lab manual for btech students

1

Experiment No.—01

Aim of the Experiment:

To determine the value of acceleration due to gravity(g) with the help of compound (bar) pendulum.

Apparatus required:

A bar pendulum with two knife edges.

Stop watch

Telescope

Meter Scale

Description:

It is heavy uniform rectangular metallic bar AB of about one meter long, having holes at a regular intervals along its length on either side of centre of gravity (CG) (fig1). The line joining centres of the holes are parallel to the edges and passing through the bar. The bar can be supported by hard steel knife edges , which can be fixed with each hole in turn. The knife edge is properly tightened by plyier so as to ensure that its sharp edge remains horizontal to the supporting platform and perpendicular to the length of the bar during its oscillations.

Theory: The working formula for determination of acceleration due to gravity by bar pendulum is given by,

g bar = 4π2 (

) graph

Where g : acceleration due to gravity L: equivalent length of pendulum T: time period of pendulum Procedure:

1. Find out the centre of gravity G of the pendulum (the midpoint of the rectangular bar i.e. the 10th hole of the supplied bar).

2. Fix two pins vertically on both ends of the bar pendulum with the help of wax or cello tape.

3. Suspend the bar about the knife edge from the hole nearest to the one end of the bar. Focus the telescope on the pin fixed at the other end of the bar pendulum. The

2

telescope may be place at a distance of 2 meters and its axis should be parallel to the ground (i.e. horizontal).

4. Make the pendulum swing in a vertical plane perpendicular to its horizontal axis of suspension. The angle of displacement or oscillation ( ) should be less than 40 .

5. Note down the time taken for 20 oscillations thrice (t1 , t2 , t3), then find out the

mean time taken for 20 oscillations i.e. t =

(t1 + t2 + t3) and calculate the time

period T (T=

).

6. Repeat the above procedures (iii) to (v) by suspending the bar from successive holes except the central hole. Record the distance (d) of the knife edge from the fixed end say A of the bar. For the holes close to CG the period gets longer and at CG it becomes infinity.

7. Invert the bar to allow similar operations for the holes on other side of CG and continue till last hole at the other end is reached. Distances are to be recorded from the same fixed end A.

8. Plot a graph with distances of knife edges from one fixed end A along X-axis and corresponding time periods along Y-axis A curve of the type shown in the fig.2 is obtained.

9. Draw three lines parallel to X-axis so as to cut these two symmetrical curves at four different points (A,B,D,E ), (A’,B’,D’,E’ ), (A”,B”,D”,E”) as shown in figure 2 . The distance between the asymmetric points on either side (AD or BE) or (A’D’ or B’E’) will evidently be equal to be lengths of equivalent simple pendulum (L). Hence find the equivalent lengths, i.e.

L1 = (AD+BE)/2 ,

L2 = (A’D’ + B’E’)/2 ,

L3 = (A”D”+ B”E”)/2

The time period (T) corresponding to these four points gives the value of this common time period T1 for the equivalent length L1, T2 for the equivalent length L2 & T3 for the equivalent length L3 .

3

Observation:

Table -1(A) (For determination of time period)

No. of holes

Distance of hole from C.G

(in cm)

Time for 20 oscillations (in seconds) Time period T (in sec)

T=

t1 t2 t3 Mean

t=

(t1+t2+t3)

1 5

2 10

3 15

4 20

5 25

6 30

7 35

8 40

9 45

Table -1(B) (For determination of time period)

No. of holes

Distance of hole from C.G

(in cm)

Time for 20 oscillations (in seconds) Time period T (in sec)

T=

t1 t2 t3 Mean

t=

(t1+t2+t3)

1 5

2 10

3 15

4 20

5 25

6 30

7 35

8 40

9 45

Table-2 (For determination of g)

Line no. Equivalent length L (in cm)

Timeperiod T (in sec)

in

Mean

in

I

II

III

4

Calculation:

gbar = 4π2 (

) graph = 4×(3.142)2×(

) = ............................

Percentage of Error:

Observed Value (gobs) = .......................

Standard Value (gstand) = 980

Percentage of error = |

|×100 =.......................%

Precautions:

1. The centre of gravity (CG) of the bar pendulum should be found with care. 2. The knife edge should be properly tightened and keep perpendicular to the levelling

plane. 3. The angle of oscillation should be small. 4. Keep the axis of the telescope parallel to the ground so as to avoid few earlier

swings.

Conclusion:

From the above calculation the value of acceleration due to gravity ‘g’ is found to be

...................................

.

5

Experiment No.—02


To determine the value of wavelength of LASER source using grating.

Apparatus required:

1. Diode LASER Source 2. Grating 3. Screen 4. Scale and base 5. Holder with stand Description:

LASER stands for Light Amplification by Stimulated Emission of Radiation. The emission of radiation in optical or microwave regions is of two types : 1) Spontaneous Emission 2) Stimulated Emission The chief advantages of using the LASER sources are : 1)These sources provide monochromatic beam of light as a result of spatial and temporal coherence. 2)The intensity of the beam is very high and it is extremely narrow and well-defined due to stimulated emission and amplification. Theory:

The LASER beam after passing through the grating will split into zero order ,first order and second order beam as shown below in figure.

Let xm : Distance between zero order spot and mth order spot (in mm)

D : Distance between screen and grating element.

(a+b) : Grating element

√ xm

f

6

From the above figure we can write,

Sin

√

From diffraction phenomena

( )

Or, = ( )

Or, = ( )

√

Putting the values of (a+b), m , xm. & f we can calculate the value of ‘ ’ . Procedure:

Place the LASER source on the holder and mount on the heavy base.

Hold the grating and screen in there respective holders and bases .

Place the grating between LASER source and screen as shown in the figure.

The laser beam after passing through the grating will split into zero order, 1st order, 2nd order

beam as shown in figure.

Mark the zero order ,1st order,2nd order spots on the screen and measure distances between

them.

Measure the distance between grating and screen.

Take the same procedure for different grating (at least 4 number of grating ).

Calculate the value of ‘ ’ for each grating and finally take the average.

Observation:

Table -1 (For determination of wavelength)

Sl. No.

Grating element

(a+b)

Order of Spectrum

(m)

(in cm)

(in cm)

Sin

√

‘ ’ (in A0)

Mean (in A0)

1 1

2 2

3 1

4 2

5 1

6 2

7 1

8 2

Percentage of Error: Observed Value ( obs) = ................................ A0

Standard Value ( stand) = ................................... A0


|×100 =...................%

7

Precautions:

i) The apparatus should be handled with care.

ii) The ruling surface of the grating should not be touched with bare hands.

iii) The laser light should not be seen directly with naked eyes.

Conclusion:

From the above experiment the value of wavelength ‘ ’ of laser light is found to be ................... A0.

8

Experiment No.—03


To determine the surface tension of water by capillary rise method.

Apparatus required:

Travelling microscope.

Beaker containing water

Capillary tube fitted with a stand

Needle

Magnifying glass

Thermometer

Description:

This experimental set up consists of at least three long capillary tubes of different diameter mounted on a glass strip G by rubber band B supported by a stand as shown in figure 1 (a).The lower ends of the capillary tubes are dipped in water taken by a beaker D and placed on an adjustable stand S2.A needle N is also fixed on the glass strip along the capillary tubes .Its height is adjusted such that the tip of the needle head touches the surface of water.

Theory:

The working formula for surface tension of water is given by,

(

)

=

Where T : Surface tension of liquid r : Radius of capillary tube g : Acceleration due to gravity ρ : Density of liquid h : Height of water columns in capillary tube

h’= h+

: Effective height of water column

9

Procedure:

1. Clean the capillary tube with some dilute caustic soda and wash out repeatedly with water . Don’t use distilled water ,as it is generally greasy .Dry the tubes with dry air.

2. Fill the gas beaker with water and note its temperature . Place the beaker on an adjustable stand.

3. Take at least three capillary tubes of different diameter. Mount them on the glass strip by a rubber band and set them vertical on the beaker . Water will rise in the capillary tubes. Fix the needle also on the glass strip parallel to the capillary tubes . Adjust its height such that the tip of the needle just touches the surface of water.

4. Focus the travelling microscope (TM) on one of the capillary tube by removing parallax between the cross wire and the image of the water column in the tube .Set the horizontal cross wire tangential to the meniscus of water at M in the tube. The meniscus of the water in the capillary tube will be inverted i.e. convex as shown in the figure 1(b) .Note the reading by vertical scale of TM (h1 say)

5. Move the travelling microscope along the horizontal scale and bring it in front of the second and third tube and repeat the step (iv) to note the reading by vertical scale of the microscope

6. Bring the travelling microscope in front of needle and lower it till the horizontal cross wire lies symmetrically between the tip of the needle and its image at N in the water as shown in figure 1(c).Note the reading on vertical scale of TM at N (h2 say). (h1-h2) gives the height’ h ‘ of the water column in the capillary tube.

7. Take out the capillary tubes from the rubber band and find the diameter at the bore of the tubes in two mutually perpendicular directions with the help of travelling microscope by taking the horizontal scale of the travelling microscope.

Observation:

Density of water in t0C=......................

Acceleration due to gravity (g) = 980

Least Count of the travelling microscope = ..........................

Table -1 (For determination of height ‘h’ of the water column in the capillary tube )

Tube No.

Reading in centimetres Height of the water column in the capillary tube h=h1-h2

(in cm)

Meniscus Base Needle head M.S.R V.S.R =

v.r × L.C T.S.R

(h1)=M.S.R+V.S.R M.S.R V.S.R =

v.r × L.C T.S.R

(h2)= M.S.R+V.S.R

1

2

3

10

Table-2 (For determination of radius ‘r’ of different capillary tube)

Tube no.

Reading in cm for Diff D = D1 D2

(in cm)

Reading in cm for Diff D

’ =

D3 D4

(in cm)

Diameter= ’

(in cm)

Radius ‘r’ (in cm)

L.H.S R.H.S Lower End Upper End M.S.R V.S.R =

v.r × L.C T.S.R (D1)= M.S.R+V.S.R

M.S.R V.S.R = v.r × L.C

T.S.R (D2)= M.S.R+V.S.R





1

2

3

11

Table-3 (For the determination of Surface Tension)

Tube No. h (in cm) r (in cm) h’= h+

(in cm) T =

(in

)

Mean ‘ T ’ (in

)

1

2

3


Observed Value (Tobs) = ..........................

Standard Value (Tstand) = ..........................


|×100 =.......................%

Precautions:

1. Tubes should be of uniform bore and water should rise freely into the tubes. 2. Tubes should be parallel to each other and vertical. 3. The surface of water should not be touched in hand. 4. The tip of the needle should just touch the water surface and not dip into it.

Conclusion:

From the above calculation the value surface tension is found to be ..........................

.

12

Experiment No.—04


To plot V-I characteristics graph of pn junction diode.

Apparatus Required:

D.C Regulated power supply 0-1.5 V D.C

D.C Regulated power supply 0-50 V D.C

P.N Junction diode

Two voltmeters (0-1.5 V) and (0-50 V) to measure forward and reverse voltage .

One millammeter (0-15 mA ) to measure forward current .

One micrometer (0- 100 μA) to measure reverse current.

Theory :

Volt-ampere characteristics or V-I characteristics of a p-n junction diode is the curve

between voltage across the junction and the circuit current.

Forward Biasing :

In forward biasing p-type is connected to positive

terminal and n-type is connected to negative

terminal .In forward biasing the potential barrier is

altogether eliminated and current starts flowing in

the circuit ,current increases sharply with increase

in forward voltage .The circuit diagram for forward

biasing is shown in figure 1.

Reverse Biasing :

In reverse biasing p-type is connected to

negative terminal and n-type is connected to

positive terminal .Potential barrier of the

junction is increased . Therefore the junction

resistance become very high and practically no

current flows through the circuit. However , a

very small current (of order μA) flows in the

circuit with reverse bias, which is called

reverse current and is due to minority carriers.

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If reverse voltage is increased continuously ,the kinetic energy of the electrons become high

enough to knock out the electrons from the semiconductor atoms. At this stage breakdown

of the junction occurs, characterised by a sudden rise of reverse current. The circuit diagram

for reverse bias is shown in figure 2 . The V-I characteristic curve is shown below

Procedure:

1. Do the connection according to the circuit diagrams.

2. Apply different voltages to the pn junction and note the corresponding reading of

the currents.

3. For forward biasing use the milliammeter and for reverse biasing use microammeter

scale.

4. Plot a graph for applied voltage and corresponding currents for both the cases.

Observation:

No.of obs. For Forward Biasing For Reverse Biasing

VoltageVF

(in volts) Current IF

(in mA) Voltage VR (in volts)

Current IR

(in μA)

1

2

3

4

5

6

7

8

9

10

Precautions:

Connections should be made carefully.

Voltages applied should be well within the safety limit of given diode.

14

Experiment No.—05


To determine the value of modulus of rigidity of the material of a rod by static method using vertical pattern apparatus (Barton’s apparatus) . Apparatus required:

Barton’s apparatus

Vernier callipers

Screw gauge

Slotted weights

Meter scale

Spirit level Description:

Upper end of a long thin rod or thick wire fixed tightly to a heavy metallic frame and lower end to a heavy metallic cylinder. A thread leave diametrically opposite sides of the cylinder ,tangentially passes over two frictionless pulleys that carry two pans of equal weights at their free ends . By placing equal weights on the pans a couple can be applied to produce a twist in the rod about its own axis. The twists produced at three different points of the rod are measured by either single or double ended pointers which moves freely over the circular scales graduated in degrees respectively .The pointers along with the respective scales can be clamped at any desired points.

Theory:

The working formula for modulus of rigidity of the material of rod is given by,

η=

(

) =

(

) graph

Where η : modulus of rigidity of the given material of the rod G : acceleration due to gravity l : length of the rod between two consecutive scales D : diameter of the cylinder r : radius of the rod M : mass suspended in the hanger θ : angle of twist

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Procedure:

1. Measure the diameter of the rod in two mutually perpendicular directions at several places with the help of screw gauge, hence find mean radius (r) of the rod.

2. Find the diameter (D) of the cylinder by vernier callipers.

3. Measure the length (L) of the rod ‘AB’. Place the 1st scale at a distance of ⁄ , the

2nd scale at a distance of ⁄ and the third scale at a distance of ⁄ from the fixed

end ‘A’ of the rod ,so that the distance between any two consecutive scale is

⁄

4. Adjust the pointers for zero weight on the hanger so that they read zero on the

respective circular scales.

5. Place gently 1kg slotted weight on both the hanger. Wait for few minutes and note down the reading of the three pointers. Let the readings be θ1, θ2 and θ3 for the 1st, 2nd and 3rd pointer respectively.

6. Increase the load in steps of 1kg till the maximum permissible load is reached. Note down the reading of the pointers on the scale at each step.

7. Decrease the load in the steps of 1kg till the zero load is reached .Note down the reading of the pointers on the scales at each step. Let it be θ4,θ5 and θ6 respectively.

Find the mean of loading and unloading for each scale. Let it be θ7=

,θ8=

,θ9=

. Find the difference between (θ8 and θ7) & (θ9 and θ8). Let them be

θ10 and θ11 respectively. Find out the mean θ10 and θ11 .Let it be ‘θ’ the angle of twist.

8. Plot a graph taking load (M) along X-axis verses angle of twist(θ) along Y-axis. The nature of the graph is a straight line as shown in figure 2. Reciprocal slope of the

straight line gives (

).

Observation:

Length of the rod ‘AB’ i.e. , L=...............cm

Distance of the 1st scale from fixed end ‘A’ i.e. , l1= ...................cm

Distance of the 2nd scale from fixed end ‘A’ i.e. , l2= ...................cm

Distance of the 3rd scale from fixed end ‘A’ i.e. , l3= ...................cm

Distance between two consecutive scales = l2 - l1 = l3 – l2 =...................cm

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Table -1 (For determination of radius ‘r’ of the rod by screw gauge )

No. of obs

Pitch in (P) in cm

L.C (in cm)

I.C.S.R (I)

No. of complete rotation (n)

F.C.S.R (F)

Diff (d) =I F

P.S.R =P×n (in cm)

C.S.R= d × L.C (in cm)

TSR= PSR+CSR (in cm)

Mean diameter (in cm)

Mean radius ‘r’ (in cm)

1

2

3

4

5

6

Table-2 (For determination of diameter ‘D’ of the cylinder by slide callipers.)

No.of obs

L.C (in cm)

M.S.R (in cm)

V.C V.S.R= V.C×L.C (in cm)

TSR=MSR+VSR (in cm)

Mean diameter ‘D’ (in cm)

1

2

3

4

5

17

Table-3 (For determination of angle of twist ‘θ’ by Barton’s Apparatus)

Calculation:

Substituting the values of g,l,r,D and (

) in the working formula to obtain the value of modulus of rigidity of the material of the rod

η=

(

) =

( )( ) ( )

( ) ( ) ( ) graph = ..........................................


Observed Value (ηobs) = .................................................

Standard Value (ηstand) = .................................................


| × 100 =........................%

No.of obs

Load (in gm)

Angle of rotation(in degree) For loading

Angle of rotation(in degree) For unloading

θ7=

(in deg)

θ8=

(in deg)

θ9=

(in deg)

θ10=θ8 – θ7

(in deg)

θ11=θ9 – θ8

(in deg)

Angle of

twist θ=

θ1 θ2 θ3 θ4 θ5 θ6

1 0

2 500

3 1000

4 1500

5 2000

6

2500

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Precautions:

Both the pulley & pans should be of same height from the ground

Pulley should be frictionless.

Load should be increased or decreased gradually and gently & should never exceed the maximum permissible limit.

As the radius of the rod occurs in forth power ,it should be measured accurately in two mutually perpendicular directions.

Conclusion:

From the above calculation the rigidity modulus ‘η’ of the given material is found to be

........................

.

19

Experiment No.—06


To determine the wavelength of the given source of light by Newton’s ring apparatus.

Apparatus required:

Sodium lamp with transformer

Newton’s ring apparatus fitted with travelling microscope

Convex lens

Spherometer

Magnifying glass

Description: It consists of an optically plane glass plate and a planoconvex lens of large radius of curvature. The curved surface of lens is in contact with the glass plate and both are enclosed in circular frame. Air film of increased thickness is formed. Thickness is zero at the point of contact and goes on increasing towards the periphery of the lens. The thickness of the film along a circle with the point of contact as the centre is same. There is another optically plane glass plate whose angle of inclination can be changed. It is kept at 450 with the horizontal. In an optical arrangement of Newton’s ring, light from a monochromatic source (sodium vapour lamp) is allowed to fall on a convex lens through a broad slit which renders into a nearly parallel beam. These beams fall on the glass plate and reflected from the lower surface. The reflected parallel beam is made incident on the air film vertically. A part of the incident ray is reflected from

the top surface of the film (glass-air boundary) and goes as ray ‘ 1 ‘without phase reversal. The other part is reflected along the air film and incident at the plane glass plate and get reflected and goes out as ray ‘ 2 ‘ with phase reversal of π as shown in fig.3 .Ray 1 and 2 satisfies the condition of interference and produce concentric circular fringes which is observed through travelling microscope.

20

Theory: The central ring is dark in the experiment. This is because of the fact that ,when light is

reflected at a denser medium, a phase change of π or a path change of

is introduced. If ‘R’

is the radius of curvature of the curved surface of the lens and λ is the wavelength of the light used ,then the diameter of the “nth ” dark ring is given by

= 4nλR .................................................(1) Similarly the diameter of (n+m)th dark ring is given by

= 4(n+m)λR ....................................(2) From (1) & (2) , the wavelength of the light is given by

Where λ : wavelength of the light source Dn+m : diameter of (n+m)th ring Dn : diameter of nth ring m : number of ring R : radius of curvature of the curved surface of the lens in contact with glass plate Procedure:

1. Clean the surface of glass plate and the lens with a neat and clean cloth. Place both of them in the circular frame, so that curved surface of the lens is in contact with the plate. Also clean the other glass plate and set it ,so that it is inclined at an angle of 450 .

2. Place the whole arrangement near a sodium lamp and adjust the slit of the lamp , so that the slit and the centre of the plate are at same height.

3. Insert a convex lens in between slit and the plate so that slit is at the focus of the lens and parallel rays are incident on the plate and see that the rays after reflection fall normally on the lens surface.

4. Find pitch and least count of the travelling microscope. If needed , level the microscope . Set the microscope tube in vertical position and adjust the position of

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microscope so that point of contact of the lens and plate is just below the centre of the objective of the microscope.

5. Focus the microscope, so that alternate dark and bright rings are clearly visible. Slightly move the lens to bring the centre of the fringes to come in view. (Newton’s rings would be visible at the centre of the lens even to the naked eye. )

6. Adjust the position of the microscope, till the point of intersection of the cross wires lies at the centre of the ring system and one of the cross wires is at right angle to the horizontal scale

7. Slide the microscope with the help of fine adjustment screw to one side, say left, till the crosswire lies tangentially at the centre, to a certain dark ring (say 20th). Note the reading of the microscope.

8. Slide the microscope backward with the slow motion screw and take readings, when the cross wire lies tangentially at the centre to 30th, 29th ,28th, 27th,.............rings and go upto 1st ring. Note the reading of microscope at each stage.

9. Keep on sliding the microscope in the same direction, till cross wire lies tangentially at the centre of the 1st ring on the right side. Note the microscope reading. Continue moving the microscope and take readings of continuously upto 30th ring.

10. Record the observations in tabular form. The difference between reading of microscope for a particular order from left hand (A) and right hand gives the diameter of all the rings. Knowing the diameters calculate their squares.

11. Find the radius of curvature (R) of the curved surface of the lens in contact with the glass plate with the help of spherometer.

12. Plot a graph by taking order of the ring (n) along X-axis and (Diameter)2 along Y-axis. The slope of the curve will give

.

Observation:

Radius of curvature of the curved surface of the plano convex lens = ............cm

Pitch = ...................................

L.C = ..................................

22

Table -1 (For determination of diameter of the ring )

Sl.no Ring no.

I.C.S.R (I)

N.C.R F.C.S.R (F)

P.S.R = ( NCR × Pitch ) (in cm)

Difference (I~F)

C.S.R = (I~F)×L.C (in cm)

Total = P.S.R

+C.S.R (in cm)

Mean ‘d2’

(in cm2)

1 n+20

2 n+18

3 n+16

4 n+14

5 n+12

6 n+10

7 n+8

8 n+6

9 n+4

10 n+2

Calculation:

Putting the value of

from the graph and ‘R‘ in the working formula λ can be

calculated by using the formula

λ =

(

)

(

)

= ............................... A0


Observed Value (λobs) = ....................... A0

Standard Value (λstand) = ...................... A0


| × 100 =.......................%

Precautions:

1. The lens and the glass plate should be thoroughly cleaned. The lens should have large radius of curvature.

2. The glass plate should be inclined at an angle of 450 so that light is incident normally on the plano-convex lens.

3. The point of intersection of the cross wires should always be placed tangentially to the rings.

4. The microscope should should always be moved in the same direction to avoid error due to backlash error.

5. The radius of curvature and diameter of the ring should be measured accurately.

Conclusion:

From the above experiment the value of ‘ λ ’ is found to be ........................... A0.

23

Experiment No.—07


To determine the Young’s modulus of the material of a given wire by Searle’s method.

Apparatus required:

Searle’s apparatus

Long wires(two of equal lengths) of given materials

Screw gauge

Meter scale

Half kilogram slotted weights and

Hanger Description:

It consists of two metallic frames held together by parallel bars . The metallic frames are suspended from a rigid support with the help of two identical wires of same material ,length and diameter. One wire is experimental wire (test wire) and the other is compensating wire (control wire) . The compensating wire carries a constant weight to keep the wire stretched or kinks free. The experimental wire carries a hanger with dead load in which slotted weights can be put to produce extension .The frame carries a spirit level one of which is tightly fixed in one frame and other end rests on the tip of

the micrometer screw attached to the other frame . Micrometer screw is adjusted so that the bubble of the spirit level stands exactly at the centre of two marks (horizontal position). On applying load, the experimental wire is elongated , one of the frame gets lowered and the bubble of the spirit level gets disturbed (move towards up i.e towards compensating wire).The micrometer screw is raised by rotation to bring the bubble of spirit level back to original position. The amount of rotation of the micrometer screw gives the amount of the elongation of the wire. Theory:

The working formula for determination of Young’s modulus ‘Y’ of the wire by Searle’s method is given by,

(

)

(

)

Where L : original length of the wire g : acceleration due to gravity d : diameter of the given wire M : Load applied on the hanger : elongation produced in the experimental wire

24

Procedure: 1. Measure the diameter of the experimental wire by the help of a screw gauge at various

positions(at last five different places) of the wire. Measure the diameter in two directions at right angle to each other at each position of the wire .Determine the mean value of the

diameter ‘d ’ and hence the cross sectional area =

.

2. Determine the breaking load of the given wire by multiplying the cross-sectional area with the breaking stress (supplied) of the material of the wire. (The limiting load put on the hanger should always be kept below half of this breaking load during the experiment. )

3. Measure the length of the wire between the upper fixed end & lower fixed end of the experimental wire, thrice by a meter scale & calculate the mean of the three values which gives the length ‘L ‘ of the wire.

4. Put the limiting load on the hanger for few minutes to keep the wire taut. Remove greater part of the limiting load from the hanger , leaving a certain portion known as dead load which is sufficient to keep the wire free from any kink.

5. Bring the bubble of the spirit level to the centre by rotating the micrometer screw in one direction (anti cock wise when loading and clock wise when unloading).Take the circular scale reading which is the initial circular scale reading (R1) or circular scale reading at the beginning of the step.

6. Add identical load (

) and wait for a few minutes, then see the position of the bubble .

Repeat the procedure to bring the bubble to the centre. Take the circular scale reading which is the final circular scale reading (R2) or circular scale reading at the end of the step.

7. Repeat the procedure (5) & (6) for load of 1kg, 1.5kg, 2kg etc. It should be noted that initial reading of any observation is same as the final reading of its previous observation.

8. Unload the experimental wire by same steps as before and repeat the procedure (5),(6) &(7) at each step until it comes to zero.

9. Calculate the total number of circular scale division (x1 or x2) rotated for each step i.e. the difference of R1 or R2 .

For loading difference x1 = R2 - R1 if R2 > R1 = (100 + R2) – R1 if R2 < R1 For unloading difference x2 = R1 – R2 if R1 > R2 = (100 + R1) – R2 if R1 < R2

10. Take the mean difference i.e. x =

(x1 + x2) for each step . Multiply the mean difference (x)

with least count (LC) which gives mean elongation of that step. 11. Determine total elongation for each additional load by adding the mean elongation for each

step. 12. Plot a graph by taking load (M) along X-axis and total elongation ( ) along Y-axis. The nature

of the graph is a straight line. Determine the slope of the curve, i.e (

).

load

25

Observation:

Length of the wire L = ..................cm.

Pitch of the screw gauge = ................cm.

Least count of the screw gauge = ..............cm.

Least count of the micrometer screw =....................cm.

Table -1 (For determination of diameter of the wire by screw gauge)

No. of

obs

I.C.S.R (I)

N.C.R F.C.S.R (F)

P.S.R = (NCR× Pitch)

(in cm)

Difference (I~F)

C.S.R = (I~F)×L.C (in cm)

Total = P.S.R +C.S.R

(in cm)

Mean ‘d’ (in cm)

1

2

3

4

5

Table -2 (For determination of elongation of wire)

No. of obs.

Load (in

gram)

Load Increasing Load decreasing Mean elongation

x=

(x1+ x2)

×L.C (in cm)

Total elongation ‘l ‘ (in cm)

R1

R2

Diff.

= x1 –x2

R1

R2

Diff.

= x1 –x2

1 0 a = a

2 500 b = a+b

3 1000 c = a+b+c

4 1500 d = a+b+c+d

5 2000 e = a+b+c+d+e

6 2500 f = a+b+c+d+e+f

Calculation:

Putting the value of (

) from the graph and L & d ,the value of Young’s modulus “Y” can

be calculated by using the formula

(

)

= ........................

26


Observed Value (Yobs) = .......................

Standard Value (Ystand) = ........................


|×100 =.......................%

Precautions:

1. Remove the kinks in the wire as much as possible by adding suitable dead load. 2. The diameter of the wire should determined at several places. 3. Don’t load the wire beyond the maximum permissible load selected form

breaking load data. 4. Micrometer screw should be rotated only in one direction in order to avoid back

lash error, while loading and unloading. 5. In all cases both for loading and unloading wait for a couple of minutes before

noting the reading of the micrometer. 6. The wire should be loaded or unloaded gently. 7. If the bubble of the spirit level is not exactly touching the two marks then any

one side of the bubble should touch the mark tangentially and this has to be taken as reference through out the experiment.

Conclusion:

From the above experiment the value of ‘ Y ’ is found to be .............................

.

27

Experiment No.—08


To plot the input and output characteristic curves for a bipolar junction transistor (B.J.T).

Apparatus required:

A transistor mounted on a board with three terminals marked e (emitter), b (base) & c (collector).

Two voltmeters of range (0-1 V) & (0-10 V) respectively.

A micro ammeter(0-200 μA )

A milli ammeter (0-10 mA) Description :

The whole circuit diagram shown above may be divided into two parts :- (i) emitter-base circuit or input circuit. (ii) emitter- collector circuit or output circuit. The emitter supplies the majority charge carriers for transistor current flow. The collector collect the current for circuit operation and the base controls the passage of current from the emitter to the collector. The input circuit is forward bias and the output circuit is reverse biased. Theory:

The emitter which is connected to positive terminal injects positive holes into n-type base region and these holes are drawn through the base region towards the collector by the negative field of the later. A few holes neutralize with electrons in the electron rich base layer. But the base layer is extremely thin and majorities of holes diffuse to the collector region and as a result collector current is increased. From the observations of variation in voltage and current, input and output characteristics can be studied. Input characteristics curves are plotted between base-emitter voltage (VBE) & base current (IB) at constant collector-emitter voltage (VCE). Output characteristics curves are plotted between collector-emitter voltage (VCE) & collector current ( Ic ) at constant base current ( IB ).

28

Procedure:

Make the circuit connections according to the circuit diagram in case of a PNP transistor.

For input characteristics keep VCE constant at a particular value say 2 volt. Note VBE & IB increase VBE ,in steps of 1 volt and note the corresponding values of IB in μ A . Plot a graph between VBE & IB at constant VCE.

Repeat the above step for other values of VCE say 2V, 4V, 6V to get family of input characteristics curves.

For output characteristics keep IB constant at a particular value say 20 μ A. Note VCE & IC .Increase VCE in steps of 0.5 V and note the corresponding values of IC in mA. Plot a graph between VCE ~ IC at constant IB.

Repeat the above step for other values of IB say 40, 60, 80 μ A to get family of output characteristic curves as shown below.

Observation:

Table -1 (For Input characteristics)

Sl. No VCE = 0 volt VCE = 2 volt VCE = 4 volt VCE = 6 volt

VBE (V) IB ( μA) VBE (V) IB ( μA) VBE (V) IB ( μA) VBE (V) IB ( μA)

1

2

3

4

5

6

7

8

9

10

11

29

Table -2 (For Output characteristics )

Sl. No IB = 20 μA IB = 40 μA IB = 60 μA IB = 80 μA

VCE (V) IC ( mA) VCE (V) IC ( mA) VCE (V) IC ( mA) VCE (V) IC ( mA)

1

2

3

4

5

6

7

8

9

10

11

Precautions:

Care should be taken that collector voltage should remain constant during the particular set of readings.

Do not exceed the ratings for the currents to protect the transistor from damage.

30

Experiment No.—09


To determine the grating element of a plane diffraction grating.

Apparatus required:

Spectrometer

Prism

Spirit level

Plane diffraction grating

Sodium vapour lamp

Description: (A) Spectrometer: A spectrometer consists mainly of the following three parts – 1. Collimator 2. Prism table & 3. Telescope 1. Collimator– This is a horizontal tube at one end of which there is a convex lens while at the other end there is an adjustable narrow slit which can be taken in or out of the tube by rack and pinion arrangement. The axis of the collimator should be horizontal and perpendicular to the vertical axis about which the prism table can rotate. The collimator can be tilted by screws below it. 2. Prism Table – It is a small circular table mounted on a vertical stand so that it can be raised or lowered or can be clamped at any position by the screws. It is provided with three levelling screws. On the surface of the table there are straight lines marked parallel and perpendicular to the line joining screws. There are also concentric circles, the common centre of which coincides with the centre of the table. The table can be rotated about a vertical axis of the instrument. The angle of rotation of the prism table can be recorded by two verniers V1 & V2 which can rotate with the table over a circular scale (usually graduated in half degrees). The table can be fixed by a screw and a smaller rotation can be imparted to it by a tangent screw. 3. Telescope – It is a small astronomical telescope provided with a compound eye-piece and a cross-wire. The axis of the telescope should also be horizontal and perpendicular to the vertical axis of rotation of the prism table. It can be rotated about the vertical axis of the instrument and the angle of rotation can be recorded with the help of two verniers V1 & V2 from scale (usually graduated in half degrees) which moves with the rotation of the telescope. For recording the readings of the scale, these two verniers are kept at 1800 apart. The telescope can also be tilted by screws. The whole apparatus is supported on a base, provided with three levelling screws. The telescope can be fixed by a screw while a slow motion can be imparted by a tangent screw.

31

(B) Grating : A diffraction grating is an arrangement which is equivalent in its action to a number of parallel and equidistant slits of same width. The transmission gratings are fabricated of a transparent solid material.The parallel rulings are inscribed on the surface with the help of a diamond scriber. The rulings made by the scriber have a rough surface which scatters the incident ray hence opaque to light. The intervals between the rulings remain transparent and play the part of slits. The width of transparent part ‘a’ and width of the ruling i.e. rough surface is ‘ b’ the (a+b) is called grating element. The number of lines

ruled per cm N is given by ( )⁄ .

Theory: When a parallel beam of light monochromatic light of wavelength λ is incident normally on a grating ,the light after diffraction gives rise to principal maxima in certain directions given by ( ) Where a : width of the transparent part b : width of the ruling surface (a+b) : grating element θn : angle of diffraction for the nth order maxima If θ1 and θ2 be the angles of diffraction in the first and the second order spectra respectively, then

( )

32

Procedure:

A. Spectrometer Adjustment: 1. Make the base of the spectrometer horizontal by adjusting the levelling

screws provided with the base using spirit level. 2. Adjust the eye-piece of the telescope until the cross-wires are clearly

focussed. Direct the telescope to a distant object and focus thee telescope until the object is seen without parallax.

3. Illuminate the slit of the collimator with sodium light. Turn the telescope to keep its axis in, line with the axis of the collimator. Seeing through the telescope adjust the distance of the slit from the collimating lens until sharp images of the illuminated slit is observed. By rotating the screw decrease the width of the slit to get a well defined narrow illuminated line.

4. Keep the spirit level on the prism table parallel to the line joining the two levelling screws and adjust until the air bubble of the spirit level comes to the centre. Then turn the spirit level perpendicular to this position and adjust the third screw to bring the air bubble at the centre.

5. Rotate the telescope until its axis makes an angle of about 1200 with the axis of the collimator. Place a spectrometer prism having no ground surface at the centre of the prism table. By rotating the prism table images of the slit formed by partial reflection at the two faces of the prism can be seen through the telescope. Adjust the levelling screws of the prism table such that, the image formed by each face of the prism is at the centre of the field of view of the telescope band extends equally to the upper and lower part and remains vertical. After optical levelling is completed the spectrometer is ready for doing experiment.

B. Grating Adjustment: 1. Bring the telescope in line with the collimator to have image of the slit on

the vertical crosswire. If necessary, clamp the telescope and give it slow motion for finer adjustment.

2. Take the reading on the scale. Read both the verniers. Call these readings θ and θ1 respectively.

3. Fix the given grating on the turn table. Now turn the telescope from its initial position through exactly 900, so that the new readings are θ+900 and θ1+900. Clamp the telescope. This now ensure that the collimator and the telescope tubes are at right angles to each other.

4. Rotate the prism table carrying the grating in such way that the image of the slit after reflection at its surface falls on the telescope. Rotating he prism table very slowly, the reflected image is made to coincide exactly with the vertical cross wire. In this position, the angle of incidence of light on the grating is 450.The reading of the position of the prism table is noted down.

5. Rotate the prism table from the above position through 450 more so that the grating plane becomes normal to the direction of light. The prism table is locked in this position. This is the normal incidence position.

6. Turn the telescope to catch the 1st order spectrum and see that again the image comes symmetrically on the intersection of the cross wire. If it is not

33

so, adjust one of the levelling screws at right angles to the grating to achieve this.

C. Measurement of 2θ: 1. Substitute the source of light, the wavelength of which is to be determined.

See that except for the telescope, all other screws are properly clamped. 2. Adjust the telescope on the first order spectrum of right hand side (RHS).

Clamp it, and by fine adjustment screw bring the intersection of the cross wire exactly in the middle of the spectrum line.

3. Note the readings (MSR, VC) on both the verniers V1 and V2. Normally the difference in their readings would be approximately 1800.

4. Now turn the telescope to catch the first order spectrum of the same line on the left hand side (LHS), and take readings (MSR, VC) of the two verniers V1’ and V2’.

5. The diff between two readings of the same verniers i.e. , (V1~V1’ ) & (V2~V2’) gives double the angle of diffraction 2θx and 2θy which gives 2θ1, hence we can calculate θ1.

6. Determine the grating element by substituting the value of and θ1 in the working formula.

7. Repeat the above procedure for the second order spectra and calculate θ2. Finally calculate the mean of the grating element.

Observation:

Wave length of the given monochromatic source of light i.e. sodium light = 5893A0 Least count of the spectrometer =........................

34

Table -1 (For determination of angle of diffraction)

Order of the

spectrum

RHS reading in degree, minute & second LHS reading in degree, minute & second 2θx = a-c (in

deg)

2θy = b-d (in

deg)

2θ =

(in deg)

θ (in

deg)

(a+b) in cm V1 V2 V1 ‘ V2’

M.S.R V.S.R T.S.R (a)

M.S.R V.S.R T.S.R (b)

M.S.R V.S.R T.S.R (c)

M.S.R V.S.R T.S.R (d)

Calculation:

The grating element of the given plane diffraction grating = .........................................cm


Observed Value (a+b)obs = ......................

Standard Value (a+b)stand = .....................

Percentage of error = |( ) ( )

( ) | × 100 =.......................%

35

Precautions:

The optical adjustment of the spectrometer and the grating must be done correctly.

The collimator slit must be strongly illuminated by the source. The slit should be as narrow as possible.

Remember that while recording your observations, you do not make any confusion in noting readings of V1 and V2 & V1’ and V2’.

The grating surface must be normal to the incident rays.

The grating is so adjusted that its ruled surface faces the telescope. Hold the grating at its side. Do not touch the face of the grating , otherwise it will get damaged.

Conclusion:

From the above experiment the value of grating element of the supplied grating is found to be ..............................cm.

36

Experiment No.—10


To verify the laws of transverse vibration of stretched string by using a sonometer .

Apparatus required:

Sonometer

Tuning forks

Rubber hammer

Wires

A hanger

Half kilogram weights

Wooden blocks

Wedges

Description:

A Sonometer consists of a hollow wooden box about one metre with bridges A and B fixed at two ends on the top surface .A uniform wire is stretched over the two bridges, one end of the

wire being fixed to the nail at one end of the box. The other passes over a smooth pulley and carries a weight hanger on which weights are placed. M and N are two movable bridges in between the fixed bridges A and B. By changing their position , the length of the vibrating segment of the wire can be altered.

Theory:

When a string fixed at two points cm apart and stretched with a tension dynes, is set to vibrate , the frequency of vibrations , n is given by

n =

√

Where is the mass of unit length of the string in gm per cm. Here a thin wire is taken as a string.

The laws of transverse vibration of string are contained in the above expression. The frequency is

i) inversely proportional to the length of the vibrating segment ,if and are constant

ii) directly proportional to the square root of the tension , if and are constant.

iii) inversely proportional to the square root of , if and are constant.

37

Procedure:

1. To verify the law of length:

Place two sharp wedges under the wire of the sonometer . Load the hanger with a

load of about 2 kilogram including hanger .See that the wire is properly stretched

between the wedges and touches both of them. Wooden blocks may be placed

under the wedges if necessary. See that there are no kinks in the wire.

Bring two wedges close to each other. Cut a piece of paper (rider) about 2 cm long

and about 2mm wide. Fold it into “V” shape .Place this paper on the wire between

wedges.

Take the tuning fork of the frequency provided. Strike gently at the end of one its

prongs with a rubber hammer to set it into vibrations. Press the stem against the

sonometer board keeping the tuning fork vertical .At the same time move one of the

wedges outwards very slowly till the rider ,kept always on the wire ,midway

between the wedges begins flutter. Strike the tuning fork again and again during

this adjustment and press against the board to keep it vibrating. At a certain fixed

distance between the wedges the rider flies off .The wire now vibrates in resonance

with the frequency of the tuning fork.

Measure the length of the wire between the wedges by a metre rod .Increase the

distance between the wedges by a few centimetres . Again adjust the apparatus to

repeat the procedure with another tuning fork.

Keeping the tension fixed find the length of the wire which vibrates in resonance

with each of the three tuning forks.

2. To verify the law of tension:

Take a load of 2 kg including hanger. Obtain the length of the wire which vibrates in

resonance with one of the tuning forks as done while verifying law of length.

Increase the load by 500 grams and repeat the experiment with the same tuning

fork. Similarly repeat the experiment with three different loads.

It is not possible to find directly the frequency with which the same length of wire

will vibrate under different loads. If 1 and 2 are the lengths of the wire vibrating

with the same frequency n1 under the loads T1 and T2 respectively ,then the

frequency of sound n2 produced by same length 1 under the load T2 can be

calculated by using the law of length as

n1 1 = n2 2

or,

38

Observation:

Table -1 (For verification of law of length)

Sl.no Frequency (n)

(in hertz)

Distance between wedges (in cm) n×

increasing decreasing mean

1

2

3

Table -2 (For verification of law of tension)

Frequency of the tuning fork n1 =.........................Hz

Sl.no Tension (in Newton)

w×9.8

Length of the wire giving frequency n1 (in metres)

Calculated frequency

for a length 1

√

increasing decreasing mean

1

2

3

Precautions:

The wire should be of a uniform area of cross section, free from kinks and should be tight.

The tuning fork should be pressed gently on the sonometer board.

The weight of the hanger should always be included in the load.

The pulley should be free from friction.

Conclusion:

From the above experiment the laws of transverse vibrations for a stretched string are verified.

lab manual for btech students

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