B.tech Physics Manual

8/3/2019 B.tech Physics Manual

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Dept. of Basic Scienceand Humanities

Engineering Physics Lab Manual


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Instructions to Students1. A prior study about the experiment is essential for good performance in the

class.Read the instruction manual carefully before coming to the lab class. If youcome unprepared to the lab; your performance would be accordingly affected.

2. You are expected to perform the experiment, complete the calculations and data

analysis, and submit the report of every experiment on the same day within the

laboratory slot assigned for it.

3. You must bring with you the following material to the lab report sheets (A4 size

paper), pen, pencil, small scale, this instruction manual, graph sheets, calculator

and a file cover and any other stationary item required.

4. At least one set of observation should be signed by the instructor.

5. It is important to estimate the maximum possible error of the results using the

given apparatus/data.

6.

Each graph should be well documented; abscissa and ordinate along with the

units should be mentioned clearly. The title of the graph should be stated on the

top of each graph paper.


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INDEX

S.No Name of the experiment Page. No

1. Dispersive power of the material of a prism Spectrometer 5

2. Determination of wavelength of a source - Diffraction Grating 11

3. Newton's Rings - Radius of curvature of Plano convex lens 15

4. Single slit diffraction using laser 19

5. Rigidity Modulus: Torsional pendulum 22

6. Melde's Experiment - Transverse and Longitudinal modes 27

7. Time constant of an R-C circuit 32

8. L-C-R circuit 38

9. Magnetic field along the axis of a current carrying coil 48

(Stewart and Gee's method)

10.Energy gap of a material of p_n junction 53

11.Evaluation of Numerical Aperture of a given Optical fiber 57

12.Bending losses of Optical fiber 60

13.Characteristics of LED And LASER 62


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Particulars of the experiments performed

S.No Date Name of the Experiment Page No


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1. Spectrometer: Dispersive power of a prismAim: To determine the dispersive power of the prism.Apparatus: Spectrometer, prism, magnifying lens, mercury vapour lamp, spiritlevel, reading lens.

Formula: -

Refractive index is

sin2

sin2

A D

A

Where A = angle of the prism

D = Angle of the minimum deviation

The dispersive power of the material of the given prism1

b g

Where b and g are the refractive indices of two colours and2

b g

.

Where b is the refractive index of the blue colour

g is the refractive index of the green colour

Description: The spectrometer mainly consists ofa)a collimator

a)a telescope

b)a prism table

c)a circular scale and the verniera) The collimator:-Consists of a convergent lens fitted to the inner end of a hollow tube, fixed to the

instrument. Another hollow tube , which exactly fits into the fixed tube and can

be moved in or out by working pinion, carries at its outer end a slit of adjustable

width. The axis of the collimator is set perpendicular to the axis of the rotation

of the prism table. The collimator is fixed to the instrument and cannot be

rotated. The collimator is used to obtain a parallel beam of light from a given

source.


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The telescope: -This is an astronomical telescope whose objective is fitted to the inner end of a

hollow tube. Exactly fitting into this tube there is another tube which can be

moved in or out by working a pinion. At the outer end, the tube carries the

Ramsdens eye piece with cross wires. The cross wires consists, generally of the

fibers from a spiders web, fixed across the tube one vertically and another

horizontally in front of the eye-piece towards the objective side. The distance of

the cross-wires from the eye-piece can be altered by pushing in or drawing out

the eye-piece. The axis of the telescope is perpendicular to the axis of rotation of

the prism table. The telescope can be turned about an axis coinciding with the

axis of rotation of the prism table and can be clamped on any position by the

screw 1S . The angle of rotation can be measured, on a circular scale which is fixed

to the telescope and moved along with it. By means of the tangent screw the

telescope, after it is clamped, can be turned through very small angles and thus

fine adjustments can be made. The telescope is used to receive the parallel beam

of light from collimator.b) The prism table:-

It is a small circular table provided with three leveling screw and is used for

keeping the prism on it. The prism table can be raised or lowered and clamped inany position by a screw. By means of another screw it can be fixed to the vernier

table and the two will then turn together. The vernier is provided with a clamped

screw and a tangent screw for fine adjustment. The prism table can be rotated

about a vertical axis passing through its centre.

c) The circular scale:-This is a circular metal plate attached to the telescope and rotated with it.

Usually graduated into half degree and the reading can be noted on two vernier

which are fixed diametrically opposite to each other.

Adjustments: Before the instrument is used for measurement purpose, thefollowing adjustments are made.

A. Eye-piece: - The telescope is turned towards a white surface say a wall andthe eye-piece is moved in or out until the cross-wires are seen clearly.

B. Telescope: - The telescope is directed towards a distant object, say a telegraphpost or a tree and by working the pinion, the telescope is adjusted until the

image of the object is formed in the plane of the cross-wires with no parallax


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between the image and the cross-wires. Now the telescope is ready to receive

a parallel beam of light.

C. Collimator: - The slit of the collimator is illuminated with sodium light. Thetelescope is brought in line with the collimator and the distance of the slit

from the collimating lens is adjusted until a clear image of the slit with well-

defined edges is formed in the plane of the cross wires without any parallax

error and also the slit is adjusted to be vertical and narrow.D. Prism table: - A spirit level is kept on the prism table parallel to the line

joining to the leveling screws. The two screws are adjusted until the air

bubbles of the spirit level comes to the centre. Then the spirit level is turned

on the table perpendicular to this position and the third screw is adjusted

until the air bubble comes to the centre. Now the surface of the prism tablewill be horizontal. After making the adjustments of the spectrometer, the

least count of the vernier is found by the relation. . .

.l m s d

L CN

where N is

the number of divisions on the vernier scale.Determination of angle of the prism (A):

Procedure: The primary adjustments of spectrometer are to be done as explained.Then the prism is placed at the centre of prism table such that both refracting

edges of the prism are facing the collimator symmetrically as shown in Fig.

Then the prism is fixed. The telescope is released and rotated to observe reflected

image of the slit from one face say AB. The tangent screw of the telescope is

worked until the reflected image coincides with vertical cross wire. The readings

of the two verniers are noted. The telescope is rotated such that the reflectedimage of the slit from second face AC is focused. Then readings of both verniers


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are noted. Then difference between the respective readings of the vernier gives

the value 2A, from which the refracting angle can be determined.

Determination of angle of minimum deviation (D):-Procedure: - The vernier table is clamped and the prism table is released. Theprism clamped centrally on the prism table such that the surface of the ground

glass is almost parallel to the axis of the collimator and the light from collimator

incident on the polished surface of the prism emerges out from the other polished

surface as shown in fig.

The telescope is turned to observe the refracted image of the slit. Looking at theimage the prism table is slowly turned such that the image moves towards the

direct position. The telescope is also moved so as to keep the image of the slit in

the field of view. At certain stage it will be found that the image changes its

direction of motion even through the prism is continued to move in the same

direction.

The position of the prism is fixed when refracted image of the slit just retraces its

path, which is the minimum position of deviation. The telescope is focused such

that the image coincides with the vertical crosswire. The readings of two verniers

are noted. Then prism is removed and the telescope rotated such that the direct

image of the slit coincides with the vertical crosswire. Then the reading of two

verniers gives the angle of minimum deviation of the prism (D). Then refractive

index of the prism is found by the formula

sin2

sin2

A D

A


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Table 1: Angle of prism

Angle of prism (A) =

S.no Readings of reflected image Difference in vernierReadings (2A)

ALeft Right

Ver I Ver II Ver I Ver II Ver I Ver II


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Table 2: Angle of minimum deviation

The refractive index of the blue colour

sin2

sin2

b

b

A D

A

The refractive index of the green colour

sin2

sin2

g

g

A D

A

Dispersive power1

b g

Result:- Dispersive power of the given prism is =

Eye piece at

1T

Deviated ray

Eye piece at2

T

Deviated rayDifference in reading (D)

sin2

sin2

A D

A

Colour 1V

2V

1V

2V 1 1V V 2 2V V

Mean

D

Blue

Green


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2. Diffraction grating: Wave length of sourceAim: To determine the wavelength of a given source of light by using the diffractiongrating in the normal incidence position

Apparatus: Plane diffraction grating, spectrometer, spirit level, reading lens, sodiumvapour lamp.

Description: a plane diffraction grating consists of a parallel sided glass plate withequidistant fine parallel lines drawn very closely upon it by means of a diamond point.

The number of lines drawn is about 15,000 per inch.

Theory: When light of wavelength is incident normally on a diffraction grating havingN lines per cm and if is the angle of diffraction in the thn order spectrum, then

sinnN

Normal incidence method 0sin

ANn

Minimum deviation method 02sin

2A

D

nN

Where = wavelength of a given spectrum

From which can be determined.

Procedure: The usual initial adjustments of the spectrometer are done. The least countof the vernier of the spectrometer is found.

1. Normal incidence:The slit of the spectrometer is illuminated with sodium vapour lamp. The telescope is

placed in line with the axis of the collimator and the direct image of the slit is observed.

The slit is narrowed and the vertical cross-wire is made to coincide with the centre of the

image of the slit (1

T in fig). The reading of one of the vernier is noted. The prism table is

clamped firmly and the telescope turned through exactly 092 and fixed in position ( 2T in

fig).


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The grating is held with the rulings vertical and mounted in its holder on the prism

table such that the plane of the grating passes through the centre of the table and the

ruled surface towards the collimator. The prism table is released and rotated until the

image of the slit is seen in the telescope by reflection on the ruled side of the grating.

The prism table is fixed after adjusting the point of intersection of the cross-wires is on

the image of the slit. Then the vernier table is released and rotated trough exactly

045 from this position so that the ruled side of the grating faces the collimator. The

vernier table is fixed in this position and the telescope is brought back to the direct

reading position. Now the light from the collimator strikes the grating normally.

2. Measurement of :The telescope is rotated so as to catch the first order diffracted image on one side, say on

the left. With sodium light two images of slit very close to each other, can be seen. They

are called1

D and2

D lines. The point of intersection of the cross wire is set on the1

D line

and its reading is noted on the both vernier. Similarly the reading corresponding to the

2D line is noted.


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Then telescope is turned to the other side i.e. right side and similarly the readings

corresponding to1

D and2

D lines of the first order spectrum are noted. Half the

difference in the readings corresponding to any one line gives the angle of diffraction ()

for those lines in the first order spectrum. The experiment is repeated for the secondspectrum. The number of lines per cm of the grating (N) is noted and the wavelength

of the spectral line is found by the relation.

sin

Nn

Observations:-Number of lines (as marked on the grating) per inch = 15,000

Number of lines per cm =15,000

2.54=5906 lines/cm


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Precautions:1. Always the grating should be held by the edges. The ruled surface should not be

touched.

2. Light from the collimator should be uniformly incident on the entire surface of

the gratin

Result: Mean value of for1

D lines = cm.

= 0A .

Mean value of for2

D lines = cm.

= 0A .

Order of

Spectrum

(n)

Line

Reading of spectrometer 2

sin

Nn

Vernier I Vernier II

Vernier

I

Vernier

IIMean

Left Right Left Right


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3. Newtons ringsAim: To determine the radius of curvature of the Plano convex lens by forming Newtonsrings.

Apparatus: A convex lens is of focal length about 100cm, two optically plane glass plates,travelling microscope, condensing lens and a sodium vapour lamp.

Formula:-The radius of curvature of given Plano convex lens is given by

2 2

4 ( )

m nD D

R cmm n

Whrere =8

5893 10 cm

Description: The convex lens is placed on the optically plane glass plate P which is onthe platform of the travelling microscope. A black paper is placed under the glass plate.

The condensing lens C is placed at a distance equal to focal length of the lens from the

sodium vapour lamp. The emergent parallel beam of light is directed towards the glass

plate G kept directly above the centre of the lens and inclined 045 to the vertical. The

beam of light is reflected from the lower surface the lens and the top surface of the glass

plate P, Newtons rings with alternate bright and dark rings are formed having a black

centre. These can be focused by microscope (It may happen that the centre of the ring

system is bright. This is due to the presence of dust particle between the lens and thick

glass plate. In such a case the surfaces of the lens and the glass place have to be

cleaned.)


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Procedure: The microscope is focused at the centre of the ring system. The microscope ismoved so that the cross wires pass over 16 or 17 dark rings. Then the microscope is

moved back until the vertical cross wire is set at end of the 16th dark ring. The reading

of the main scale and the number of vernier coincidence are noted from which the

reading of the microscope can be determined. The microscope is moved so that the

vertical cross-wire is set at the end of the 14th dark ring. The reading of the microscopeis noted. Similarly the readings of the microscope with cross-wire set successively at the

end of the 12th, 10th, 8th 2nd dark ring. The microscope corresponding to 2nd, 4th, 8th, 10th

16th dark ring on the other side of the centre are noted. From these observations, the

diameter of the 2nd, 4th, 6th ..16th dark rings can be found.

The convex lens L is removed and its radius of the curvature R is determined either by a

spherometer or by Boys method. A graph is drawn with the number of dark rings on the

x-axis and the square of the diameter of the ring 2( )D on the y-axis. The graph is a

straight line passing through the origin. From the graph, the values 2nD and

2

mD corresponding to nth and mth are found.

Or taking the standard wavelength of sodium light, the radius of curvature of the lens

can be calculated. The value of radius of curvature of the lens is verified using

spherometer.

Precautions:-1. While taking the observations the microscope should be moved only in one

direction to avoid the error due to back-lash.

2. The lens L and the glass plate p, should be perfectly clean.

3. The slow motion tangent screw alone should be moved in taking observations.

4. The reading of the central rings up to 5 need not be considered as they will be

hazy and indistinct.

5.


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Observations

S.NoNo. of dark

Rings

Microscope reading Diameter

D = b - a

2D

Left (a) Right (b)

1 2

2 4

3 6

4 8

5 10

6 12

7 14

8 16


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A graph is drawn with the number of dark rings on the x-axis and the square of the

diameter of the ring 2( )D on the y-axis. The graph is a straight line passing through the

origin. From the graph, the values 2nD and2

mD corresponding to nth and mth are found.

APPLICATIONS1. Newtons rings are employed to detect and measure small changes in radii of

curvature and in the length of bodies.

2. These kinds of observations have been used for determining elastic constants ofmaterials.

3.

The flatness of glass surface can be tested by making use of Newtons rings.

4. The thickness of a thin object like a mica-sheet can be determined.

5. The refractive index of a liquid like water or oil can be determined.

Result: The radius of curvature of given Plano convex lens is R = cm (Exp)The radius of curvature of given Plano convex lens is R = cm (Graph)


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4. Single Slit Diffraction Using LaserAIMTo determine the wave length of the given laser source using a single using a single slit

and by diffraction pattern.APPARATUSDiode laser with round base, Single Slit, Travelling Microscope

FORMULA:0sina

An

Where a is the width of the slit is the angle of diffraction

n is the order of diffraction

THEORYWhen diffraction of light occurs as it passes through a slit, the angle to the minima in

the

Diffraction pattern is given by a sin = n ; (n= 1,2,3,...)

Where a is the slit width, is the angle from the center of the pattern to the m th

minimum, is the wavelength of the light, and m is the order of the minimum (1 for the

first minimum, 2 for the second minimum, counting from the center out). See Figure 1.1.


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Since the angles are usually small, it can be assumed that

sin tan

From trigonometry,

tan = y / L

where y is the distance on the screen from the center of the pattern to the mth minimum

and D is the distance from the slit to the screen as shown in Figure 1.1. The diffraction

equation can thus be solved for the slit width:

PROCEDURE1. Place the single slit parallel to the laser source such that the rays are incident on

the slit width.

2. Adjust the slit width such that we see clear diffraction pattern of the slit on

screen or wall.

3. Determine the distance L from the slit to the screen and distance between the

maxima is Y.

4. Take the readings on left and right side.

5. Vary the slit distance from the screen i.e. take the readings at different L.

6. The corresponding Y is measured.

7.

Measure the slit width (a) by microscope.


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OBSERVATION TABLESlit width(a) = ------------------------------ cm

Order of the

maximaL cm

Y Cm

sinY

L

sina

n

left Right Mean

PRECAUTIONS1. The laser beam should not penetrate into e yes as this may damages the eyes

permanently

2. The laser should be operated at a constant voltage 220V obtained from a stabilizer.

This avoids the flickering of the laser beam.

REASULT

The wavelength of the given LASER is =.......................


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5.Rigidity Modulus: Torsional pendulumAim: - To determine the rigidity modulus of the material of the given wire by dynamicalmethod using torsional pendulum.

Apparatus: - Torsional pendulum, stop watch, a vertical pointer, screw gauge andvernier calipers.

Formula: - The rigidity modulus of the given wire is2

4 2 2

4

MR l dynes

a T cm

Where M = mass of the disc (grams)

R = radius of the disc (cm)

l = is the length of the wire between two chucks (cm)

T = is the time period of the pendulum (sec)

a = radius of the wire (cm)

Description: - Tensional pendulum consists of a uniform metal disc suspended by a wirewhose rigidity modulus to be determined. The lower end of the wire is gripped in achuck fixed at the centre of the disc and the upper end is gripped in another chuck fixed

to a wall bracket as in fig.


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Theory: when the disc is turned through a small angle in the horizontal oscillationsabout the axis of the wire. The time period of oscillations given by

2 ---------------------------- (1)I

TC

Where I is the moment of inertia of the disc about the axis of rotation and C is thecouple per unit twist of the wire.

But ----------------------------------- (2)2

nC

l

Where A is the radius of the wire l is its length and n is the rigidity module.From equation (1) and (2) we have

4 2

8------------------------- (3)

I ln

a T

In the case of a circular disc whose geometric axis coincide with the axis of rotation, the

moment of inertia I is given by2

2

MRI

Where M is the mass of the disc and R is the radius. On substituting values of I inequation (3), we get

2

4 2

8------------------------- (4)

2

MR ln

a T

Procedure: A meter wire whose n is to be determined is taken. The disc is suspendedfrom one end of the wire. The other end of the wire is passed through the chuck fixed to

the wall bracket and is rigidly fixed. The length l of the wire between the chucks isadjusted to a convenient value (50 cm). A pin is fixed vertically on the edge of disc and a

vertical pointer is placed in front of the disc against the pin to serve as a reference to

count the oscillations.

The disc is turned in the horizontal plane through a small angle, so as to twist the wire

and released. There should not be any up and down and lateral movements of the disc.


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When it is executing torsional oscillations, time for 20 oscillations is noted twice and

mean is taken. The time period (T) is then calculated.2

l

TValue is calculated.

The experiment is repeated for different values of land in each case the time period isdetermined. The value

2

l

Tis calculated for each length. The observations are tabulated.

From the observations mean2

l

Tvalue is calculated.

The mass M of the disc is measured with a rough balance and its radius R iscalculated with vernier calipers. The radius of the wire a is determined very accurately

with screw gauge, at three of four different places and means value is taken since it

occurs in fourth power.Substituting these values in equation (4) n is calculated.A graph is drawn taking the value of l on the X-axis and the corresponding values of

2T on the Y-axis. It is a straight line graph passing through origin. From the graph

2

l

Tis

calculated.

Substituting this value of2

l

Talso n is calculated.

Precautions:1.

The wire should not be free from kings.2. The disc should not wobble.

Observations:Least count of screw gauge (L.C) = . Cm

Average radius of the wire (a) = .. cm

Mass of the disc (M) = cm

Mean radius of the disc (R) = . cm


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TABULAR FORMSi) Radius of the Wire (by Screw gauge)

S. No. PSR HSR L.C PSR + (HSR LC)Diameter

(cm)

Radius,

a(cm)

ii) To find l/T2 :

S.no Length

( l )

Time period for 20 oscillations

Period

T

2T 2

l

T

Trial I Trial II Mean

Mean 2l

T =


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The rigidity modulus of the given wire is2

4 2

4=

MR l

a T

EXPECTED GRAPHSA graph is drawn between l on x-axis and T2 and y-axis which is expected to be asbelow:

The rigidity modulus of the given wire is2

4 2

4=

MR l

a T

Result:- Rigidity modulus (n) of the wire dynes/ 2cm (Expt)Rigidity modulus (n) of the wire dynes/ 2cm (Graph)


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6. Meldes ExperimentAim: To determine the frequency of an electrically driven tuning fork.

Apparatus: An electrically maintained tuning fork, a light smooth pulley fixed to astand, a light scale pan, thread, a storage cell, rheostat, plug key and connecting wires.

Description: A fork can be maintained in the state of continuous vibration electrically.one terminal of the coil of an electromagnet is connected to the make and break

arrangement and the other end of the coil to the cell, rheostat and plug key connected in

series. In the normal position when the circuit is closed, the electromagnet attracts the

prong of the fork towards it. This breaks electrical circuit and the prong moves back

closing the circuit. The electromagnet again attracts the prong towards it. This isrepeated again and again and the fork is maintained in a state of continuous vibration.

One end of the thread of length about 3 meters is joined to a screw attached to one prong

of the fork and the other end is passed over a smooth pulley and light pan is fixed at the

other end of the thread. When the fork is vibrated electrically, stationary waves of well

defined loops are formed.

Melds apparatus can be arranged in two modes of vibration

a) When the direction of motion of the prong is at right angles to the length of the

string, the vibrations of the thread represent the transverse mode of vibration.

b) When the direction of motion of the prong is along the length of the thread, the

vibrations of the thread represent longitudinal mode of vibration.Procedure:

1.

The apparatus is arranged in transverse mode of vibration of the thread. A

suitable load is placed in the pan. The tuning fork is excited electrically. The

length of thread is adjusted by moving the pulley until well defined loops are

formed in it. The distance between a definite number of well defined loops is

measured with a meter scale from which the average length lof a single loop isdetermined.

dl cmx


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2. The total load attached to the thread inclusive of the mass of the pan is noted. If

it is Mg, the tension applied on the string is T = Mg. where g is acceleration due

to gravity.

The mass of the thread is determined correct to a milligram. The mass per unit

length of the string is then determined. The frequency n of the tuning fork is

founded by the relation

1Hz

2

Tn

l

The experiment repeated for various tensions and the observations are tabulated

in table.1 and n is calculated.

3. The apparatus is arranged in longitudinal mode of vibration of the thread. The

experiment is done in similar manner as in 1. The average length l of a loop, thetension T applied to the thread and the mass per unit length of the thread are

found. the frequency of the tuning fork is found by the relation

1Hz

Tn

l

The experiment is repeated with different tensions and the observations are

tabulated in table.2 and n is calculated.


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Precautions:1. A thin and inelastic thread should be used.

2. The loops should be well defined and confined to single plane.

The mean of the two average frequencies in the transverse and longitudinal modes gives

the correct frequency of the tuning fork.

OBSERVATIONS1. Mass of the string (thread) = w = .. gm (correct to a mg)

2. Length of the string (thread) = y = .. cm

3. Linear density of the thread = =(w/y) = gm / cm

4. Mass of the pan = m = .. gm (correct to a mg)

Mass per unit length of the thread (m) = grams

Table.1 Transverse Mode

S.no T = Mg Length of

P loops = L

Length of

Each loop

T

l


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AverageT

l=

Then1

2

Tn

l =

Table.2 Longitudinal Mode

S.no T = Mg Length of

P loops = L

Length of

Each loop

T

l

AverageT

l=

Then1 T

n

l

=


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APPLICATIONS1. Vibrations of bars or rods, vibrations of metallic plates, vibrations of belts,

vibrations of diaphragm, forced vibrations of a sound box in a gramophone or a

loud speaker in a radio etc.

2. In the case of a rectangular bar the frequency of vibrations is proportional to the

length of its side in the plane of vibration, and inversely proportional to the

breadth in that plane. The frequency is independent of the thickness at right

angles to the plane of vibrations.

3. The vibrations produced in bridges of road ways and railways can be experienced

while standing on it when a heavy vehicle or a train passes over it.

Result: The frequency of the tuning fork n = Hz (Longitudinal Mode)The frequency of the tuning fork n = Hz(Transverse)


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7. Time Constant of RC-circuitAim:

1. To study the charging and discharging of a capacitor through a resistance byplotting a graph

2. To determine the time constant of C.R. circuit

Apparatus:-Battery eliminator, resistors, capacitors, galvanometer, stop clock, tap key, connecting

wires.Formula:Capacitive time constant of the CR circuit is t RC

Where C = capacitance of the condenser

R = resistance

Procedure:-1. To study the charging of a condenser:-The experimental arrangement for the study of the charging and discharging of a

condenser through a resistance is shown in fig.


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A condenser C, resistance R, a tap key K are to be connected to a battery B. connect a

volt meter V parallel to the condenser, by means of which the potential difference across

the plates of the condenser can be measured. Adjust the voltmeter knob so that it reads

zero. Switch on the power supply press the tap key K and simultaneously start a stop

clock. When the tap key, K is pressed the current flows and the plates of the condenser

get charged. Note the voltmeter reading, V at suitable regular intervals of time (say 5

seconds) till the voltage reaches a maximum value0

V i.e. the condenser gets fully

charged. Note the observations in table repeat the experiment for different sets R and C

values.

Graph:

Draw a graph with the time, t along the X-axis and the voltage, V (across the condenser)

along the Y-axis. A curve shown in figure will be obtained. Draw a line parallel to X-axis

at 0.63V0. This line cuts the curve at one point. The value of time on the x-axis

corresponding to V=0.63V0 gives the capacitive time constant of the CR circuit,

Calculate the theoretical value of the time constant CR using the formula and compare

it with that obtained from the graph.


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2. To study the discharging of condenser:-Switch on the power supply, keeping the circuit elements as they were. Press the tap

key K. then the reading in the voltmeter gradually increases and reaches a constant

value 0V after some time i.e. the condenser gets fully charged. Now release the tap key,

K and immediately start a stop clock. When the tap key is released the condenser starts

discharging through the resistance and in consequence the voltmeter reading gradually

decreases. Note the voltmeter reading at suitable regular intervals of time till the

voltage across the plates of the condenser reaches a minimum value. Note the

observations in table. Repeat the experiment for different sets of R and C values.

Graph:

Draw a graph with the time, t along the X-axis and the voltage, V (across the condenser)along the Y-axis. A curve shown in figure will be obtained. Draw a line parallel to X-axis

at 00.36V V . This line cuts the curve at one point. From this point draw a line parallel

to y-axis which meets the x-axis at one point. The value of time on the x-axis

corresponding to 00.36V V gives the capacitive time constant of the CR circuit,

Calculate the theoretical value of the time constant CR using the formula and compareit

with that obtained from the graph.


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OBSERVATION TABLE

Set: IC = F R = K CR = Sec

S.NoTime (t)

Sec

Voltmeter reading

Charging Discharging


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Set: IIC = F R = K CR = Sec

S.No

Time (t)

Sec

Voltmeter reading



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Comparison table:-

S.No

Time constant CR (sec)


Theoretical Experimental Theoretical Experimental

Set I

Set I

Calculations:-1. Charging of the condenser:-

Set I Set IIC = F = farad C = F = faradR = K = ohm R = K = ohmCR = Sec CR = Sec

2. Discharging of the condenser:-

Set I Set IIC = F = farad C = F = faradR = K = ohm R = K = ohmCR = Sec CR = Sec

Experimental values:-1. Charging of the condenser (from graph)

Capacitive time constant CR =c

t = sec

2. discharging of the condenser (from graph)

Capacitive time constant CR = ct = sec


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8. LCR CIRCUITAimTo study the series and parallel resonance circuit find to and frequency and quality

factor.ApparatusFunction generator, an inductance coil, three capacitors, a resistance box, a.c.

voltmeters, multimeter, one a.c. milliammeter, connecting wires.

FormulaSeries resonant circuit:-Theoretical

The resonance frequency is 01

2f LC

Quality factor =1 L

QR C

Where0

f is the resonance frequency

L is the inductance

C is the capacitance

R is the resistance and

Experimental (from graph)The resonance frequency of the circuit

0f = Hz

Band width of the resonant circuit 2 1f f Hz

Quality factor 0 0

2 1

f fQ

f f

Parallel resonant circuit:-TheoreticalThe resonance frequency is

2

0 2

1 1Hz

2

Rf

LC L

Quality factor = 0 0

2 1

f fQ

f f

Where 0f is the resonance frequency


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L is the inductance

C is the capacitance

R is the resistance and

Experimental (from graph)The resonance frequency of the circuit

0f = Hz

Band width of the resonant circuit 2 1f f Hz

Quality factor 0 0

2 1

f fQ

f f

2 1f f is the band width and 1f , 2f can be obtained for graph.

Theory:-Circuits containing an inductor L, a capacitor C, and a resistor R, have special

characteristics useful in many applications. Their frequency characteristics (impedance,

voltage, or current vs. frequency) have a sharp maximum or minimum at certain

frequencies. These circuits can hence be used for selecting or rejecting specific

frequencies and are also called tuning circuits. These circuits are therefore very

important in the operation of television receivers, radio receivers, and transmitters. In

this section, we will present two types of LCR circuits, viz., series and parallel, and also

discuss the formulae applicable for typical resonant circuits.

A series LCR circuit includes a series combination of an inductor, resistor and capacitor

whereas; a parallel LCR circuit contains a parallel combination of inductor and

capacitor with the resistance placed in series with the inductor. Both series and parallel

resonant circuits may be found in radio receivers and transmitters.

Series resonance circuit:-


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When an alternating e.m.f 0 sin t was applied to circuit having an inductance L,

capacitance C and resistance R in series as shown in fig. The current in the circuit at

any instant of time t is given by the following equation

Where it can also be proved that the maximum current io is

And from above equation the phase difference between the applied e.m.fand the

resultant current is given by

From equation (1) the impendence Z of the impedance of the circuit is given by

The L - C - R series circuit has a very large capacitive reactance (1

C) at low

frequencies and a very large inductance reactance ( L ) at high frequencies. So at a

particular frequency, the total reactance in the circuit is zero (1

LC

).Under this

situation, the resultant impedance of the circuit is minimum. The particular frequency

of A.C at which impedance of a series L - C - R circuit becomes minimum is called the

resonant frequency and the circuit is called as series resonant circuit.

At resonance frequency


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Or

The resonant frequency fo of the series resonant circuit is given by

The above equaton shows that the resonant frequency depends on the product of L and

C and does not depend on R. The variation of the peak value of current with the

frequency of the applied e.m.fis shown in fig.

Let f1 and f2 be these limiting values of frequency. Then the width of the band is

The Quality factor is defined as

Q-factor is also defined in terms of reactance and resistance of the circuit at resonance,


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Parallel resonant circuit:-

A parallel resonant circuit is shown in fig. Here an inductance L and a resistance R are

connected in series in one branch and a condenser of capacity C in another branch. A

source of alternating e.m.fis connected to this circuit. From the above fig admittance (Y)

can be calculated as

Where Z is the impedance of the circuit. The admittance is minimum or impedance is

maximum at a particular frequency (f), which is given by

At this frequency admittance is minimum and hence the current is minimum. such a

The impedance (or) dynamic resistance of the circuit

The quality factor


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Procedure:-Series resonant circuit:-

1. Connect the circuit as shown in the circuit diagram.

2. Apply input signal using signal generator.

3. Take the output across the resistor and feed it to Ammeter input sockets.

4. Vary the frequency till the Ammeter records a sharp rise and fall, adjust the

signal such that the Ammeter defection is the maximum possible. This is the

resonant frequency of the connected combination of the circuit.

5. Adjust the signal generator amplitude such that to get full-scale deflection. In

Ammeter now reduce the frequency till the deflection falls considerably. Then

increase the frequency in regular intervals & note down the Ammeter readings.

6.

Plot a graph between the meter defection divisions and frequency.

7. Repeat the procedure using different combinations of L, C & R and study how Q

is affected. Also study how Resonant Frequency depends upon different

combinations of L.C.R.

Parallel resonant circuit:-1. Connect the circuit as per the circuit diagram.

2.

Apply input signal, from a reliable signal generator. The output should be 10Vonly.

3. Take the output across the tank circuit and connect to Ammeter input sockets.

4. Vary the frequency till the Ammeter records sharp fall. Adjust the signal such

that the deflection falls down considerably. Then increase the frequency in

regular intervals and note down the deflection.

5. Adjust the signal generators amplitude such that, to get full-scale deflection.

Now reduce the frequency till the deflection falls down considerably. Then

increase the frequency in regular intervals & note down the deflection.

6. Plot graph between the meter deflection divisions and frequency.

7. Repeat the procedure for different values of R and study how Q is affected. Also

study how resonant frequency depends on different combinations of L.C.R.


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Graph: -1. For series resonant circuit

2. For Parallel resonant circuit


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Observations:-Table:-I For series resonant circuit:-

S.No Frequency Current


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Table:-II for Parallel resonant circuit:-

S.No Frequency Current


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Result:-The theoretical and experimental values of the resonance frequency,

0f and the

quality factor Q, are calculated and compared. They are found to be equal.

Series combination:-

S.No Parameters Theoretical valuesExperimental

values

1Resonance frequency(

0f )

2Quality factor

Parallel combination:-

S.No Parameters Theoretical valuesExperimental

values

1Resonance frequency(

0f )

2Quality factor


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9. STUDY OF MAGNETIC FIELD ALONG THE AXIS OF A CIRCULAR COIL -STEWART AND GEES APPARATUS

AIMTo study the variation of magnetic field along the axis of a circular coil carrying current.

EQUIPMENT & COMPONENTSStewart and Gees type of tangent galvanometer, Rheostat, Ammeter, deflection

magnetometer, Battery eliminator, 4way & 2 way key.

FORMULAThe magnetic field (B) at a point on the axis of a circular coil carrying current "i" is

given by the expression

20

3 2

2 2

n i a B Telsa

2 x + a

Where 'n is the number of turns,a the mean radius of the coil,

x is the distance of the point from the center of the coil along the axis, andi is the current passing through the coil.

DIAGRAM OF EXPERIMENTAL SETUP


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DESCRIPTIONThe apparatus consists of a circular frame "c" made up of non-magnetic substance. An

insulated Copper wire is wounded on the frame. The ends of the wire are connected to

the other two terminals. By selecting a pair of terminals the number of turns used canbe changed. The frame is fixed to a long base B at the middle in a vertical plane along

the breadth side. The base has leveling screws. A rectangular non-magnetic metal frame

is supported on the uprights. The plane of the frame contains the axis of the coil and

this frame passes through the circular coil. A magnetic compass like that one used in

deflection magnetometer is supported on a movable platform. This platform can be

moved on the frame along the axis of the coil. The compass is so arranged that the

center of the magnetic needle always lie on the axis of the coil.

The apparatus is arranged so that the plane of coil is in the magnetic meridian. The

frame with compass is kept at the center of the coil and the base is rotated so that the

plane of the coil is parallel to the magnetic needle in the compass. The compass is

rotated so that the aluminum pointer reads 00-00. Now the rectangular frame is along

East-West directions. When a current "i" flows through the coil the magnetic field

produced is in the perpendicular direction to the plane of the coil. The magnetic needle

in the compass is under the influence of two magnetic fields. "B" due to coil carrying

current and the earth's magnetic field "Be" which are mutually perpendicular. The

needle deflects through an angle '' satisfying the tangent law.

PROCEDURE

With the help of the deflection magnetometer and a chalk, a long line of about one meter

is drawn on the working table, to represent the magnetic meridian. Another line

perpendicular to the line is also drawn. The Stewart and Gees galvanometer is set with

its coil in the magnetic meridian as shown in the fig. The external circuit is connected as

shown in the fig, keeping the ammeter, rheostat away from the deflection

magnetometer. This precaution is very much required because, the magnetic field

produced by the current passing through the rheostat and the permanent magnetic field

due to the magnet inside the ammeter affect the magnetometer reading, if they are close

to it.


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The magnetometer is set at the center of the coil and rotated to make the aluminum

pointer reads (00-00) in the magnetometer. The key K, is closed and the rheostat is

adjusted so as the deflection in the magnetometer is about 60. The current in the

commutator is reversed and the deflection in the magnetometer is observed. The

deflection in the magnetometer before and after reversal of current should not differ

much. In case of sufficient difference say above 2 or 3, necessary adjustments are to be

made.

The deflections before and after reversal of current are noted when d=0. The readings

are noted in Table. The magnetometer is moved towards East along the axis of the coil

in steps of 2cm at a time. At each position, the key is closed and the deflections before

and after reversal of current are noted. The mean deflection be denoted as E. The

magnetometer is further moved towards east in steps of 2cm each time and thedeflections before and after reversal of current be noted, until the deflection falls to 30.

The experiment is repeated by shifting the magnetometer towards West from the center

of the coil in steps of 2cm, each time and deflections are noted before and after the

reversal of current. The mean deflection is denoted as w.

It will be found that for each distance (x) the value in the last two columns of the second

table are found to be equal verifying equation (1) & (2).

A graph is drawn between x [the distance of the deflection magnetometer from the

center of the coil along x-axis and the corresponding Tan e and Tan w along y-axis.

The shape of the curve is shown in the figure. The point A and B marked on the curve lie

at distance equal to half of radius of the coil (a/2) on either side of the coil.

OBSERVATIONSHorizontal component of earths

magnetic field Be

= 0.38 104 Tesla (or Wb.m2)

Radius of a coil a = .. meter

(Diameter of coil / 2)

Current carrying in the ammeter = . Amps

0 = 4 107


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TABULAR FORMSDistance

from the

Center of

Coil x

Deflection in East

Direction

Mean

E

Deflection in West

Direction

Mean

W2

E W

Tan

1 2 3 4 1 2 3 4

Distance in meter (x) Theoretical B Practical B


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EXPECTED GRAPH

RESULTIntensity of magnetic field of earth is calculated and verified for standard tables


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10. ENERGY GAP OF MATERIAL OF P-N JUNCTION

AIM:-

To determine the energy band gap material given semiconductor diode.

EQUIPMENT AND COMPONENTS:-

D.C Power Supply, Semi-conductor diode (Germanium or Silicon), thermometer, heating

arrangement to heat the diode, Voltmeter, Microammeter and connecting wires.

FORMULA:- 41.9833 10g E slope eV

THEORY:-The Energy gap (Eg) of a material is defined as the minimum amount of energy required

for an electron to get excited from the top of the valance band to the bottom of the

conduction band. The energy gap for metals is zero since valance band and conduction

band overlap each other whereas the energy gap for the insulators is very high. The

energy gap for the semiconductors lies between the values for metals and the insulators.

The resistance of a semiconductor varies with the temperature as 0 (exp )gE

kTR R ----- (1)

Where is the resistance of the semiconductor at absolute zero.

K is the Boltzman constant and T is the temperature of the material.

By applying logarithms of both sides of the equitation (1), we get

) --------- (2)

This is a linear equation between 10loge and

1

Tits slope is obtained from:

Slope = Eg


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Eg = Slope

41.9833 10g E slope eV

Circuit Diagram:-

DESCRIPTIONThe experimental arrangement comprises an oil bath which is provided with sockets at

its mouth. The sockets are used to insert the thermometer and the semiconductor diode

in the oil bath. A heating element is fixed inside the oil bath which used to raise the

temperature of the oil bath by connecting to the AC main supply. The reverse biasing

voltage can be adjusted by means of the voltmeter and the reverse saturation current

can be measured with the help of a microammeter.

Connecting the two terminals of the given semiconductor diode (Germanium or Silicon)

to the DC Power supply and microammeter in such a way that the diode is reverse

biased. Immerse the diode in the oil bath. Insert the thermometer in the oil bath at the

same level as that of the diode.

Switch on the DC Power supply and adjust the reverse bias voltage to 5 Volts. Switch on

the AC main supply, then the temperature of the oil bath gradually increase.

Consequently, the current through the diode also increases. Note the value of thecurrent of every 5c increase of the temperature, when the temperature of the oil bath


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reaches to about 65c, and then switch off the AC supply. Stir the oil by means of a

stirrer. Then, the temperature of the oil bath will rise and stabilizes at about 70c. Note

the temperature of the oil bath and the current through the diode. After few minutes,

the temperature of the oil bath will begin to fall and the current through the diode

decreases. Note the value of the current of every 5c decrease of the temperature, till

the temperature of the oil bath falls to the room temperature.

Tabulate the values of current and temperature. Repeat the experiment for two or three

different voltages.

Graph:- Draw the graph taking on the Xaxis and R10log on the Yaxis. One shouldget a straight line which does not pass through the origin. Find the slope of the straight

line.

41.9833 10g E slope eV BC

slopeAC


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OBSERVATIONS

RESULT

Energy gap of the given semiconductor = ______________ eV.

S.NoTemperature

(T) Current (A)Mean

Current Resistance

c KIncreasing

temperatureDecreasing

temperature(A)

R= V/t in

x10ohms 1

T

130

2 353 404 455 506 557 608 659 70


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11. Numerical Aperture of Optical fiberAim:-To measure the Numerical aperture (NA) of the given fiber.

Apparatus:-Numerical aperture measurement Jig. Optical fiber cable with source. Numerical

aperture of any optical system is a measure of how much light can be collected by the

optical system.

Formula:-Numerical aperture max

2 2( ) sin

4

WNA

L W

1

max

sin ( )NA

max2c

Where L is the distance of the screen from the fiber end in meters. W is the diameter of

the spot in meter.

Principle:-Numerical aperture (NA) refers to maximum angle at which the light incident on the

fiber end is totally internally reflected and transmitted properly along the fiber. The

cone formed by the rotation of this angle along the axis of the fiber is the cone of

acceptance of the fiber. The light ray should strike the fiber end it will get refracted and

leave the fiber.

Setup for NA measurement

a. One end of the meter fiber cable is connected to the PO of the source and the

other end to NA JIG.

b. The Ac main is plugged light must appear at the end of the fiber on the NA Jig.

The set PO knob is tuned clock wise to set to a maximum Po. The light intensity

would increase.


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c. The white screen with four concentric circles (10, 15, 20, and 25mm diameters) is

held vertically at a suitable distance to make the red spot from the emitting fiber

coincide with the 10 mm circle. The circumference of the spot must coincide with

the circle. The distance of the screen from the fiber end L is recorded and the

diameter of the spot 'W' is noted. The diameter of the circle can be accurately

measured with a scale.The numerical aperture is calculated from the

formula max2 2

( ) sin4

WNA

L W

d. The same procedure is repeated for 15mm, 20mm and 25mm diameters.

Table:-Circle

Distance between

source and screen

L (mm)

Diameter of the

spot W (mm) 2 24

WNA

L W

(degrees)

1

2

3

4

5

6

7

8


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Calculations:-Numerical aperture

max

2 2

( ) sin

4

WNA

L W

1

max sin ( )NA

max2c (degrees)

Result:-The Numerical aperture is measured as ...................................

The acceptance angle is calculated as .................................... (degrees)


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Table:Wavelength =

Length of the cable =

S.NoMandrelDiameter

mandrelradius 0

P LP


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13. Characteristics of LED And LASERAimTo study the volt-Ampere characteristics of LED and a LASER source

ApparatusMillivoltmeter, microammeter, light emitting diode and low intensity laser, power

supply, connecting wires.

TheoryIn LED or LASER, the input supply is electrical energy and the output from these is

light energy. That is, LED and LASER convert the electrical energy into light energy. Alaser beam is highly coherent, monochromatic and intense and hence should not be seen

directly with eye. The light coming out of an LED is not highly intense and highly

monochromatic and hence it can be seen directly with our eye. The volt- ampere

characteristics of these two devices are studied here and comparison is made between

these devices.

ProcedureThe circuit diagram id connected as shown in the figure. 1.0 to 10 v D.C power supply is

connected to a LED and a micro ammeter in series as shown in figure.

A Millivoltmeter is connected across the terminals of the LED. The power is switched

ON, and varied slowly. The reading in the microammeter and the reading in the miili

voltmeter is noted. The procedure is repeated by slowly varying the power supply and at


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each step the reading of the microammeter and Millivoltmeter are recorded. The

readings are tabulated in Table-I and a graph is drawn between voltage and current.

The LED is now disconnected from the circuit and a low power LASER diode is

connected in its place. The micro ammeter is replaced with a milli ammeter and themilli voltmeter is replaced by voltmeter since the firing voltage of a LASER and LED are

different.

ObservationsTable-I

S.No Reading in the Milliammeter Voltage across LED


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Table-IIS.No Reading in the Microammeter Voltage across LASER

Model Graph V-I characteristics of LED P-I characteristics of LASER


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Least count of the travelling microscope:

Least count of the spectrometer:of 1 MSD

count =. of vernier scale divisions

valueLeast

No

Value of the one main scale division = 0 '1 302

Number of vernier scale divisions = 30'

'of 1 MSD 30count = 1. of vernier scale divisions 30

valueLeast

No

L.C 1minute Screw guage

of 1 MSD

count = . of vernier scale divisions

value

Least No

Value of the one main scale division = 0.1cm

B.tech Physics Manual

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