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 nonuniform 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: Mgl 3 E N / m2 3 4bd y 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.
1
2
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.
3
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
1
50
2
100
3
150
4
200
5
250
6
300
7
350
Microscope readings During increasing load During Decreasing load MSR x10-2m
VSR x10-2m
TR x10-2 m
MSR x10-2m
VSR X10-2 m
TR x10-2 m
Mean x10-2 m
Mean M/Y =
4
Average depression Y (for M=50g) x10-2 m
M/Y x10-1 Kg/m
__________________ Kg/m
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 x10-2m
V.S.C Divisions
V.S.R = V.S.C x L.C x10-2m
Breadth = M.S.R + V.S.R + Z.C x10-2m
1 2 3 4 5
Mean Breadth of the beam (b) = _______x10-3 m
5
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 10-3m
H.S.C divisions
H.S.R( = H.S.C XL.C) X 10-3m
Thickness = (P.S.R + H.S.R+Z.C) X 10-3m
1 2 3 4 5
Mean Thickness of the beam (d) = _______x10 -3 m
6
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): E
Mgl 3 4bd 3 y
N / m2
E=
7
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
8
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:
I
Moment of inertia of the disc
Rigidity modulus of the material of the wire n =
MR 2
2
kg m2
8 I L N/m2 4 2 r T
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.
9
Table I. Determination of Time period of Oscillation x 10-3 Kg
Mass of the disc (M) =
Length of the pendulum (L) x10-2 m
Time for 10 oscillations (second) Trial I
Trial II
Trial III
Mean
Mean
10
L = T2
Time Period (T) second
L T2
x10-2 m/s2
x10-2 m/s2
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
x10-3 m
Mean diameter of the wire (2r) =
Calculations: Circumference of the Disc Radius of the Disc Mass of the disc Radius of the wire
2πR = R = M = r =
I
Moment of inertia of the disc
11
MR 2
2
kg m2
x10-2 m x10-2 m x10-3 kg x 10-3 m
Rigidity modulus of the material of the wire is
n=
8 I L N/m2 4 2 r T
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/T 2. 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.
12
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.
13
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
14
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 D
( R2 R1 ) ( S2 S1 ) 2
A D Sin 2 Refractive index of the prism A Sin 2 R Dispersive power of the material of the prism V Y 1 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.
15
16
(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 MSR
Vernier II
VSR
One of the polished surface
TR X1=
Other polished surface
TR
Y2=
X = 2A = X1 ~ X2
X Y 4
VSR
Y1=
X2=
Angle of prism A
MSR
Y = 2A = Y1 ~Y2
=
17
Table II: Angle of minimum deviation and refractive index Angle of prism „A‟ =
Vernier I Direct ray Reading
Minimum deviated ray Reading
MSR
VSR
Vernier II TR R1
MSR
VSR
TR S1 Angle of minimum deviation ( R R1 ) ( S2 S1 ) D 2 2
MSR
VSR
TR R2
MSR
VSR
TR S2
Violet Blue Green Yellow Red
18
Refractive index
A D Sin 2 A Sin 2
(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 sin i refraction. i.e., = which is a constant known as refractive index. sin r
19
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
20
V R Y 1
Result: Angle of the given prism Dispersive power of the material of the given glass prism
21
A= =
22
YOUNG’S MODULUS BY UNIFORM BENDING Expt.No: Date : Aim: To determine the Young‟s modulus of the material of the given beam by UniformBending 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 3gDl 2 M E= Nm-2 3 2bd Y 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.
23
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 10-3m
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
24
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 Microscope readings x10-2 m S.No
Load M x10-3 kg
Loading MSR
1
50
2
100
3
150
4
200
5
250
6
300
7
350
VSR
Mean
Average elevation
x10-2m
Y (for M=50g) x10-2m
Unloading TR
MSR
VSR
TR
M/Y X10-1 Kg/m
Mean M/Y = __________________ Kg/m
25
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.
26
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 x10-2m
V.S.C Divisions
V.S.R = V.S.C x L.C x10-2m
Breadth (b)=( M.S.R + V.S.R+Z.C) x10-2m
1 2 3 4 5 Mean Breadth of the beam (b) =
27
x10-2m
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 =
Distance between the two knife edges
Kg/m
l=
x 10-2 m
D=
x 10-2 m
Distance between the weight hanger and the adjacent knife edge
Young‟s modulus of the given material of the beam
3gDl 2 M E= Nm-2 3 2bd Y
28
Result: The Young‟s Modulus of the material of the given beam by Uniform Bending method is E = ____________ N/m2
29
30
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 gr 4 (ht ) Ns / m2 8lV 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) h h2 h 1 h0 (metre) 2 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 pressurehead „h‟ decreases, the time of flow„t‟ increases. The product ‟ht‟ is also calculated.
31
ho = _________ x 10-2 m
TABLE I: To find the ht
S.No
1 2 3 4 5 6 7 8 9 10 11
Burette reading
Time for every 5cc flow of liquid (t)
cc 0 5 10 15 20 25 30 35 40 45 50
Sec
Time Height of of initial Range flow reading for 5cc h1 liquid cc Sec x10-2 m 0-5 5-10 10-15 15-20 20-25 25-30 30-35 35-40 40-45 45-50
Height of final reading h2
h
x10-2 m
x10-2m
Mean ht = Table II: To Measure the Diameter of the capillary tube
h1 h2 h0 2
ht
m-sec
m-sec L.C = 0.001cm
Horizontal cross wire Vertical cross wire M.S.R VSC MSR+(VSCXL.C) M.S.R VSC MSR+(VSCXL.C) Position Position cm div cm cm div cm Top Left
Bottom
Difference d1=
Right
cm
Average diameter of the capillary tube
d= =
Average radius of the capillary tube(r)
=
32
d1 d 2 2
Difference d2 = cm x 10-2 m
x10-2 m
cm
(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.
33
Calculations: Radius of the capillary tube(r) Density of water () Length of the capillary tube (l) Volume of the water (V) Acceleration due to gravity (g) Average Value of „ht‟
= x10-2 m = 1000 kg/m3 = x10-2 m = x10-6 m3 2 = 9.8 m/s = m-sec
Co-efficient of viscosity of the given liquid is
gr 4 (ht ) 8lV
Ns / m2
Result: The coefficient of viscosity of the given liquid ( water ) =______________Ns/ m2
34
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
Eg
2k 2.303 log 10 RT eV 19 1/ T 1.6 x10
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. Q We know RT = R . Thus keeping the resistance in Q the same, the resistance P 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 0 10 C rise in temperature, the resistance of the thermistor is found out. The readings are entered in the tabular column.
35
Table I: To find the resistance of the thermistor at different temperatures Temp.of Temp.of thermistor thermistor S.No t T=t+273 C˚
K
Resistance in
1 10 3 T
P
Q
R
K-1
Ohm
Ohm
Ohm
Resistance of the thermistor Q Rt R P Ohm
1 2 3 4 5 6 7 8 9 10 Graph: Y A dy 2.303 log RT
B
C
dx
O
1/T (K-1)
X
36
2.303 log Rt Ohm
1 along X- axis and 2.303 log10 RT along Y axis. A T straight line is obtained and the slope of the line is calculated.
A graph is drawn by taking
Band gap (Eg) = 2k X slope of the straight line dy dy 2.303 log 10 RT = 2k X , where dx dx 1/ T
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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 =
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eV
RESISTIVITY OF A WIRE –CAREY-FOSTER’S BRIDGE Expt.No: Date : AIM i) ii)
To determine the Resistance of a given coil of a wire. 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 R Ohm / m X (l1 l2 )
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 S R (l3 l4 ) 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 Sr 2 P Ohm-m L
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Circuit Diagram of Carey-Foster’s Bridge.
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i) To find the resistance per unit length of the wire in the bridge:
Sl. No.
Resistance dialed in box R
Unit
Balancing length Before Interchange (l1)
After Interchange (l2)
cm
cm
ohm
(l1~l2)
cm
X
R l1 ~ l 2
ohm/m
1 2 3 4 5 Mean X=…………………… ohm/m iv)
To find the Resistance the given coil of wire: Balancing length
Sl. No.
Resistance dialed in box R R
Unit
ohm
Before interchange (l3)
After Interchange (l4)
(l3~l4)
X R (l3 l4 )
cm
cm
cm
ohm/m
1 2 3 4 5 Mean X = …………………. ohm/m
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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.
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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) =………………. x10-3m
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Calculation:
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RESULT: i)
The Resistance of the given coil of wire =……………………Ohm
ii)
The specific resistance of the given coil of wire =………………Ohm-m
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