1. TORSIONAL PENDULUM - Vidyarthiplus

1

AIM

To determine the moment of inertia of the metallic disc and the rigidity

modulus of the material of the wire.

APPARATUS REQUIRED

Torsion pendulum, two equal masses, Stop-clock, Screw gauge and Meter

scale

FORMULA

The moment of inertia of the metallic disc

2 2

1 0 2

2 2

2 1

2 -

-

m d d TI Kg m

T T

The Rigidity modulus of the material of the wire

-2

2 4

0

8

I lNm

T r

Symbol Explanation Unit

m Mass of any one of the cylindrical masses Kg

r Radius of the suspended wire meter

l Length of the suspension wire meter

d1 Minimum distance between the suspension wire and the

centre of mass of the cylinder meter

d2 Maximum distance between the suspension wire and the

centre of mass of the cylinder meter

T0 Time period when no masses are placed sec

T1 Time period when two identical masses are placed at the

maximum distance sec

I Moment of inertia of the disc kg-m2

PROCEDURE

One end of the long uniform metallic wire whose rigidity modulus to be

determined is clamped. On the other lower end, a heavy metallic disc is attached by

means of a chuck. The length of the suspension wire is fixed to a particular value say,

60 or 70 cm. Now the disc is slightly twisted so that it executes torsional oscillations.

1. TORSIONAL PENDULUM

Expt. No. Date:

www.Vidyarthiplus.com


2

Care should be taken that the disc oscillates without wobbling. First few oscillations

are omitted. A mark is made on the disc such that time taken for 10 oscillations (to

and fro motion) are noted using stop-clock. Two trials are taken. The average of these

two trials gives the time period T0.

Now equal masses are placed on either side of the disc close to the

suspension wire. The distance d1 from the centre of one of mass and the suspension

wire is noted. Now the disc with masses at the minimum distance is made to execute

torsional oscillations. Time for 10 oscillations is noted. Two trials are taken. From this

mean period T1 is calculated.

Now the two masses are placed at the extreme ends of the disc and the

distance d2 from the centre of the one of the masses and the point of suspension wire

is noted. The disc is now subjected to torsional oscillations. Time for 10 oscillations is

noted. Two trials are taken. From this time period T2 is calculated.

Now the masses of any one of the cylinders is found. The radius of the

wire is measured by means of screw gauge and the length is measured using meter

scale. From this data the moment of inertia and the rigidity modulus of the material of

the wire are determined.

DIAGRAM

Fig. 1. Torsional Pendulum



3

Table : 1.1 To determine the Time period:

Length of the suspension wire = …….. x 10-2

m

Position of the equal

masses

Time for 10 oscillations Time period (Time for one

oscillation)

sec

Trial-1

sec

Trial-2

sec

Mean

sec

Without masses

With mass at

minimum distance d1=

------ x 10-2

m

With mass at

maximum distance

d2= ------ x 10-2

m

Table 1.2 To find the radius (r) of the wire:

LC = 0.01 mm ZE = ± ----- div

ZC = ± (ZE x LC) = ------ x 10-3

m

S.No.

Pitch

Scale

Reading

(PSR)

x 10-3

m

Head

Scale

Coincidence

(HSC)

Div

Head

Scale

Reading

(HSR)

x 10-3

m

Observed

Reading =

(PSR + HSR)

x 10-3

m

Correct

Reading =

(OR ± ZC)

x 10-3

m

1.

2.

3.

4.

5.

Mean =

CALCULATION

Mass of any one of the cylindrical masses m = x 10-3

kg.

Radius of the suspended wire r = x 10-3

m

Minimum distance between the suspension

wire and the centre of mass of the cylinder d1 = x 10-2

m

Maximum distance between the suspension

wire and the centre of mass of the cylinder d2 = x 10-2

m



4

Length of the suspended wire l = x 10-2

m

Time period without masses T0 = sec

Time period when two identical masses are

placed at the minimum distance “d1” T1 = sec

Time period when two identical masses are

placed at the maximum distance “d2” T2 = sec

The moment of inertia of the metallic disc is given by

2 2

1 0 2

2 2

2 1

2 -

-

m d d TI Kg m

T T

The Rigidity modulus of the material of the wire is given by

-2

2 4

0

8

I lNm

T r

RESULT

1. The moment of inertia of the metallic disc (I) = kg m2

2. The Rigidity modulus of the material of the wire ( ) = Nm-2

VIVA-VOCE QUESTIONS

1. What is torsion pendulum?

2. What is a rigid body?

3. Why it is called torsion pendulum?

4. What is the type of oscillation executing in torsion pendulum?

5. On what factors the time of oscillation depends?

6. Is there any rigidity modulus for fluids?



5

AIM

To determine the young‟s modulus of the material of a beam supported on two

knife edges and loaded at the middle point.

APPARATUS REQUIRED:

A uniform rectangular beam, two equal knife edges, a weight hanger with

slotted weight, vernier microscope, pin, screw gauge and vernier caliper.

FORMULA:

3-2

3

4

m g lE Nm

bd y


y Mean depression for a load meter

g Acceleration due to gravity m/s2

l Distance between the two knife edges meter

b Breadth of the beam (meter scale) meter

d Thickness of the beam (meter scale) meter

M Load applied kg

PROCEDURE

The given beam is symmetrically supported on two knife edges. A

weight hanger is supported by means of a loop of thread from the point C, exactly

midway between the knife edges. A pin is fixed vertically at C by some wax. The

length of the beam (l) between the knife edges is set for 60 cm. A traveling

microscope is focused on the tip of the pin such that the horizontal cross wire

coincides with the tip of the pin. The reading in the vertical traverse scale is noted for

dead load. In equal steps of m Kg added to the weight hanger, the corresponding

readings for loading are noted. Similarly readings are noted while unloading. The

breadth and the thickness of the beam are measured with a vernier calipers and screw

gauge respectively. From the data Young‟s modulus of the beam is calculated.

2. YOUNG’S MODULUS – NON-UNIFORM BENDING

Expt. No. Date:



6

Table 2.1 To find the depression (y)

LC = 0.001 cm TR = MSR + (VSC x LC)

S.No.

Load

x 10-3

kg

Traveling Microscope Reading

Mean

cm

Depression

„y‟ for M kg

x10-2

m

Loading Unloading

MSR

cm

VSC

div

TR

cm

MSR

cm

VSC

div

TR

cm

1. W

2. W+50

3. W+100

4. W+150

5. W+200

6. W+250

7. W+300

Mean (y)

Fig. 2.



7

Table 2.2. To find the breadth of the beam using vernier caliper

LC = 0.01cm VSR = VSC x LC

S.No.

MSR

x 10-3

m

VSC

Div

VSR

x 10-3

m

OR =

(MSR +

VSR)

x 10-3

m

CR=

(OR ± ZC)

x 10-3

m

1.

2.

3.

4.

5.

Mean =

Table 2.3. To find the thickness of the beam using Screw gauge

LC = 0.01 mm ZE = ± ----- div

ZC = ± (ZE x LC) =------ x 10-3

m

S.No. PSR

x 10-3

m

HSC

Div

(HSR

x 10-3

m

OR =

(PSR + HSR)

x 10-3

m

CR =

(OR ± ZC)

x 10-3

m

1.

2.

3.

4.

5.

Mean =

CALCULATION:

Load applied at mid point m = -------------- x10-3

kg.

Acceleration due to gravity g =--------------ms-2.

Breadth of the beam b = -------------- x10-2

m

Thickness of the beam d = ------------- x10-3

m

Length of the beam between the knife edges l = -------------- x 10 -2

m



8

Young‟s modulus of the beam 3

-2

3

4

m g lE Nm

bd y

RESULT:

Young‟s modulus of the material of the given beam E= ------------- Nm-2

.

VIVA QUESTIONS:

1. Define young‟s modulus.

2. How are longitudinal strain and stress produced in your experiment?

3. Define Hook‟s law.

4. Will the value of young‟s modulus obtained by you change if the length,

thickness or breadth of the bar is altered?

5. What are stress and strain?



9

AIM

To determine the coefficient of viscosity of the given liquid by poiseuille‟s

flow method.

APPARATUS REQUIRED

Graduated burette, Burette stand, Capillary tube, Rubber tube, Pinch clip ,

Wooden stand, Beaker , Liquid, Stop watch, Meter scale, Traveling microscope etc.

FORMULA

Coefficient of viscosity of the liquid 4

-2 8

g r htN s m

l v

Symbols Explanation Unit

g Acceleration due to gravity m/s2

ρ Density of the liquid Kg/m3

r Radius of the bore of the capillary tube meter

l Length of the capillary tube meter

V Volume of the liquid collected meter3

h (h1 + h2)/2 – h0 meter

h1 Height from the table to initial level of water in the burette meter

h2 Height from the table to final level of water in the burette meter

h0 Height from the table to mid portion of capillary tube meter

t Time taken for the liquid flow second

PROCEDURE

Fix a clean dry burette in the stand which is as shown in figure 9.1. The well

cleaned capillary tube of uniform cross section is attached to the lower end of the

burette using rubber tube. The capillary tube is kept parallel to the work table

(horizontal) using wooden stand, in order to get uniform flow of liquid without any

gravitational effect. The mass(m1) of the clean and empty beaker ( if the density of

3. COEFFICIENT OF VISCOSITY OF A LIQUID BY

POISEUILLE’S METHOD

Expt. No. Date:



10

the liquid is not given) can be found using a physical balance and place it on the work

table right below the free end of the capillary tube to collect the liquid.

To stop any flow of liquid the pinch clip is fit to the rubber tube and close it.

The burette is filled with the given liquid whose coefficient of viscosity is to be

determined using a funnel above the zero mark. The liquid must be free from

contamination in the form of precipitates or dirt etc. The pinch clip should be open

completely and the liquid is allowed to flow in a streamlined manner (flowing freely)

through the capillary tube drop by drop. The capillary tube should not be having any

bubbles, if any it has to be removed completely first.

A short length of thread is tied at the free end of the capillary tube and makes

it hanging from it so that the flowing liquid does not run along the surface of the tube,

but falls inside the beaker in the form of drops through the tip of the hanging thread.

Start the stop watch and note the time when the lower meniscus of the liquid crosses

zero mark, 5, 10, 15 ………..40 cc in table 9.1. Using meter scale, the height h1 from

the surface of the table to the zero mark of the burette and the height h2 from the

surface of the table to 5cc mark of the burette for the first observation ( when the

liquid flows from zero mark to 5 cc mark).

The h1 and h2 values for other observations also should be recorded. The

height h0 from the surface of the table to the mid portion of the capillary tube can be

measured. The time taken for the flow of 5 cc of liquid can be calculated. The

pressure head (h) and also the product ht is also calculated. It is observed that the

height (h) decreases, the time of flow of liquid (t) increases and the product (ht) is a

constant.

Determination of the radius of the bore of the capillary tube:

The radius of the bore of the capillary tube is measured by using the traveling

microscope must be done very carefully. The preliminary adjustment of the

microscope and the least should be made. The capillary tube form the experimental

set up is detached and mount it over a stand in such a way that it is parallel to the

work table. The microscope is adjusted to view the inner diameter of the capillary

tube as shown in figure 9.2.

The vertical cross wire of the microscope is made to coincide with the left

edge v1 of the capillary bore (Fig 9.3) and the reading should be noted in table 9.2

from the horizontal scale of the microscope. Now the vertical cross wire is made to



11

coincide with the right edge v2 of the capillary tube and the reading should be noted.

The horizontal cross wire is adjusted to coincide with bottom h2 of the capillary bore

and the reading should be noted. The diameter of the capillary bore is calculated by

finding the difference between v1 and v2 and h1 and h2. The mean diameter (2r) and

the radius (r) of the bore.

Determination of coefficient of viscosity of the liquid:

The length of the capillary tube (l) is measured using the meter scale. The

relevant values can be substituted in the formula and the coefficient of viscosity of the

liquid can be found.

DIAGRAM:

Fig. 3. Coefficient of viscosity of a given liquid



12

Table 3.1. Determination of ‘ ht’

h 0 = ……….x 10 – 2

m

S.No. Burette

reading

Time note

while crossing

level

Range Time for

flow of 5 cc

liquid

Height of

initial

reading h1

Height of

initial

reading h2

Pressure head

h = (h1+h2)/2 – h0

ht

Unit cc second cc second cm cm cm cm-sec

0 0 – 5

5 5 – 10

10 10 – 15

15 15 – 20

20 20 – 25

25 25 – 30

30 30 – 35

35 35 – 40

40 40 – 45

45 45 – 50

50



13

Table 3.2. Determination of the diameter of the capillary bore

TR = MSR + (VSC X LC) LC = 0.001cm

Horizontal Cross Wire Vertical Cross Wire

Position MSR

cm

VSC

div

MSR +

(VSCxLC) Position

MSR

cm

VSC

div

MSR +

(VSCxLC)

Top

Left

Bottom

Right

Difference (d1) = ----- cm Difference (d2) = ----- cm

2

21 dddDiameterMean

= ------- cm

2

drRadius = ------- cm

CALCULATION:

Volume of the liquid collected V = ……………..x 10-6

kg

Density of the given liquid = ………kg/m3

Acceleration due to gravity g = 9.8 ms-2

Radius of the capillary tube r = …………..x 10 – 2

m

Length of the capillary tube l = ………….x10-2

m

Volume of the liquid v = 5 x 10 -6

m3

Mean value of ht = ……………ms

Coefficient of viscosity of the

Given liquid = 4

-2 8

g r htN s m

l v

= ………….

RESULT:

The coefficient of viscosity of the given liquid = ……………..Nsm-2

.



14

VIVA QUESTIONS:

1. Define Viscosity?

2. Define coefficient of viscosity.

3. What is pressure gradient?

4. Differentiate between the streamline flow and turbulent flow.

5. Give examples for highly viscous liquids.

6. Why the capillary tube should be of uniform cross section?

7. What is fluid resistance

8. What are the factors up on which the rate of flow of liquid through the capillary

tube depends?

9. Velocity of ultrasonic waves in a liquid and compressibility of the liquid by

ultrasonic interferometer



15

AIM:

To determine the dispersive power of the prism using spectrometer.

APPARATUS:

Spectrometer, Flint glass prism, mercury vapour lamp, reading lens, spirit

level.

FORMULA:

1. Refractive index of the prism,

sin 2

sin / 2

A D

A

2. Dispersive power of the prism, 1 2

12

– 1

Where 1 2

12

( )

2


A Angle of the prism degrees

D Angle of minimum deviation degrees

1 Refractive index of the prism

For first co lour nil

2 Refractive index of the prism

For second co lour nil

Table 4.1. To find the angle of the prism (A)

L.C = 1 T.R = M.S.R + (VSC L.C)

Reflected

image VERNIER A VERNIER B 2A= R1R2 A

MSR VSC TR MSR VSC TR Va Vb Va Vb

Left

Right

4. SPECTROMETER – DISPERSIVE POWER OF

THE PRISM

Expt. No. Date:



16

PROCEDURE:

The preliminary adjustments of the spectrometer are made as usual... (Namely

eye piece adjustment for distinct vision of the cross wires Telescope adjustment for the

instant object and collimator adjustment for parallel rays)

(1) Measurement of the angle of the prism (A):

Fig. 4.1. Measurement of the angle of the prism

The given prism is mounted vertically at the center of the prism table with Its

refracting edge facing the collimator, so that the parallel rays of light from the

collimator fall almost equally on the two faces of the prism as shown In fig 1.1. The

telescope is rotated to catch the reflected image from one of the faces of the prism and

fixed in that position. By adjusting the tangential screw, the image is made to

coincide with the vertical cross wire. The main scale and Vernier scale readings are

noted from both the vernier A and vernier B.

Similarly readings are taken for the image reflected by other refracting face of

the prism. The difference between the two readings gives 2A, where A is the Angle

of the prism. From this value, the angle of the prism is calculated.



17

(ii) To find the angle of minimum deviation „D‟:

Fig. 4.2. Angle of Minimum Deviation

The prism is mounted such that light emerging from the collimator is incident on

one of the refracting face of the prism. Rotate the telescope slowly to catch the

refracted image of any one of the colour which emerges from other refracting face of

the prism.

The prism table is rotated in such a direction that the refracted image move

towards the direct ray. The telescope is rotated carefully to the image in the field of

view. At one stage, the image retraces its original path. This is the position of

minimum deviation .At this stage fixes the telescope and adjusts the tangential screw

to coincide the image of each co lour with vertical cross wire. The corresponding

readings are tabulated. The prism is removed and the direct ray reading is noted.

DETERMINATION OF ANGLE OF MINIMUM DEVIATION



18

The difference between the direct ray and refracted ray reading for each color

gives the angle of minimum deviation (D). By subtracting „A‟ and „D‟ values,‟ ‟ for

each and every colour can be calculated. By choosing any two colors and using

dispersive formula, „‟ can be calculated.

Table 4.2. Determination of the angle of minimum deviation ‘D’

L.C = 1 TR = MSR + (VSC L.C)

Refracted

ray

readings

Vernier A Vernier B

Va

R1R2

deg

Vb

R1R2

deg

Mean

D

Va+Va/2

deg

Lines of

spectrum

MSR

deg

VSC

div

TR

Deg

R1

MSR

deg

VSC

div

TR

Deg

R1

Direct ray

R2

R2

Table 4.3. Determination of ’’

S.No Refractive index

1 2( )

2

1

2



19

RESULT:

(1) Angle of the prism „A‟ = ---------------------

(2) Angle of minimum deviation „D‟ = --------------------------

(3) Refractive index of the material of the given prism „‟ = -----------

(4 ) Mean dispersive power of the given prism „‟ = --------------------

VIVA-VOCE QUESTIONS:

1. Define refractive index

2. How does refractive index changes with wavelength of light?

3. What is the condition for obtaining minimum deviation

4. Define dispersive power.

5. Which lines have the greatest deviation from the direct ray? Why?

6. What is the significance of dispersive power?



20

AIM:

To determine the thickness of the thin wire by forming interference fringes using

air-wedge arrangement.

APPARATUS:

Travelling microscope, Sodium vapour lamp, two optically plane rectangular

glass plates, Condensing lens and Reading lens

FORMULA:

Thickness of the thin wire is given by

2

lt m


λ Wavelength of the sodium vapour lamp (λ=5893Х10-

10m)

Meter

l Distance between the specimen wire and the edge of

contact Meter

β Mean width of one fringe Meter

PROCEDURE:

The principle used in this experiment is interference (i.e., Superposition of

two light waves). When a beam of monochromatic light falls normally on a glass plates,

interference takes place between light reflected from the lower surface of the top glass

plate and the upper surface of the lower glass plate resulting in the production of

alternative bright and dark fringes.

An air-wedge is formed by keeping two planes rectangular glass plate kept

contact in one end and it is tied by a rubber band. On the other side of the glass plate a

thin wire whose thickness to be determined is introduced. This arrangement is placed on

the horizontal bed of the travelling microscope.

Now the light from the source is allowed to fall on the condenser lens. This lens renders

back parallel beam of light. This parallel beam of light is allowed to fall on the glass plate

which is kept at an angle of 450 to the horizontal plane. Now the light gets reflected. This

5. AIR WEDGE

Expt. No. Date:



21

DIAGRAM

Fig. 5. Air wedge arrangement



22

reflected beam is allowed to fall on the two plane glass plates. Now the interference takes

place between light reflected from top and bottom surface of the glass plates and the

fringes consisting of alternate bright and dark bands through the travelling microscope.

The microscope is adjusted so that the bright and dark fringes near the

edge of contact are made to coincide with the vertical cross wire of the telescope and it is

taken as nth

fringe. The reading from the horizontal scale of the travelling microscope is

noted. Now the microscope is slowly moved with the help of horizontal screw until the

vertical cross wire coincides with the (n+5) th

fringe and the corresponding reading is

noted. Likewise the procedure is repeated up to 50 fringes (n+5, n+10, n+15….).From the

observed reading mean width of one fringe (β) is calculated.

Now the microscope is moved towards the specimen wire and the reading

(R2) is noted. Similarly the microscope is moved towards the edge of contact and the

reading (R1) is noted. From the difference (R2~ R1) the length between the specimen wire

and the edge of contact is determined. By knowing the values of λ, β and l the thickness

of the given material is determined.

Table 5.1. To determine the distance between the edge of contact and the specimen

wire

Position

Microscope reading

MSR

Х10-2

m VSC

TR

Х10-2

m

Rubber band

(edge of

contact)

(R1)

Specimen wire (R2)

l = R2~ R1 …….. Х10-2

m



23

Table 5.2. To determine the band width (β):

Order of

the fringe

Microscope reading Width of 5

fringes

Х10-2

m

Mean width

of one

fringe(β)

Х10-2

m

MSR

Х10-2

m VSC

TR

Х10-2

m

n

n+5

.

.

.

.

n+50

β=……. Х10-2

m

CALCULATION

Wavelength of the sodium vapour lamp, λ = 5893 Х 10-10

m

Distance between the specimen wire and the edge of contact, l = …… Х 10-2

m

Mean width of one fringe, β = ………. Х 10-2

m

Thickness of the thin wire is given by,

2

lt m

RESULT

Thickness of the thin wire = …………meter.

VIVA-VOCE QUESTIONS:

1. What is interference?

2. What is an air-wedge arrangement?

3. How interference fringes are formed in an air-wedge arrangement?

4. Why straight line fringes are formed in an air wedge arrangement?



24

AIM:

To determine the number of lines per metre of the grating and the wavelengths

of the prominent lines of the mercury spectrum.

APPARATUS:

Spectrometer, grating, sodium and Mercury vapour lamps etc.

FORMULA:

sin

N m


Angle of diffraction degree

N Number of lines per metre in the grating lines/meter

m Order of the diffraction ---

PROCEDURE

(A) To standardize the grating using sodium light:

The preliminary adjustments of the spectrometer are made. The slit is illuminated

with sodium light. The telescope is brought in a line with the collimator and the direct

reading is taken on both the verniers. The prism table is firmly clamped and the telescope

is turned through 900 and fixed in this position (Fig.1). The grating is mounted on the

table so that the rulings on it are parallel to the slit. The grating platform is rotated till the

image of the slit reflected from the surface of the grating is seen in the telescope.

The platform is fixed in the position at which the vertical crosswire coincides with the

fixed edge of the image of the slit. The vernier table is rotated through exactly 450 in the

proper direction, so that the surface of the grating becomes normal to the collimator. The

prism table is a fixed in this position, now the grating is adjusted for normal incidence.

The telescope is now released and brought to the position of the direct image. On

either side of it are seen the diffracted images of the first order.

The telescope is turned to the left to view the first order diffracted image. The vertical

crosswire is made to coincide with the fixed edge of the image of the slit. Readings of

6. SPECTROMETER - GRATING

Expt. No. Date:



25

both the verniers are taken (fig-2).The telescope is turned to the right. Reading are noted

when the crosswire coincides with the first order image on the right. The difference

between the two readings gives 2. Hence is determined (=5893 A0, m=1).The

number of lines per metre N of the grating is calculated using the relation

sin

N m

(B) Determination of Wavelength of the prominent line of the Mercury spectrum:

Without disturbing the spectrometer replace the sodium vapour lamp by Mercury

vapour lamp whose wavelengths are to be determined. Rotate the telescope and observe

the dispersed diffracted spectral lines of Mercury light of first order and second order on

either side of central undispersed direct image are shown in Fig.3. Take reading on both

side for the first order diffraction pattern. The angle of diffraction for the different lines

of the first order is measured. The wavelength of each line is calculated using the

relation

sin

N m

m



26

Fig. 6.1. To set the normal incident position



27

Fig. 6.2 Diffracted rays from grating



28

Table. 6.1. Determination of number of lines per metre of the grating

Wavelength of the sodium line =5893x10-10 m

LC = 1‟ ;VSR =VSC x LC

For first order spectrum m = 1 TR = MSR + VSR

Reading of the diffracted image Difference between

the readings Mean 2

Angle of

diffraction

N = sin/m lines/m

Left Right Left Right

Ver A

A1

VerB

B1

VerA

A2

Ver B

B2 2

A1 A2

2

B1 B2 M

S

R

VS

R

T

R

MS

R

VS

R

T

R

MS

R

VS

R

T

R

MS

R

VS

R TR



29

Table 6.2. Determination of wavelength of mercury spectral lines

Number of lines per metre of the grating N = --------------

LC = 1‟; VSR =VSC x LC

For first order spectrum m = 1 (TR = MSR + VSR)

Colour of

the

spectral

line

Reading of the diffracted image

Difference

between the

readings

Mean

2

Angle of

diffraction

=

sin/Nm

A

Left Right Left Right

Ver A

A1

VerB

B1

VerA

A2

Ver B

B2 2

A1 A2

2

B1 B2 MSR VSR TR MSR VSR TR MSR VSR TR MSR VSR TR

Red

Yellow II

Yellow I

Green

Bluish

green

Blue

Violet



30

RESULT:

The number of lines in the given grating is=--------------lines/m

The wavelength of violet colour is=------------o

A

The wavelength of Blue colour is=------------

o

A

The wavelength of Orange colour is=------------

o

A

The wavelength of red color is=------------

o

A

VIVA-QUESTION:

1. What is diffraction grating? How it is constructed? How does it produce

diffraction?

2. What are requisites of a good grating?

3. Mention the different types of a grating which one is better.

4. What is grating element?

5. What is dispersive power of grating?



31

AIM

To determine the coefficient of thermal conductivity of a bad conductor.

APPARATUS REQUIRED

Lee‟s disc apparatus, bad conductors, stop-clock, thermometers, screw gauge,

vernier calipers, steam boiler

FORMULA

Thermal conductivity of a bad conductor

-1 -1

221 2

2 1W m K

r 2r 2h

MSd r h dK

dt


M Mass of the metallic disc kg

S Specific heat capacity of the material of the disc J kg-1

K-1

(dθ/dt)θ2 Rate of cooling at θ2 0C/s

r Radius of metallic disc meter

h Thickness of metallic disc meter

d Thickness of bad conductor meter

θ1 Steady temperature of a steam chamber 0C

θ2 Steady temperature of the metallic disc 0C

THEORY

The thickness of the bad conductor say card board and thickness of the metallic

disc are determined using a screw gauge. The radius of the metallic disc is found using a

vernier caliper. The mass of a metallic disc is also found using a common balance. The

readings are tabulated.

7. LEES’S DISC – THERMAL CONDUCTIVITY OF A BAD

CONDUCTOR

Expt. No. Date:



32

The whole Lees disc apparatus is suspended from a stand as shown in the figure.

The given bad conductor is placed in between the metallic disc and the steam chamber.

Two thermometers T1 and T2 are inserted into the respective holes.

Steam from the steam boiler is passed into the steam chamber until the

temperature of the steam chamber and the metallic disc are stead. The Steady temperature

(θ1) of the steam chamber and (θ2) of the metallic disc recorded by the thermometers are

noted.

Now the bad conductor is removed and the steam chamber is placed in direct

contact with the metallic disc. The temperature of the disc rapidly rises when the

temperature of the disc rises about 10 C above θ2 C, the steam chamber is carefully

removed after cutting of the steam supply.

When the temperature of the disc reaches 10 C above the steady temperature of

the disc i.e. (θ2+ 10)C, stop clock is started. Time for every one degree Celsius fall of

temperature is noted until the metallic disc attains a temperature (θ2 - 10)C.



33

Fig. 7.1. Lee’s disc arrangement

GRAPH

Fig. 7.2. Cooling Curve

A graph is drawn taking time along the x-axis and temperature along the y-axis.

The cooling curve is obtained .To obtain the rate of the cooling (dθ/dt)θ 2

From this graph, a triangle is drawn by taking 1C above and 1C below the steady

temperature θ2. Then the slope AB / BC gives the rate of cooling at (dθ/dt)θ 2

From these readings and using the given formula thermal conductivity of the

given bad conductor is calculated.



34

Table 7.1. To find radius of the metallic disc (r) using Vernier Caliper

Least count = 0.01cm

S.No. MSR

cm

VSC

div.

VSR =(VSCXLC)

cm

Observed reading =MSR +

VSR

cm

1.

2.

3.

4.

5.

Mean (r) = …….. x 10-2

m

Table 7.2. To find thickness of the bad conductor (d) using Screw gauge

Zero error = ± ………div

Least count = 0.01mm Zero correction = ± ………mm

S.No. PSR

mm

HSC

div.

Observed Reading = PSR +

(HSCXLC) mm

Correct reading = OR

±ZC mm

1.

2.

3.

4.

5.

Mean (t) = …….. x 10-3

m

Table 7.3. To find thickness of the metallic disc (h) using Screw gauge

Zero error = ± ………div

Least count = 0.01mm Zero correction = ± ………mm

S.No. PSR

mm

HSC

div.

Observed Reading = PSR

+(HSCXLC) mm

Correct reading = OR

±ZC mm

1.

2.

3.

4.

5.

Mean (h) = …….. x 10-3

m



35

Table 7.4. Determine the rate of cooling of metallic disc (dθ/dt)θ 2

S.No. Temperature (θ)

˚C

Time (t)

Second

1.

2.

3.

4.

5.

6.

7.

8.

9.

10.

RESULT

Thermal conductivity of the given bad conductor = ---------- Wm-1

K-1

VIVA-QUESTION

1. Define thermal conductivity.

2. Can this method be used for good conductors?

3. Is there any reason to take the specimen in the form of a disc?

4. Does the value of thermal conductivity depend on the dimension of the specimen?

5. What are conduction, conviction and radiations?



36

AIM

To determine the velocity of ultrasonic waves in a given liquid and the

compressibility of the liquid

APPARATUS REQUIRED

Ultrasonic interferometer (High frequency generator, measuring cell)

experimental liquid etc.

FORMULA

Velocity of the ultrasonic wave in liquid 2

v d f

x (m/s

-1)

Compressibility of the liquid 2

1

v

(m

2N

-1)


d distance moved by the micrometer meter

f Frequency of the ultrasonic wave Hertz

x Number of maxima readings of anode current ---

density of the given liquid m/s-1

V Velocity of the given liquid Kg/m3

PROCEDURE:

The measuring cell which is an especially double walled cell for maintaining the

temperature of the liquid constant during the experiment is filled up with given liquid.

The measuring cell is connected to the output terminal of the high frequency generator

through a coaxial cable provided with the instrument. The micrometer screw is initially

set as 25 mm. The generator is switched on to excite the quartz crystal at its frequency to

generate ultrasonic waves in the liquid. This has to be done only after filling the liquid in

the measuring cell and not earlier. The generator consists of two knobs namely gain and

adj knobs, which for sensitivity regulation for greater deflection and for initial adjustment

of micrometer at zero initially. The adj knob is adjusted slightly to adjust the position of

the needle on the ammeter which is used to notice the number of maximum deflections.

The gain knob is rotated and set it to show maximum reading in the ammeter. The

8. ULTRSONIC INTERFEROMETER

Date: Expt. No.



37

micrometer screw is adjusted which is on the top of the measuring cell which can lower

or raise the reflector in the liquid in the measuring cell through a known distance, to

move downwards.

Fig. 8. Ultrasonic Interferometer

The ammeter readings vary from maximum to minimum and from minimum to

maximum value and in between these maxima to minima there occur extra peaks due to a

number of reasons, but they do not affect the value of /2. The rotation of the micrometer

screw is continued in the same direction as before. The micrometer reading for the first

maximum is noted down and then for successive maxima shown by the interferometer

and 20 such readings are recorded. The distance moved by the micrometer screw for x

maxima is found and its mean value is found. The velocity of the ultrasonic waves in the

liquid medium using the relation v = 2df/x. The density of the liquid if given is noted, if

not given it standard value from the table has to be noted down. Then by substituting all

the values in the formula the compressibility of the given liquid can also be found.



38

Table 8.1. Determination of the distance moved by the micrometer screw

LC = 0.01 mm

TR = PSR +(HSC xLC) x = ----------

Order of the

maxima

Pitch Scale

Reading

(PSR)

Head Scale

Coincidence

(HSC)

Micrometer

Reading

(TR)

Distance moved by

the micrometer

screw (d)

Unit mm div mm Mm

n

n+3

n+6

n+9

n+12

Mean d = -------------------mm

RESULT:

The velocity of the ultrasonic waves in liquid v = …………..ms-1

The compressibility of the ultrasonic waves in liquid = …..m2N

-1

VIVA QUESTIONS

1. What are ultrasonic waves?

2. Define piezo – electric effect.

3. Define an acoustic grating.

4. Explain inverse piezo – electric effect.

5. Are ultrasonic waves electro-magnetic waves? Give proper reasons.



39

AIM:

To determine the band gap of a semiconductor.

APPARATUS REQUIRED:

Power supply, Voltmeter, Micro ammeter, Diode, Thermometer, Oil, Beaker.

FORMULA:

The width of the forbidden energy gap

Eg = 0.198 x Slope

PROCEDURE

Make the circuit connections is made as shown in the figure. Note that the given

semiconductor (Ge or Si diode) whose band gap is to be determined must be connected to

the circuit through long wires soldered at its terminals such that it is reverse biased. Take

oil or water in the beaker and immerse the reverse biased diode with leads in the liquid

inside the beaker. Insert the thermometer in the beaker such that its mercury bulb is just

at the height of the diode.

Heat the liquid upto 70C using the heating system. Switch off the heating system

and allow the liquid to cool on its own. Switch on the regulated power supply and by

adjusting its knob set the current 0.5 V through the diode. When the temperature of the

diode in the liquid is 60C, note the current I flowing through the diode as shown in the

microammeter.

As the temperature of the diode falls, the current flowing through it decreases.

Note the current as shown by the micro ammeter for every one degree Celsius fall of the

temperature of the liquid until it falls to 50C.

9. BAND GAP OF A SEMICONDUCTOR

Expt. No. Date:



40

Graph

Fig.9.1. Variation of current with inverse temp. in a reverse biased pn-diode

Draw graph with 103/ T along x- axis and log I along y-axis. The graph will be a

straight line. Determine the slope of the log I versus 103/ T from the graph. Substituting

the value of the slope and the Boltzmann‟s constant in the formula, calculate the band gap

(Eg) of the semiconductor.

DIAGRAM

Fig. 9.2. Experimental set up for band gap determination



41

Table 9 Determination of band gap

0C = 273 K

S.No. Temperature in

Celsius

Temperature in

Kelvin

Current in

microampere I

Log

I

103/

T

1.

2.

3.

4.

5.

6.

7.

RESULT:

Band gap of a semiconductor = ……. eV

VIVA QUESTIONS:

1. What are semiconductors and how can you classify them?

2. Define Fermi level.

3. Define band gap or forbidden energy gap in a semiconductor material.

4. Define extrinsic semiconductor and give examples.

5. Define intrinsic or pure semiconductor and give examples.

6. Can water be used in place of oil for band gap determination?

7. How does the band gap change with temperature in semiconductors?



42

AIM:

To determine the size of the micro particle using laser.

APPARATUS REQUIRED:

Laser source, Fine micro particles of nearly uniform size (Lycopodium powder),

Glass plate, White screen, Stands, Meter Scale

THEORY:

When laser is passed through a glass plate spread with fine micro particles, the beam

gets diffracted by the particles and circular rings are obtained on the screen. By

measuring the radii of the rings and the distance between the glass plate and the screen,

the size of the particle can be determined.

FORMULA:

Size of the microparticle (diameter) =

2 2

2

n X 2d

X

n

n


n Order of diffraction ---

Wavelength of the laser source meter

Xn Distance of the nth

order ring from the central spot of

the diffraction pattern meter

l Distance between the glass plate and the screen meter

PROCEDURE:

Sprinkle a thin uniform layer of lycopodium powder on a glass plate. Mount the

screen and glass plate upright. The light from laser source transmitted through the layer

of lycopodium in the glass plate is adjusted to form a diffracted image in the centre of the

screen. Diffracted circular fringes of laser co lour will e visible on the screen.

10. (a) PARTICLE SIZE DETERMINATION BY LASER

Expt. No. Date:



43

After adjusting the distance of the glass plate from the screen so that the first ring

radius (x1) and second ring radius (x2) are measured from the central spot. Note the

distance (l) between screen and plate. Repeat the experiment radius of the first and

second rings after adjusting the distance between screen and plate. Calculate the value of

the diameter of the particle taking value from the previous experiment.

DIAGRAM :

Fig.10.1.Particle size determination by Laser

Table 10.1. Determination of size of the micro particle

= ………× 10-10

m

Mean 2d = ………… × 10-10

m

= ………… × 10-6

m

S.No.

Distance

between the

glass plate

and the

screen ( )

Order of

diffractio

n

(n)

Distance

between the

central spot

and the nth

fringe

Xn2

2

2 2

X n

Particle size

2 2

2

n X 2d

X

n

n

Unit × 10-2

m × 10-2

m ×10-4

M × 10-4

m × 10-2

m × 10-10

m

1

2

3

1

2

3

LASER

l

Glass Plate with

fine particles

Screen



44

CALCULATION:

1. Xn = x1

9 2 2

1

2

1

1 .. 10 X 2d

X

RESULT:

The average size of the micro particle measured using laser 2d = ………. m.

VIVA VOCA QUESTIONS:

1. How will you determine the size of the particle using laser?

2. What type of laser you use for the experiment? What is its wavelength?

3. What will you do to get clear diffraction pattern on the screen?

4. What is the difference between the diffraction by powder particle and grating?

5. Why is the diffraction pattern produced not in the form of concentric rings?

6. How will you measure the radii of rings?

7. What will happen to the order of spectrum, if the distance between the particle and

screen is increased?

8. What will happen to the order of spectrum, if particle size is decreased?



45

AIM:

To determine the wavelength of the laser of the given laser source of light and

angle of divergence using grating.

APPARATUS REQUIRED:

Laser source, Laser Grating with stand (2500 lines per inch), Screen, Scale

THEORY:

When laser is incident normally on a plane diffraction grating, diffraction takes

place. The mth

order maxima of the wavelength, will be formed in a direction if

d sin m

Where d is the distance between two lines in the grating.

FORMULA:

Wavelength of the laser sin

Nm

metre


N Number of rulings in the grating lines/meter

m Order of spectrum No unit

Angle of diffraction Degree

r1 Diameter of the beam spot at a distance D1 cm

r2 Diameter of the beam spot at a distance D2 cm

10. (b) LASER PARAMETERS

Expt. No. Date:



46

Laser

source

x 1

x

x 2

Grating

Laser

l

DIAGRAM:

PROCEDURE:

1. To find the number of lines per meter in the grating

Fig. 10.2. Laser Grating

The initial adjustments of the spectrometer are made. The direct ray is coincided

with the vertical crosswire and the telescope is fixed. Now the vernier table is released

and both the verniers are made to coincide with 0º and 180º and the vernier table is fixed.

The telescope is released and moved towards the right side through 90º and fixed. The

grating is mounted on the grating table and rotated to the reflected image and coincided

with vertical crosswire. Now the vernier table is rotated 45º towards collimator and

grating will become perpendicular to the light rays. Telescope is moved to left and right

and the perpendicular order ray is coincided and the readings are noted in both the scales.

The number of lines per unit length of the grating can be calculated as follows

sin N

m

Where, is the wavelength of sodium light (5893 × 10 -10

m)



47

Table 10.2. To find the number of lines per unit length in the grating

Least count = 1 Order of diffraction (m) = 1

Ray

Vernier A Vernier B

M.S.R V.S.C T.R M.S.R V.S.C T.R

degree div degree Degree div degree

Left side R1 S1

Right side R2 S2

2 = R1- R2

=

2 = S1- S2

=

Mean =

2. To find the wave length of the laser light

Fig. 10.2 (a). Angle of divergence determination

The laser source is focused on the screen. The grating is made exactly

perpendicular to the light rays. If we use a 1, 00, 00 lines per meter on the grating, nearly

15 orders of diffracted images are formed. The diffracted images can be viewed on the

screen. The image has central maxima and several orders in the right and left of the

central maxima. The distance(x1) of the left side first order dot is measured from the

central maxima and is noted down. Similarly the distance (x2) of the first order dot on the

right from the central maxima is also measured. All the distances of the dots are

measured and noted down in the tabular column.



48

Table 10.2 (a) Determination of wavelength of laser

Observation I l……×10-2

m

N = ……………

Order

of

diffraction

Distance of the

centre of the spot

from the central

maxima

1 2x xx =

2

xtan

1 x tan

Wavelength

1

sin

Nm

Left

(x1)

Right

(x2)

unit ×10-2

m ×10-2

m ×10-2

m m

1.

2.

3.

4.

5.

Mean 1 = ………….. m

= ............×10-10

m

= ………….. Ǻ

CALCULATION:

The wavelength of the given source of light is

1

sin

Nm

m

1

sin sin .......... .................

1 ..........m

Nm

To find the angle of divergence ():

Angle of divergence gives the degree of directionality of the laser beam. As

shown in fig the laser source and a stand are kept at some distance say „d1‟ and the

diameter of the spot „r1‟ is measured. By varying the Distance to „d2‟, the diameter of

the spot „r2‟ is measured. By substituting these values in the given formula, the angle of

divergence can be calculated. The experiment is repeated for various values of d1 and d2

and the mean angle of divergence is determined.



49

Table 10.2. (b) To find the angle of divergence

S.No.

r1

m

r2

m

d1

m

d2

m

Angle of divergence

2 1

2 1

r - r

d d

degrees

RESULT:

(i) The wavelength of the laser = ………….. Ǻ

(ii) The angle of divergence = …………….

PRECAUTIONS:

The experiment should be done in a dark room.

The grating should have a less number of lines.

Direct view of the laser should be avoided.

VIVA QUESTIONS:

1. What does the term LASER stands for?

2. What is the principle of laser?

3. What are the properties of laser?

4. What are the different types of lasers available? Which one is used in this experiment?

5. What is stimulated emission?

6. Explain the basic mechanism of lasing action.

7. Mention a few applications of laser.

8. Distinguish between laser source and convention light sources.

9. What is an optical cavity?

10. What is population inversion? Explain why it is easier to achieve it in a four level

laser compared to that in a three level laser?

11. What is the wavelength of laser light from (a) Ruby laser, (b) He-Ne laser, and (c)

CO2 laser?



50

12. What are the precautions to be taken while doing experiments with laser?

13. Will laser undergo diffraction through ordinary grating? Explain.

14. What is the difference between the phenomena that occur when light passes through

the prism and the grating?

15. What type of adjustments you will do to get clear diffraction pattern, if the screen

used in the experiments is (a) white wall (b) white chart pasted on the wall, and (c)

graduated scale?

16. What will the impact on the diffraction pattern on the screen, if the number rulings

per meter on the grating are changed?

17. What are central maximum and maxima?

18. Are the spectra of different orders of the same intensity?

19. What is the difference between laser grating and spectrometer grating?

20. Whether laser beam used in this experiment is a convergent beam (or) divergent

beam? Give reasons.

21. Compare the angle of divergence for an ordinary beam with a laser beam.



51

AIM:

To determine the numerical aperture and acceptance angle of the given optical fibre.

APPARATUS REQUIRED:

Optical fiber cable, Laser source, Numerical aperture, White screen, with

concentric circles, scale.

THEORY:

Numerical aperture is a basic parameter of an optical fiber. It is a measure of light

gathering power or degree of openness of the fiber. It is the product of the refractive

index of the incident medium and the sine of the maximum ray angle.

FORMULAE:

(i) Numerical aperture of the optical fiber 2 2

wNA=

4l +w

Where w – diameter of the spot (m)

l - Distance of the screen from fiber end (m)

(i i) Acceptance angle 1

a 2 sin NA (unit: degree)

PROCEDURE:

The numerical aperture jig consists of an iron or plastic stand with a moving

screen. In this screen, a number of concentric rings of varying diameter are present. In

front of it, a stand with a circular slit in the centre is provided which is connected to the

laser light source through the optical fiber cable. By moving the screen back and forth the

laser light from the circular slit is made to fall exactly on the circles with different

diameters. The distance „l‟ between the circular slit in the jig and screen for various

circular diameters are noted on a moving scale situated at the bottom of the jig. Thus by

knowing the values of l and w, the value of the numerical aperture is calculated. The

maximum divergent angle (the acceptance angle) is also determined.

10. (c) NUMERICAL APERTURE AND ACCEPTANCE

ANGLE OF AN OPTICAL FIBRE

Expt. No. Date:



52

DIAGRAM:

Numerical aperture jig

Fig: Experimental arrangement of fiber cable with source

Laser

Screen

Fig. 10.3. Determination of Numerical Aperture

Table 10.3. Determination of Numerical Aperture and Acceptance angle

S.No Diameter of the

circle / spot (w)

Distance

between the

fiber end and

screen (l)

Numerical

aperture

2 2

wNA=

4l +w

Acceptance angle

1

a 2 sin NA

Unit × 10-3

m

× 10-2

m

Degree

1

2

3

4

5

6

7

Laser source

Optical fiber cable

Fiber

1



53

RESULT:

1. The numerical aperture of the given optical fiber NA = ……………No unit

2. The acceptance angle of the given optical fiber a = ………………Degree

PRECAUTIONS:

1. The optical fiber cables should not be bent and twisted to the higher

extent.

2. Avoid direct viewing of laser light

3. The knob in the power meter must be handled properly.

VIVA QUESTIONS:

1. What is an optical fiber? Explain briefly its structure.

2. What are the characteristics of optic fiber?

3. What is the need for a jacket in a optical fiber?

4. Why the relative index of cladding must always be higher than that of core?

5. Why light from a laser source and not from a LED is preferred for an optical

fiber?

6. How does an optical fiber work?

7. What is the principle used in optical fiber?

8. What is attenuation?

9. What are the reasons for the loss in optical fiber?

10. What are the different types of optical fibers?

11. Mention a few applications of optical fiber?

12. What are the advantages of optical communications over the other modes of

communications?

13. Define critical angle.

14. Define acceptance angle.

15. On what factors does the critical angle of incidence of core – cladding interface

depend?

16. Define numerical aperture.

17. On what factors does the numerical aperture depend?

18. What is the mathematical expression for numerical aperture?



54

AIM:

To determine the young‟s modulus of the material of the beam by uniform

bending method.

APPARATUS REQUIRED:

A uniform rectangular beam, two equal knife edges, two weight hanger with

slotted weight, vernier microscope, pin, screw gauge, vernier caliper.

FORMULA:

2

-2

3

3

2

M g aE Nm

b d y


E Young‟s modulus of the material of the beam Nm-2

M Load producing the depression Kg

g Acceleration due to gravity ms-2

l Length of the beam between the two knife edges m

a distance between the point of application of load and

nearest knife edge m

b Breadth of the beam m

d Thickness of the beam m

y Elevation produced for a load m

PROCEDURE

The given beam is symmetrically supported on two knife edges. Two

weight hangers are suspended at equal distance from the knife edges. A pin is fixed

vertically at C by some wax. The length of the beam (l) between the knife edges is set for

60 cm. A traveling microscope is focused on the tip of the pin such that the horizontal

cross wire coincides with the tip of the pin. The reading in the vertical traverse scale is

noted for dead load. In equal steps of m Kg added to the weight hangers; the

corresponding readings for loading are noted. Similarly readings are noted while

11. YOUNG’S MODULUS BY UNIFORM BENDING

Expt. No. Date:



55

unloading. The breadth and the thickness of the beam are measured with a vernier

calipers and screw gauge respectively. From the data Young‟s modulus of the beam is

calculated.

Table 11.1 To find the depression (y)

LC = 0.001 cm TR = MSR + (VSC * LC)

Table 11.2. To find the breadth of the beam using vernier caliper

LC = 0.01cm

OR = MSR + (VSC x LC)

S.No. MSR

cm

VSC

div.

VSR =(VSCXLC)

cm

OR =MSR + VSR

x10-2

m

1.

2.

3.

4.

5.

Mean (b) =

S.No. Load

x 10-3

kg

Traveling Microscope Reading

Mean

cm

Elevation ‘y’

for M kg

x10-2

m

Increasing load Decreasing load

MSR

cm

VSC

div

TR

cm

MSR

cm

VSCd

iv

TR

cm

1. W

2. W+50

3. W+100

4. W+150

5. W+200

6. W+250

7. W+300

Mean (y) =



56

Table 11.3. To find the thickness of the beam using Screw gauge

LC = 0.01 mm ZE = ± ----- div

ZC = ± (ZE x LC) =------ x 10-3

m

S.No. PSR

x 10-3

m

HSC

Div

OR =

PSR+ (HSC x LC)

x 10-3

m

CR = OR ± ZC

x 10-3

m

1

2

3

4

5

Mean =

CALCULATION:

Load applied at mid point m = -------------- x10-3

kg.

Acceleration due to gravity g =--------------ms-2.

Breadth of the beam b = -------------- x10-2

m

Thickness of the beam d = ------------- x10-3

m

Distance between the points of application

of load and nearest knife edge a= ---------------- x10-2

m

Length of the beam between the knife edges l = -------------- x 10 -2

m

Young‟s modulus of the beam 2

-2

3

3

2

M g aE Nm

b d y

RESULT:

Young‟s modulus of the material of the given beam E==----------------- Nm-2



57

VIVA QUESTIONS:

1. What is uniform bending?

2. Why should the beam be placed symmetrically on two knife edges?

3. How will you bring the beam to the elastic mode?

4. How should the adding of weights to the weight hangers on the beam be done?

5. Why should the measurement of thickness of the beam be done very accurately?



58

AIM

To determine the specific resistance of the material of the given wire.

APPARATUS REQUIRED

Carey foster bridge, coil of the given wire, Lechlanche cell (Bt), Key, Two equal

resistances P & Q, Galvanometer, high resistance, Jockey, Known resistance box (R).

FORMULA

1. Resistance of the given coil of wire 1 2 bX R – r Ohm

2. Specific resistance of the given coil of wire 2X r

ohm-metre


rb Resistance per meter length of the bridge wire ohm/meter

X Unknown resistance ohm

la, lb, l1 & l2 Balancing lengths meter

R Known value of resistance in the resistance box meter

r Radius of the given coil of wire meter

l Length of the given coil of wire meter

CIRCUIT DIAGRAM

Fig. 12. CAREY-FOSTER’S BRIDGE

12. CAREY-FOSTER’S BRIDGE

Expt. No. Date:



59

Table 12.1. Determination of unknown resistance X

S.No.

Resistance

introduced in the

box R

ohm

Balancing length AJ(cm) 1 2 bX R – r

ohm

With R in the

left gap(l1)

With R in the

right gap(l2)

1.

2.

3.

4.

5.

6.

Table12.2. To find the radius of the given coil of wire.

LC = 0.01 mm ZE = ± ----- div

ZC = ± (ZE x LC) =------ x 10-3

m

S.No. PSR

x 10-3

m

HSC

Div

OR =

PSR+ (HSC x LC)

x 10-3

m

CR = OR ± ZC

x 10-3

m

1

2

3

4

5

Mean(diameter d) =

Radius of the wire = d/2 = --------x 10-3

m

THEORY

The Carey -Foster Bridge consist of a one meter wire (AB) of uniform resistance

stretched on a wooden board. Carey –Foster Bridge is similar to that of a metre –bridge,

with a difference of having four gaps, in which proper resistances can be inserted as

shown in the figure.



60

The total circuit is divided into two parts viz., primary and secondary circuit. In

the primary circuit the lechlanche cell (Bt) and key (K) is connected. In the secondary

circuit the galvanometer (G), high resistance (HR) and Jockey (J) is connected in series.

PROCEDURE

To find the unknown resistance(X) and specific resistance ().

The primary and the secondary circuits are connected as shown in the figure. The

equal resistances P and Q are included in the two inner gaps (1 & 2). Resistance box R is

included in the left gap 3 and unknown resistance X is included in the right gap 4.Known

value of resistances R are included (say 0.2, 0.3 ohms etc.,) and the balancing length (AJ

= l1) is measured in each case and tabulated.

The position of R and X is interchanged. The experiment is repeated for the same

values of R (say 0.2, 0.3 ohms etc.,) and the balancing length (AJ = l2) is measured and

tabulated.

In order to determine the resistance (rb) per metre length of the bridge wire, a

thick copper strip of zero resistance is placed in the left gap (3) and standard resistance of

0.1 ohms is placed at right gap (4) and balancing length (AJ = la) is noted and tabulated.

Now by placing the copper strip at the right gap (4) and 0.1 ohms at the left gap (3), the

balancing length (AJ= lb) is noted and tabulated.

Substituting the values of la and lb in the given formula, the value of rb is

calculated. By substituting this value in the given formula, the unknown resistance (X) of

the given coil of wire is calculated.

Specific resistance

The radius of the given coil of wire(r) is found using screw gauge and the length

of the wire (l) is measured. By substituting the value for X, r and l in the given formula ,

the specific resistance of the given coil of wire can be determined.

CALCULATION

Radius of the given coil of wire r =-----------------metre

Length of the given coil of wire l= ---------------- metre

Specific resistance of the given coil of wire 2X r

ohm-metre



61

RESULT

The unknown resistance of the given coil of wire(X) =--------ohms

Specific resistance of the given coil of wire = ------------ohm-metre

VIVA QUESTIONS:

1. What is Carey-Foster Bridge?

2. What is meant by specific resistance?

3. What is meant by balancing length?

4. What is meant by Wheatstone network?

5. What is the use of interchanging the values of R and X in the circuit?



62

AIM

To determine the hysteresis loss in the transformer core using B-H curve unit.

APPARATUS REQUIRED

B-H curve unit, Cathode ray Oscilloscope (CRO), Patch cords

FORMULA

Hysteresis 1 2v H

2 1

N R Closs S S Area of the loop

N R V

joule

cycle-1

m-3


N1 Number of turns in the primary coil ---

N2 Number of turns in the secondary coil ---

V Volume of the core m3

Sv Vertical sensitivity of CRO Vm-1

SH Horizontal sensitivity of CRO Vm-1

R1 & R2 Resistances in the circuit ohm

C Capacitance of the capacitor in the circuit Farad

PROCEDURE

The experimental arrangement is as shown in the figure.

One of the specimens used in the unit is made using transformer stampings. There

are two winding on the specimen (primary and secondary). The primary is fed to low A.C

voltage (50 Hz). This produces a magnetic field H in the specimen. The voltage across R1

(resistance connected in series with primary) is proportional to the magnetic field.

It is given to the input in the CRO. The A.C magnetic field induces a voltage in the

secondary coil. The voltage induced is proportional to dB/dt.

13. B-H CURVE USING CRO

Expt. No. Date:



63

This voltage is applied to passive integration circuit. The output of the integrator is

proportional to B and fed to the vertical input of the C.R.O

As a result of the application of voltage proportional to H the horizontal axis and a

voltage proportional to B is the vertical axis, the loop is formed as shown in figure. A

measurement of the area of the loop leads to the evaluation of the energy loss in the

specimen.

SPECIMEN

Fig. 13.1. Top view of the B-H Curve unit

The top view of the unit is shown in the figure. There are 12 terminals on the panel,

six patch cords are supplied with the kit.

The value of R1 can be selected by connecting terminal D to A,B or C(A-D=50

ohm); B-D=150 ohm; C-D=50 ohm)



64

A is connected to D. The primary terminals of the specimen is connected to p,p

secondary to s,s terminals. The CRO is calibrated as per the instructions given in the

Instruction manual of the CRO. CRO is adjusted to work on the external mode (the time

base is switched off). The horizontal and vertical position controls are adjusted such that

the spot is at the centre of the CRO screen.

The terminal marked GND is connected to the ground of the CRO. The H is

connected to the Horizontal input of the CRO. The terminals V are connected to the

vertical input of the CRO. The power supply of the unit is switched on. The hysteresis loop

is formed. The horizontal and vertical gains are adjusted such that the loop occupies

maximum area on the screen of the CRO. Once this adjustment is made, the gain controls

should not be disturbed. The loop is traced on a translucent graph paper. The area of the

loop is estimated.

The connections from CRO are removed without disturbing the horizontal and

vertical gain controls. The vertical sensitivity of the CRO is determined by applying a

known A.C. voltage say 1 volt (peak to peak).

If the spot deflects by x cms for 1 volt, the vertical sensitivity is 1/(x10-2

) (volt/m).

Let it be SV. The horizontal sensitivity of CRO is determined by applying a known A.C

voltage say 1 volt (peak to peak). Let the horizontal sensitivity be SH (volt/m).

The hysteresis loss is calculated by using the given formula.

Calculation of the volume of the transformer core

lo – outer length of the core

bo – outer breadth of the core

li – inner length of the core

bi – inner breadth of the core

t – Thickness of the core

o o i iV b b t

Calculation of area of the loop from (transluscent graph sheet)

There are 100 small squares in 1cm2 area of the graph

1 cm2= area of 100 small square

Area of 1 small square (1mm2) = 1/100 cm

2=0.01 cm

2

Area of the loop= number of small square 0.01 cm2



65

Fig. 13.2. Hysteresis loop

Observations

Number of turns in the primary N1=

Number of turns in the secondary N2=

Resistance R1= ohm

Resistance R2= ohm

Capacitance of the capacitor C= F

Vertical sensitivity of CRO SV= Vm-1

Horizontal sensitivity of CRO SH= Vm-1

CALCULATION

Area of the loop= m2

(from the graph)

Hysteresis 1 2v H

2 1

N R Closs S S Area of the loop

N R V

RESULT

Energy loss=…………………………….. joules cycle-1

m-3



66

VIVA QUESTIONS:

1. Explain the significance of the hysteresis loop.

2. What is meant by cycle of magnetization?

3. What is meant by retentivity and coercivity?

4. What is the use of finding the area of the loop?

5. Give any two ferro-magnetic materials used in finding the energy losses?



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