructed using IC and their Truth tables and

voltage tables verified.


17

5. Verification of Demorgans law using logic gates.

AIM :

To verify DeMorgans law using Logic gates

Apparatus Required

IC - 7400, 7402, 7404, 7408,7432

Demaorgans Law

De-Morgan's law has two conditions, or two laws called De-Morgan's Laws. We

can often use these laws to reduce expressions

First Law

The compliment of the product of two variables is equal to the sum of the

compliment of each variable

Fig.1. Demorgans First law

Table. 1. Verification of First law

A B ______

BA BA.

0 0

0 1

1 0

1 1


18

Second Law

The compliment of the sum of two variables is equal to the product of the

compliment of each variable.

Fig.2. Demorgans First law

Table. 1. Verification of First law

A B ______

.BA BA

0 0

0 1

1 0

1 1

Results

Demorgan’s Laws are verified using Logic gates.


19

Practical II: C++ Programming (DKPP2)

Contents Page no.

1 Solution of Simultaneous Equation-Gauss Elimination Method 20

2 Curve Fitting Cauchy’s Constant – Least Square Method 23

3 Newton Raphson Method 26

4 Matrix Multiplication 29

5 Euler’s Method- Radio Active Decay Problem 32


20

1. SOLUTION OF SIMULTANEOUS EQUATION-GAUSS ELIMINATION METHOD

Aim:

To write a C++ program to solve the solution of simultaneous equation-gauss elimination

method.

Algorithm:


21

Program:


22

Output:

Result:

The C++ program is written for finding the solution of simultaneous equation by using Gauss –

Elimination method. The program is executed and the values are verified manually.


23

2. CURVE FITTING CAUCHY’S CONSTANT – LEAST SQUARE METHOD

Aim:

To write a C++ program to find the Cauchy’s constants A and B by least square method

Algorithm:


24

Program:


25

Output:

Result:

The C++ program is written for finding the Cauchy’s constant A and B by using least

square method. The program is executed and the values are verified manually.


26

3. NEWTON RAPHSON METHOD

Aim:

To write a C++ program to find the solution using Newton Raphson method and verification

Algorithm:


27

Program:


28

Output:

Result:

The C++ program is written to find the root of on equation by Newton Rapson method. The

program is executed and the values are verified manually.


29

4. MATRIX MULTIPLICATION

Aim:

To write a C++ program to multiply the two matrices and print the resultant matrix.

Algorithm:


30

Program:


31

Output:

Result:

The C++ program is written multiply the two matrices and print the resultant matrix. The



32

5. EULER’S METHOD- RADIO ACTIVE DECAY PROBLEM

Aim:

To write a C++ program to solve the radioactive decay problem using Euler’s method.

Algorithm:


33

Program:


34

Output:

Result:

The C++ program is written to solve the radioactive decay problem using Euler’s method. The


Documents

II-year M.Sc. Physics Practical Experiments (DD&CE)