1

YOUNG’S MODULUS BY NON-UNIFORM BENDING

Expt.No:

Date :

Aim:

To determine the Young‟s modulus of the material of the given beam by non-

uniform bending.

Objective:

To detect the maximum stress applied to the given beam by Non-uniform bending

method.

Apparatus required:

Travelling microscope, two knife edge supports, weight hanger with set of

weights, pin, meter scale, vernier calipers and screw gauge.

Formula:

The Young‟s modulus of the material of the beam (meter scale) is:

2

3

3

/4

mNybd

MglE

Where

E =Young‟s Modulus of the material of the beam (N/m2)

y =depression at the center of the beam (m)

M=Mass suspended at the center of the beam (Kg)

g = acceleration due to gravity (9.8 m/s2)

l =distance between the two knife edges (m)

b = breadth of the beam (m)

d = thickness of the beam (m)

Theory:

Here the given beam (meter scale) is supported symmetrically on two knife edges

and loaded at its centre. The maximum depression is produced at its centre. Since the load

is applied only at one point of the beam, the bending is not uniform throughout the beam

and the bending of the beam is called non-uniform bending.

Procedure:

Using two knife edges, the meter scale is placed horizontally. Exactly midway

between the knife edges, a pin index using clay is affixed such that its tip is facing

upwards. At that point a weight hanger is suspended. The microscope is adjusted such

that the tip of the image of the pin is exactly at the centre of the cross wires. The loads are

added to the hangers in steps of 50 gm and the microscope is adjusted so that the tip of

the image of the pin just coincides with the horizontal cross wires in each case and the

microscope readings are noted. After reaching the maximum load, the hanger is unloaded

in the same steps of 50 gm and the microscope readings are noted again.

The experiment is repeated for the different lengths of beam. This can be done by

altering the length between the knife edges. Finally the breadth of the scale is measured

using vernier calipers and the thickness using screw gauge respectively at different points

on the beam and mean value is taken. From the observations, the young's modulus of the

beam is calculated by using the given formula.

2

3

Precautions:

1. The beam must be kept horizontal.

2. Since the value of thickness (d) is small and it occurs to the third power in the

expression for y, it must be measured with a screw gauge.

3. While taking readings, the microscope must be rotated in the same direction, so

as to avoid the back-lash error.

4. After loading or removing weights, some time must be allowed before taking if

the readings

Applications:

The elastic property of the material is useful while studying materials for

industrial applications such as construction of bridges, railway wagons etc.,

Viva-Voce

1. What is Hooke‟s Law?

The stress applied to a body is directly proportional to the strain produced in the

body.

2. What is modulus of elasticity?

The ratio of stress to strain is a constant and is known as modulus of elasticity.

3. What is Young‟s modulus?

Young‟s modulus is defined as the ratio of the longitudinal stress to the

longitudinal strain.

4. What is a beam?

When the length of the rod of uniform cross-section is very large compared to its

breadth such that the shearing stress over any section of the rod can be neglected, the rod

is called a beam.

5. What is the change produced in depression when the thickness of the bar is doubled?

If thickness is doubled, then the depression is reduced to 1/8 of its previous value.

6. What is the change produced in depression when the breadth of the bar is doubled?

If breadth is doubled, then the depression is reduced to l/2 of its previous value.

7. What is the change in Young‟s modulus when the thickness and breadth of the bar is

doubled?

Young‟s modulus does not change.

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

Due to depression, the upper or the concave side of the beam becomes smaller

than the lower or the convex side of the beam. As a result, longitudinal strain is produced.

The change in length will be due to the force acting along the length of the beam. These

forces will give rise to longitudinal stress.

4

Least count of Traveling microscope (L.C) = 0.001cm (or) 0.001 x10-2

m V.S.R = V.S.C x L.C

T.R = M.S.R+ V.S.R

Distance between the two knife edges (l) = __________ x10-2

m

Table I: To find the average value of M/Y

S.No

Load

M

x10-3

kg

Microscope readings Mean

x10-2

m

Average

depression

Y (for

M=50g)

x10-2

m

M/Y

x10-1

Kg/m

During increasing load During Decreasing load

MSR

x10-2

m

VSR

x10-2

m

TR

x10-2

m

MSR

x10-2

m

VSR

X10-2

m

TR

x10-2

m

1 50

2 100

3 150

4 200

5 250

6 300

7 350

Mean M/Y = __________________ Kg/m

5

Table II: To find the breadth of the beam using vernier caliper

Least count of vernier caliper (L.C) = 0.01cm or 0.01 x10-2

m

Zero error (Z.E) =) ______divisions

Zero correction (Z.C) = (Z.E x L.C) =________x10-2

m

S.No

M.S.R

x10-2

m

V.S.C

Divisions

V.S.R = V.S.C x L.C

x10-2

m

Breadth = M.S.R + V.S.R + Z.C

x10-2

m

1

2

3

4

5

Mean Breadth of the beam (b) = _______x10-3

m

6

Table III: To find the Thickness of the beam using Screw Gauge

Least Count of Screw Gauge (L.C) = 0.01 mm (or) 0.01 x 10-3

m

Zero Error (Z.E) = _______ Divisions

Zero Correction (Z.C) = (Z.E x L.C) = ______ x 10-3

m

S .No P.S.R

x 10-3

m

H.S.C

divisions

H.S.R( = H.S.C XL.C)

X 10-3

m

Thickness = (P.S.R + H.S.R+Z.C)

X 10-3

m

1

2

3

4

5

Mean Thickness of the beam (d) = _______x10-3

m

7

Calculation:

Acceleration due to gravity g = 9.8 m/s2

Distance between the two knife edges l = _____________ x 10-2

m

Breadth of the beam b = _____________ x 10-2

m

Thickness of the beam d = _____________ x 10-3

m

Average value of M/y = _____________ kg/m

Young‟s modulus of the material of the beam (meter scale):

2

3

3

/4

mNybd

MglE

E =

8

9. Which dimension breadth, thickness, or length of the bar should be measured very

carefully and why?

The thickness of the bar should be measured very carefully since its magnitude is

small and it occurs in the expression in the power of three. An inaccuracy in the

measurement of the thickness will produce the greatest proportional error in E.

Result:

The Young‟s modulus of the material of the beam (meter scale)

by Non- Uniform bending E = ___________N/m2

9

TORSIONAL PENDULUM-- RIGIDITY MODULUS

Expt.No:

Date :

Aim:

To determine the rigidity modulus of the material of the wire and the moment of

inertia of a circular disc about its axis of suspension by the method of torsional

oscillations.

Objective:

To understand the concept of moment of inertia and rigidity modulus using

torsional pendulum.

Apparatus required:

Circular disc with chuck, given wire (suspension wire), stop clock, two equal

cylindrical masses, screw gauge and metre scale.

Formula:

Moment of inertia of the disc 2

2MR

I kg m2

Rigidity modulus of the material of the wire n = 24

8

T

L

r

I N/m

2

Where

M = mass of the disc (kg)

T = Period of oscillation of the Torsion pendulum (second)

R = Radius of the Torsion disc (metre)

L = length of the suspension wire (metre)

r = Radius of the Pendulum wire (metre)

Theory:

Torsion pendulum consists of a metal wire clamped to a rigid support at one end

and carries a heavy circular disc at the other end. When the suspension wire of the disc is

slightly twisted, the disc at the bottom of the wire executes torsional oscillations such that

the angular acceleration of the disc is directly proportional to its angular displacement

and the oscillations are simple harmonic.

10

Table I. Determination of Time period of Oscillation

Mass of the disc (M) = x 10-3

Kg

Length of

the

pendulum

(L)

x10-2

m

Time for 10 oscillations (second) Time

Period (T)

second

2T

L

x10-2

m/s2

Trial I

Trial II

Trial III

Mean

Mean 2T

L= x10

-2m/s

2

11

Table II: Determination of the diameter of the suspension wire using screw gauge

Least count L.C = 0.01 x 10-3

m

Zero Error (Z.E) = _______ Divisions

Zero Correction (Z.C) = (Z.E x L.C) = ______ x 10-3

m

S.No P.S.R

x10-3

m

H.S.C

Divisions

H.S.R =H.S.C x L.C

X10-3

m

T R =( P.S.R + H.S.R+ Z.C)

x10-3

m

Mean diameter of the wire (2r) = x10-3

m

Calculations:

Circumference of the Disc 2πR = x10-2

m

Radius of the Disc R = x10-2

m

Mass of the disc M = x10-3

kg

Radius of the wire r = x 10-3

m

Moment of inertia of the disc 2

2MR

I kg m2

12

Rigidity modulus of the material of the wire is n = 24

8

T

L

r

IN/m

2

Procedure:

One end of a long, uniform wire whose rigidity modulus is to be determined is

clamped by a vertical chuck. To the lower end, a heavy uniform circular disc is attached

by another chuck. The length of the suspension „l‟ (from top portion of chuck to the

clamp) is fixed to a particular value (say 60 cm or 70 cm).The suspended disc is slightly

twisted so that it executes torsional oscillations. The first few oscillations are omitted. By

using the pointer, (a mark made in the disc) the time taken for l0 complete oscillations are

noted. Three trials are taken. Then the mean time period T (time for one oscillation) is

found. The above procedure is repeated for three different length of pendulum wire. From

the above values of L and T calculate L/T2.

The diameter of the wire is accurately measured at various places along its length

with screw gauge. From this, the radius of the wire is calculated. The circumference of

the disc is measured and from that the radius of the disc is calculated. The moment of

inertia of the disc and the rigidity modulus of the wire are calculated using the given

formulae.

13

Precautions:

l. The suspension wire should be well clamped, thin long and free from kinks.

2 The period of oscillations should be measured accurately since they occur in second

power in the formula.

3. Radius of the wire should be measured very carefully since it occurs in fourth power.

Applications:

1. This method is used to find the moment of inertia of any irregular materials and the

elastic limit of the given wire.

2. By knowing the moment of inertia, the time period of oscillations can be found.

Viva-Voce

1. What is torsional pendulum?

A body suspended from a rigid support by means of a long and thin elastic wire is

called a torsional pendulum.

2. Why is it called a torsional pendulum? `

It executes in torsional oscillations, it is called as a torsional pendulum.

3. What is the shape of rigid body you can use for a torsional pendulum?

Sphere, cylinder and circular disc.

4. What are the factors affecting the time period of the pendulum?

The factors affecting the time period of the pendulum are moment of inertia of the

rigid body, rigidity modulus, length, radius and material of the wire. `

5. How does the torsional pendulum oscillate? (OR) What is meant by torsional

oscillations?

When the torsional pendulum is given a slight rotation by applying a torque, the

wire is twisted. Now a restoring couple is developed in the wire due to elasticity on the

removal of external torque, the restoring couple tends to untwist the wire, so that the

pendulum oscillates. Such oscillations are called torsional oscillation.

6. What is the type of oscillation produced in a torsional pendulum?

Simple harmonic oscillation.

14

Result:

Moment of inertia of the circular disc about the axis

passing through its centre (I) =_________x 10-3

kg m2

Rigidity modulus of the material of the wire (n) =______________ N/m2

15

DISPERSIVE POWER OF A PRISM - SPECTROMETER

Expt. No:

Date :

Aim: To determine the

(i) Refractive index of the given glass prism for different colours.

(ii) Dispersive power of the material of the prism using spectrometer

Apparatus Required

Spectrometer, Mercury vapour lamp, Glass prism, Reading lens and spirit level.

Formula

Angle of minimum deviation 2

)()( 1212 SSRRD

Refractive index of the prism

2

2

ASin

DASin

Dispersive power of the material of the prism 1

Y

RV

Where

A Angle of the prism (degree)

D Angle of minimum deviation (degree)

v Refractive index of the prism for violet line

R Refractive index of the prism for red line.

Y Refractive index of the prism for yellow line.

R1 Direct Ray for vernier I

R2 Minimum deviated ray for vernier I

S1 Direct Ray for vernier II

S2 Minimum deviated ray for vernier II

Procedure:

The following initial adjustments of the spectrometer are made first.

(i) The spectrometer and the prism table are arranged in horizontal position by

using the leveling screws.

(ii) The telescope is turned towards a distant object to receive a clear and sharp

image.

(iii) The slit is illuminated by a sodium vapour lamp and the slit and the

collimator are suitably adjusted to receive a narrow, vertical image of the slit.

(iv) The telescope is turned to receive the direct ray, so that the vertical slit

coincides with the vertical crosswire.

16

17

(iv) The telescope is turned to receive the direct ray, so that the vertical slit

coincides with the vertical crosswire.

Table I.: Determination of the angle of prism ‘A’

Least count = 1`

Rays

reflected

from

Vernier I Vernier II

MSR VSR TR MSR VSR TR

One of the

polished

surface

X1=

Y1=

Other

polished

surface

X2=

Y2=

X = 2A = X1 ~ X2 Y = 2A = Y1 ~Y2

Angle of prism 4

YXA

=

18

Table II: Angle of minimum deviation and refractive index

Angle of prism „A‟ =

Direct ray

Reading

Vernier I Vernier II

Angle of minimum

deviation

2

)()( 1212 SSRRD

Refractive index

2

2

ASin

DASin

MSR VSR TR

R1 MSR VSR

TR

S1

Minimum

deviated

ray

Reading

MSR VSR TR

R2 MSR VSR

TR

S2

Violet

Blue

Green

Yellow

Red

19

(i) Determination of Angle of prism (A)

The given glass prism is mounted vertically at the centre of the prism table with

its two refracting faces facing the collimator and the base of the prism faces the telescope.

Now the parallel rays of light coming out of the collimator falls almost equally on the two

refracting faces of the prism ABC and gets reflected. The telescope turned to receive the

reflected image from one face (left) of the prism and fixed in that position. The tangential

screw is adjusted until the vertical cross wire coincides with the fixed edge of the image

of the slit. Now the readings on both the verniers( Ver A and Ver B) are noted.

Similarly the readings corresponding to the reflected image of the slit on the other

face (right) are also taken. The difference between the two readings of the same vernier

gives twice the angle of the prism (2A). From the mean value of 2A the angle of the

prism A is determined.

(ii) Determination of angle of minimum deviation (D)

The prism is mounted on the prism table in such a way that the light from the

collimator incident on one of the refracting faces of the prism. Here the light enters in to

the prism and gets diffracted. The diffracted ray moves parallel to the base of the prism

and gets dispersed. Now the telescope is turned to receive the dispersed spectrum coming

out of the other refracting face of the prism.

By viewing the spectrum, the prism table is slowly rotated either in clockwise or

in anticlockwise direction in such a way that the spectrum moves towards the direct ray.

At a particular position the spectrum retraces its path. When it retraces its path, stop the

rotation of the prism table. This is the minimum deviation position.

The telescope is turned and the horizontal crosswire is made to coincide with the violet

slit. Then both vernier scale readings (Ver A and Ver B) are noted. The experiment is

repeated for yellow and red slits. The prism is removed and the direct reading of the slit is

taken. The difference between the direct reading and the refracted ray reading

corresponding to the minimum deviation gives the angle of minimum deviation D. The

dispersive power is calculated by using the given formula.

Viva - Voce

1. What is a spectrometer?

The instrument which is used to analyze the spectrum of different light sources is

called a spectrometer.

2. What is the function of a collimator in a spectrometer?

The main function of the collimator is to produce a parallel beam of light and it

made the light to incident on the prism.

3. Define refractive index.

It is defined as the ratio of the sine of the angle of incidence to the sine of angle of

refraction. i.e., = r

i

sin

sinwhich is a constant known as refractive index.

20

4. How does the refractive index changes with wavelength of light?

Higher the wave length, smaller is the refractive index. The refractive index of the

prism for violet is greater than that of red.

5. Does the deviation depend on the angle of the prism?

Yes, greater the angle of the prism more is the deviation.

Calculation:

Dispersive power of the material of the prism 1

Y

RV

21

Result:

Angle of the given prism A =

Dispersive power of the material of the given glass prism =

22

23

YOUNG’S MODULUS BY UNIFORM BENDING

Expt.No:

Date :

Aim:

To determine the Young‟s modulus of the material of the given beam by Uniform-

Bending

Objective:

To detect the maximum stress applied to the given beam by Uniform Bending

method.

Apparatus Required:

Travelling Microscope, Two knife edge supports, Two Weight hangers, Slotted

weights, Pin, Screw gauge, Vernier Calipers.

Formula:

Young‟s modulus of the given material of the beam

E =Ybd

MgDl3

2

2

3 Nm

-2

Where,

E = Young‟s Modulus of the material of the beam (Pascal or N/m2)

Y = Elevation produced for „M‟ Kilogram of load (m)

M = Mass suspended on either sides of the beam (Kg)

g = Acceleration due to gravity (9.8 m/sec2)

l = Distance between the two knife edges (m)

b = Breadth of the beam (m)

d = Thickness of the beam (m)

D = Distance between the weight hanger and any one of the adjacent

Knife edge (m)

Procedure:

The given beam is placed over the two knife edges (A & B) at a distance of 70 cm

or 80 cm. Two weight hangers are suspended, one each on either side of the knife edge at

equal distance from the knife edge. Since the load is applied at both points of the beam,

the bending is uniform throughout the beam and the bending of the beam is called

Uniform Bending. A pin is fixed vertically exactly at the centre of the beam.

A traveling microscope is placed in front of this arrangement. Taking the weight

hangers alone as the dead load, the tip of the pin is focused by the microscope and is

adjusted in such a way that the tip of the pin just touches the horizontal cross wire. The

reading on the vertical scale of the traveling microscope is noted.

Now, equal weights are added on both the weight hangers, in steps of 50 grams.

Each time the position of the pin is focused and the readings are noted from the

microscope. The procedure is followed until the maximum load is reached.

24

Table I: To find the Thickness of the beam using Screw Gauge

Least Count of Screw Gauge (L.C) = 0.01 mm

(L.C) = 0.01 x 10-3

m

Zero Error (Z.E) = _______ Divisions

Zero Correction (Z.C) = (Z.E x L.C) = ______ x 10-3

m

S.No P.S.R

x 10-3

m

H.S.C

divisions

H.S.R = H.S.C X L.C

X 10-3

m

Thickness = (P.S.R + H.S.R + Z.C)

X 10-3

m

1

2

3

4

5

Mean Thickness of the beam (d) = _______x10-3

m

25

Least count of Traveling microscope (L.C) = 0.001cm (or) 0.001 x10-2m V.S.R = V.S.D x L.C

T.R = M.S.R+ V.S.R

Distance between the two knife edges (l) = __________ x10-2m

Distance between the weight hanger and any one of the adjacent knife edge (D) =__________x10-2

m

Table II: To find the average value of M/Y

S.No

Load

M

x10-3 kg

Microscope readings x10-2

m

Mean

x10-2m

Average elevation

Y (for M=50g)

x10-2m

M/Y

X10-1 Kg/m

Loading Unloading

MSR

VSR

TR

MSR

VSR

TR

1 50

2 100

3 150

4 200

5 250

6 300

7 350

Mean M/Y = __________________ Kg/m

26

The same procedure is repeated by unloading the weight from both the weight hanger in

steps of same 50 grams and the readings are tabulated in the tabular column. From the

readings, the mean of (M/y) is calculated. The thickness and the breadth of the beam are

measured using screw gauge and vernier calipers respectively and are tabulated. By

substituting all the values in the given formula, the Young‟s modulus of the given

material of the beam can be calculated.

Viva-Voce:

1. What is stress? Give its unit.

The force applied on a body per unit area is known as stress. Its unit is N/m2.

2. What is strain? Give its unit.

The ratio of change in dimension to original dimension is called strain. It is a

ratio, hence it has no unit.

3. What is elasticity?

The property of the body to regain its original shape and size, after the removal of

the applied stress.

4. What are the factors affecting the elasticity of a material?

a. Effect of stress

b. Effect of change in temperature

c. Effect of Impurities

d. Effect of hammering, rolling and annealing

e. Effect of crystalline nature.

5. What is uniform bending?

The beam is loaded uniformly on its both ends, the bent forms an arc of a circle

and elevation is made on the beam. This bending is called uniform bending.

27

Table III: To find the breadth of the beam using vernier calipers

Least count of vernier caliper (L.C) = 0.01cm or 0.01 x10-2m

Zero error (Z.E) = ______divisions

Zero correction (Z.C) = (Z.E x LC) = ________x10-2m

S.No M.S.R

x10-2

m

V.S.C

Divisions

V.S.R = V.S.C x L.C

x10-2

m

Breadth (b)=( M.S.R +

V.S.R+Z.C)

x10-2

m

1

2

3

4

5

Mean Breadth of the beam (b) = x10-2m

28

Calculation:

Mass suspended on either sides of the beam (M) = 50 x 10-3

Kg

Breadth of the beam b = x 10-2

m

Thickness of the beam d= x 10-3

m

Acceleration due to gravity g= 9.8 m/sec2

Mean Value of M/y = Kg/m

Distance between the two knife edges l = x 10-2

m

Distance between the weight hanger and

the adjacent knife edge D = x 10-2

m

Young‟s modulus of the given material of the beam

E =Ybd

MgDl3

2

2

3 Nm

-2

29

Result:

The Young‟s Modulus of the material of the given beam

by Uniform Bending method is E = ____________ N/m2

30

31

VISCOSITY OF A LIQUID BY POISEUlLLE’S FLOW METHOD

Expt. No:

Date :

Aim:

To find the Co-efficient of viscosity of a given liquid (water) by using Poiseuille‟s

flow method.

Apparatus required:

Graduated burette without stopper, Retort stand with clamp, Capillary tube,

Beaker, Water, Stop watch, Meter scale, Rubber tube, Pinch cock and travelling

microscope.

Formula

Co-efficient of viscosity of the given liquid is

lV

htgr

8

)(4 Ns / m

2

Where

g Acceleration due to gravity (m/s2)

Density of the liquid (kg/m3)

r Radius of the capillary tube (metre)

l Length of the capillary tube (metre)

V Volume of the liquid collected (metre3)

021

2h

hhh

(metre)

h1 Height from table to initial level of water in the burette (metre)

h2 Height nom table to the final level of water in the burette (metre)

h0 Height from table to mid portion of capillary tube (metre)

t Time taken for the liquid flow (second)

Procedure

(i) Measurement of time for liquid flow:

The experimental set up is as shown in the figure. A graduated burette is washed

with water and also with the given liquid whose viscosity is to be determined. The burette

is then fixed vertically in a stand. A capillary tube is connected to the tip of the burette by

means of a rubber tube and is held parallel to the table so that the flow of liquid is

streamlined.

The given liquid is filled in the burette slightly above the zero-mark. Now the

pinch clip is released. When the level of liquid reaches the zero-mark the stop-clock is

started and the time is noted. Similarly the time is noted when the liquid level crosses 5,

10, 15 ...... 50 cc. The time taken for the flow of every 5cc of the liquid„t‟ are determined.

The pressure head (h) is calculated by using a meter-scale. It is seen that as pressure-

head „h‟ decreases, the time of flow„t‟ increases. The product ‟ht‟ is also calculated.

32

TABLE I: To find the ht ho = _________ x 10-2

m

S.No Burette

reading

Time for

every 5cc

flow of liquid

(t)

Range

Time

of

flow

for 5cc

liquid

Height of

initial

reading

h1

Height of

final

reading

h2

021

2h

hhh

ht

cc Sec cc Sec x10-2

m x10-2

m x10-2

m m-sec

1 0 0-5

2 5 5-10

3 10 10-15

4 15 15-20

5 20 20-25

6 25 25-30

7 30 30-35

8 35 35-40

9 40 40-45

10 45 45-50

11 50

Mean ht = m-sec

Table II: To Measure the Diameter of the capillary tube L.C = 0.001cm

Horizontal cross wire Vertical cross wire

Position M.S.R

cm

VSC

div

MSR+(VSCXL.C)

cm Position

M.S.R

cm

VSC

div

MSR+(VSCXL.C)

cm

Top

Left

Bottom

Right

Difference d1= cm Difference d2 = cm

Average diameter of the capillary tube d = 2

21 dd cm

= x 10-2

m

Average radius of the capillary tube(r) = x10-2

m

33

(ii) To find radius of the capillary tube (r) by using travelling microscope:

The capillary tube is held horizontally. The bore of the capillary tube is focused

with the help of a travelling microscope. The horizontal crosswire of the travelling

microscope is made to coincide with the top of the bore of the capillary tube. The reading

in the vertical scale is noted. Now, the travelling microscope is moved so that the

horizontal crosswire coincides with the bottom of the bore of the capillary tube and the

vertical scale readings are noted. The difference between the two readings gives the

diameter of the bore. Similarly using vertical crosswire, the readings in the horizontal

scale corresponding to left and right edges of the bore of the capillary tube are taken. The

difference between the two readings gives the diameter. The readings are tabulated. The

average diameter and hence the radius of the capillary tube are determined.

By using the given formula, the co-efficient of viscosity of the given liquid is

calculated.

Viva-Voce

1. Define the term coefficient of viscosity.

The tangential force acting per unit area over two adjacent layers of the liquid for

a unit velocity gradient is referred to as the coefficient of viscosity.

2. What is the effect of temperature on viscosity?

The coefficient of viscosity decreases with rise in temperature in the case of

liquids, but for gases it increases with rise in temperature.

3. Can you find the viscosity of a highly viscous liquid using poiseuille‟s flow method?

No, the flow of highly viscous liquid through the capillary tube is not uniform. So

Stoke‟s method can be used for highly viscous liquid.

4. Is there any difference between friction and viscosity?

Friction and viscosity have some similarities and same differences between them.

For liquids at rest, friction works but viscosity does not because viscosity arises only

when there is a relative motion between the layers of a liquid.

34

Calculations:

Radius of the capillary tube(r) = x10-2

m

Density of water () = 1000 kg/m3

Length of the capillary tube (l) = x10-2

m

Volume of the water (V) = x10-6

m3

Acceleration due to gravity (g) = 9.8 m/s2

Average Value of „ht‟ = m-sec

Co-efficient of viscosity of the given liquid is

lV

htgr

8

)(4 Ns / m

2

Result:

The coefficient of viscosity of the given liquid ( water ) =______________Ns/ m2

35

DETERMINATION OF BAND- GAP OF A SEMICONDUCTOR

Expt. No:

Date :

Aim:

To find the band gap of the material of the given thermistor (semiconductor) using

post office box.

Apparatus required:

Post office box, Power supply, Thermistor, Thermometer, Galvanometer,

insulating coil and Glass beakers.

Formula:

Band gap for the given thermistor

eVT

R

x

kE T

g

/1

log303.2

106.1

2 10

19

k Bo1tzmann's constant ( 1.38X10-23

J/K )

RT Resistance of the thermistor (ohm)

T Temperature of Thermistor (Kelvin)

Procedure

The Post office box has three variable resistances P, Q and R. The given

thermistor whose band gap energy is to be determined is connected with these resistances

to form a wheatstone's bridge. The band gap energy of the semiconductor used in the

thermistor is calculated by finding the value of resistance of the thermistor at a particular

temperature. The connections are made as shown in the diagram. A 10 ohm resistance is

dialed in P and Q. Then the resistance in R is adjusted by pressing the tab key until the

deflection in the galvanometer crosses zero reading of the galvanometer, say from left to

right. After finding an approximate resistance for this, two resistances in R, which differ

by l ohm, are to be found out such that the deflections in the galvanometer for these

resistances will be on either side of zero reading of galvanometer.

We know RT = RP

Q . Thus keeping the resistance in Q the same, the resistance

in p is changed to 10, 100, 1000, ohms. Thus the resistance of the thermistor is found out

accurately to two decimal at room temperature. The lower value may be assumed to be

RT (0.01 R).

Then the thermistor is heated by keeping it immersed in insulating coil. For every

100 C rise in temperature, the resistance of the thermistor is found out. The readings are

entered in the tabular column.

36

Y

A

B C

dx

dy

2.303 log RT

O

Table I: To find the resistance of the thermistor at different temperatures

S.No

Temp.of

thermistor

t

Temp.of

thermistor

T=t+273

3101 T

Resistance in Resistance of

the thermistor

RP

QRt

2.303 log Rt

P Q R

C˚ K K-1

Ohm Ohm Ohm Ohm Ohm

1

2

3

4

5

6

7

8

9

10

Graph:

X 1/T (K-1

)

37

A graph is drawn by taking T

1 along X- axis and 2.303 log10 RT along Y axis. A

straight line is obtained and the slope of the line is calculated.

Band gap (Eg) = 2k X slope of the straight line

= 2k X ,dx

dy where

T

R

dx

dy T

/1

log303.2 10

38

Viva-Voce

1. What is band gap energy?

The forbidden energy level between the conduction band and the valence band.

2. Define Fermi Energy level.

The highest energy level that can be occupied by the electrons at 0 Kelvin.

3. What are intrinsic semiconductors? Give examples.

Intrinsic semi-conductors are semi-conductors in pure form. These materials are

having an energy gap of the order of 1 eV. Charge carriers are generated due to breaking

of covalent bonds. (Example: Germanium and Silicon)

4. What are extrinsic semi-conductors? Give examples.

A semi-conducting material in which charge carriers originate from impurity

atoms added to the material is called "extrinsic semi-conductors”. The addition of

impurity increases the carrier concentration and hence conductivity of the conductor.

Result

Band gap (Eg) of the semi-conducting material of the thermistor = eV

39

RESISTIVITY OF A WIRE –CAREY-FOSTER’S BRIDGE

Expt.No:

Date :

AIM

To determine the

i) Resistance of a given coil of a wire.

ii) Specific Resistance or Resistivity of the given wire.

APPARATUS REQUIRED

Carey–Foster‟s bridge, sensitive galvanometer, Leclanche cell, High resistance

box, two equal resistances, Fractional resistance boxes, copper strip, Plug key, given coil

of wire and connecting wires etc.

FORMULA

i) The Resistance per unit length of the wire in the Carey-Foster‟s bridge is

)( 21 ll

RX

Ohm / m

Where

R- Resistance dialed in the resistance box.

l 1- Balancing length before interchanging the resistance box R and the copper

strip.

l 2 - Balancing length after interchanging the resistance box R and the copper strip.

ii) The Resistance of the given coil of wire is

)( 43 llRS Ohm

Where

l3-Balancing length before interchanging the resistance boxes R and S.

l4-Balancing length after interchanging the resistance boxes R and S.

iii) The specific Resistance of the material of the wire is

L

rSP

2 Ohm-m

40

Circuit Diagram of Carey-Foster’s Bridge.

41

i) To find the resistance per unit length of the wire in the bridge:

Sl. No.

Resistance

dialed in box

R

Balancing length

(l1~l2) 21 l~l

RX Before

Interchange

(l1)

After

Interchange

(l2)

Unit ohm cm cm cm ohm/m

1

2

3

4

5

Mean X=…………………… ohm/m

iv) To find the Resistance the given coil of wire:

Sl. No.

Resistance dialed in

box R

R

Balancing length

(l3~l4)

)( 43 llRX Before

interchange

(l3)

After

Interchange

(l4)

Unit ohm cm cm cm ohm/m

1

2

3

4

5

Mean X = …………………. ohm/m

42

PROCEDURE

The Carey-Foster‟s bridge consists of one meter thin wire stretched on a wooden

board. The two ends A and B of the wire are fixed to an inverted “L” shaped copper

metal strip metal strip at the two ends of the board. Three more copper strips are fixed

in a linear way with the front terminals of the inverted “L” shaped strip by forming

four gaps as shown in figure. A meter scale is also attached with the wooden board to

measure the balancing lengths.

i) Resistance per unit length of the wire in the bridge:

Connect the two resistance boxes P and Q in the inner gaps (gap no.2 and3) of the

Carey _Foster‟s bridge. A fractional resistance box R and a copper metal strip are

connected in the outer gaps (gap no.1 and 4).A Leclanche cell and a plug key are

connected in series with the central terminals of the and third metal strips in the

bridge. A galvanometer and a jockey “J” are connected in series with the central

terminal of the second metal strip as shown in the diagram. The correctness of the

circuit can be verified by pressing the jockey at the two ends A an B of the wire in the

bridge.

A known resistance (Say 0.1 ohm) is dialed in the resistance box R. The

jockey is moved between the points A and B of the wire in the bridge until a null

deflection is obtained. The balancing length 11 is noted. Now the resistance box R

and the metal strip are interchanged and the new balancing length 12 is also noted.

The experiment can be repeated for different values of resistances in the box R. By

using the given formula, the resistance per unit length of the wire in the bridge can be

calculated. Finally the mean value of the resistance per unit length is calculated.

ii) Resistance of the given coil of wire:

The fractional resistance box R is connected in the first gap and the given coil of

wire whose specific resistance is to be calculated is connected in the fourth gap of the

bridge. A known a resistance is dialed in the box R. The jockey is moved on the

bridge wire to find the balancing length 13. Now the resistance box R and the given

coil of wire are interchanged and the new balancing length 14 is also noted. The

experiment can be repeated for different values of resistances in box R. By using the

given formula the value of the unknown resistance can be calculated.

iii) The specific resistance of the given coil of wire:

The radius of the given wire is calculated by using a screw gauge. The length

of the given wire is also calculated using a meter scale. By using the mean value of

radius (r) and the length (l), the specific resistance of the given coil of wire can be

calculated.

43

iv) To find the radius of the given coil of wire by using screw gauge:

Least Count =…………………………..mm

Zero error =………………………..div.

Zero correction = ZE x L.C

=………………………mm

Sl.No PSR HSC HSR=(HSCX L.C) TR=PSR+HSR

Unit mm div mm mm

1

2

3

4

5

Mean radius of the wire (r) =………………. x10-3

m

44

Calculation:

45

RESULT:

i) The Resistance of the given coil of wire =……………………Ohm

ii) The specific resistance of the given coil of wire =………………Ohm-m