Download - Physics Manual
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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:
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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
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3
Table : 1.1 To determine the Time period:
Length of the suspension wire = .. x 10-2m
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
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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?
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5
AIM
To determine the youngs 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
Symbol Explanation Unit
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 Youngs modulus of the beam is calculated.
2. YOUNGS MODULUS NON-UNIFORM BENDING
Expt. No. Date:
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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.
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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
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8
Youngs modulus of the beam 3
-2
3
4
m g lE Nm
bd y
RESULT:
Youngs modulus of the material of the given beam E= ------------- Nm-2 .
VIVA QUESTIONS:
1. Define youngs modulus.
2. How are longitudinal strain and stress produced in your experiment?
3. Define Hooks law.
4. Will the value of youngs modulus obtained by you change if the length,
thickness or breadth of the bar is altered?
5. What are stress and strain?
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AIM
To determine the coefficient of viscosity of the given liquid by poiseuilles
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
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
POISEUILLES METHOD
Expt. No. Date:
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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
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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
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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
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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 10-6kg
Density of the given liquid = kg/m3
Acceleration due to gravity g = 9.8 ms-2
Radius of the capillary tube r = ..x 10 2m
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.
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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
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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
Symbol Explanation Unit
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:
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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.
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(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
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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
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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?
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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
Symbol Explanation Unit
Wavelength of the sodium vapour lamp (=589310-
10m)
Meter
l Distance between the specimen wire and the edge of
contact Meter
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:
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21
DIAGRAM
Fig. 5. Air wedge arrangement
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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 () 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 , 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
10-2m VSC
TR
10-2m
Rubber band
(edge of
contact)
(R1)
Specimen wire (R2)
l = R2~ R1 .. 10-2
m
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23
Table 5.2. To determine the band width ():
Order of
the fringe
Microscope reading Width of 5
fringes
10-2m
Mean width
of one
fringe() 10-2m
MSR
10-2m VSC
TR
10-2m
n
n+5
.
.
.
.
n+50
=. 10-2m
CALCULATION
Wavelength of the sodium vapour lamp, = 5893 10-10m
Distance between the specimen wire and the edge of contact, l = 10-2m
Mean width of one fringe, = . 10-2m
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?
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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
Symbol Explanation Unit
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:
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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
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26
Fig. 6.1. To set the normal incident position
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27
Fig. 6.2 Diffracted rays from grating
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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
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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
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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?
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31
AIM
To determine the coefficient of thermal conductivity of a bad conductor.
APPARATUS REQUIRED
Lees 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
Symbol Explanation Unit
M Mass of the metallic disc kg
S Specific heat capacity of the material of the disc J kg-1
K-1
(d/dt)2 Rate of cooling at 2 0C/s
r Radius of metallic disc meter
h Thickness of metallic disc meter
d Thickness of bad conductor meter
1 Steady temperature of a steam chamber 0C
2 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. LEESS 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
(1) of the steam chamber and (2) 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 2 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. (2+ 10)C, stop clock is started. Time for every one degree Celsius fall of
temperature is noted until the metallic disc attains a temperature (2 - 10)C.
-
33
Fig. 7.1. Lees 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 (d/dt) 2
From this graph, a triangle is drawn by taking 1C above and 1C below the steady
temperature 2. Then the slope AB / BC gives the rate of cooling at (d/dt) 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 (d/dt) 2
S.No. Temperature () 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
(m2N-1)
Symbol Explanation Unit
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 Boltzmanns 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
Symbol Explanation Unit
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 21 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
Symbol Explanation Unit
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 0 and 180 and the vernier table is fixed.
The telescope is released and moved towards the right side through 90 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 45 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 l10-2 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
= ..
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 = ..
(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 1a 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
1a 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 youngs 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
Symbol Explanation Unit
E Youngs 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. YOUNGS 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 Youngs 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
Youngs modulus of the beam 2
-2
3
3
2
M g aE Nm
b d y
RESULT:
Youngs 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
Symbol Explanation Unit
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-FOSTERS BRIDGE
12. CAREY-FOSTERS 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
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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?
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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 2 v H2 1
N R Closs S S Area of the loop
N R V
joule
cycle-1
m-3
Symbol Explanation Unit
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:
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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)
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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 (1mm
2) = 1/100 cm
2=0.01 cm
2
Area of the loop= number of small square 0.01 cm2
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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 2 v H2 1
N R Closs S S Area of the loop
N R V
RESULT
Energy loss=.. joules cycle-1m-3
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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?