EP Physics Lab Manuals

8/2/2019 EP Physics Lab Manuals

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ENGINEERING PHYSICS LABList of experiments

(Any twelve experiments compulsory)

1) Newtons Rings - Radius of curvature of Plano convex lens.

2) Determination of wavelength of a source - Diffraction Grating.

3) Dispersive power of the material of a prism - Spectrometer

4) Study the characteristics of LED and LASER sources.

5) Time constant of an R-C circuit.

6) L-C-R Circuit.

7) Energy gap pf a material of p-n junction.

8) Torsional Pendulum.

9) Meldes experiment - Transverse and longitudinal modes.

10) Bending losses of fibers.

11) Evaluation of numerical aperture of given fiber.

12) Magnetic field along the axis of current carrying coil Stewart and Gees

method.

13) Thermo electric effect See beck effect and Peltier effect.

14) Study the characteristics of p-i-n and avalanche photodiode detectors.

15) Single slit diffraction using laser.


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1. NEWTONS RINGS

AIM: -To Determine (a) The wavelength of sodium vapour light(b) The radius of curvature of the surface of the lens, by forming Newtons

rings

APPARATUS: - Newtons ring set & plane mirror.

THEORY: - Let R = Radium of curvature of the surface of the lens In conduct withthe glass plate (P1)

D1=Diameter of the n1th ring D2= Diameter of the n2th ringThen, the relation gives the wavelength of the light radiation:

(D22-D1

2)

= --------------- -------------------- (1)

4R (n2-n1)The radius of curvature of the lens is determined with a spherometer. The values of

D1 and D2are very small and occur to the second power in equation (1). Hence they are tobe measured carefully with the traveling microscope. Care is to be taken in moving themicroscope to travel in a direction without moving back and forth while taking readings.This is very essential since the variation in the diameter of the rings is in the seconddecimal place and any back and forth movement of the microscope will result in wrongreadings .it can be seen from equation (1) that the diameter of the rings increase with theincrease in the radius of curvature R of the lens. With a lens of radius of curvature ofabout 100 cm, the rings formed will be convenient for measurement. Hence, it is desirableto select a Plano convex lens of long focal length for forming rings.

PROCEDURE: -

The apparatus consists of a light source. The light from it is rendered parallel bymeans of a convex lens. The parallel rays are incident on a plane glass plate through themagnifying glass inclined at 45o to the path of incident rays. Alternate bright & dark ringsare observed through a traveling microscope.The point of intersection of cross wires in themicroscope is brought to the center of ring system, if necessary, tuning the cross wiressuch that one of them is perpendicular to the line of travel of the microscope. The wiremay be set tangential to any one ring; & starting from the center of the ring system, themicroscope is moved on to one side, say left, across the field of view counting the number

of rings. After passing beyond 25th

ring, the direction of motion of the microscope isreversed and the cross wire is set at the 20th dark ring, tangential to it. The reading on themicroscope scale is noted. Similarly, the readings with the cross-wires set on 18th, 16th,14th,2nd dark rings are noted. The microscope is moved in the same direction and thereadings corresponding to the 2nd, 4th, 6th. dark ring on the right side are noted.Readings are to be taken with the microscope moving in one & the same direction toavoid errors due to backlash. The observations are recorded in table 1. The Plano convexlens is taken out from the traveling microscope and the radius of curvature is determinedby a spherometer. A graph is drawn with the number of rings as abscissa (X-axis) and thesquare of diameter of the ring as ordinate (Y-axis). The nature of the graph will be straightline as shown in the fig. From graph the values of D12 and D22 corresponding to two

number n1 and n2 are noted. Using these values in equation (1) the wavelength of thesource is calculated. To determine the radius of curvature, R, of the lens; the wavelength, of the source used is to be taken standard tables.


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Arrangement of Newtons Ring

OBSERVATIONS: -Radius of curvature of the lens in contact with glass R = cm.

TABULAR COLUMN:-

S.No ofrings n

Microscope ReadingLeft side L1 Ride sideR1

Diameter of nth

ring (L1 ~ R1)Square ofdiameter of thering.

2. DIFFRACTION GRATING NORMAL INCIDENCE &MINIMUM

DEVATION

AIM: -To determine the wavelength of a given light radiation using diffraction grating with(a) Normal incidence and (b) Minimum deviation method.

APPARATUS: - Spectrometer, Sodium Vapour Lamp & Grating.DESCRIPTION: -

A plane diffraction grating consists of a parallel-sided glass plate with equidistant parallellines drawn very closely on it by means of a diamond point. 15,000 lines per inch or (15,000/ 25.u)lines per cm are drawn on the grating. Such gratings are known as original gratings. Butthegratings used in the laboratory are exact replicas of the original gratings on a celluloid film. TheCelluloid film is fixed over as optically plane glass plate. Care should be taken while handling theGrating. It should be handled by the edge of the plate.THEORY: -

A parallel beam of monochromatic light from the collimator of a spectrometer is made to fallnormally on a plane diffraction grating erected vertically on the prism table. The telescope initiallyin line with the collimator is slowly turned to one side. A line spectrum will be noticed and onfurther turning the telescope the line spectrum will again be noticed. While the former is called thefirst order spectrum, the later is called the second order spectrum. On further rotating thetelescope, the third order spectrum may also be noticed, depending on the quality of the grating.But the number of orders of spectra that can be observed with a given grating limited. With thelight normally incident on a grating having N lines per cm, if is the angle of diffraction of a radiation of wavelength in the n thorder spectrum, then

n N= Sin

Or =Sin/nNOr = (Sin x 2.54)/( n x 15,000) --------(1)

Knowing and n, the wavelength of light radiation is calculated using equation (1) for the normalincidence method. Again when a parallel beam of monochromatic light is incident upon a grating is


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diffracted in such a way that the angle of deviation is minimum; then the wavelength ( ) of the radiation is given by:

= 2Sin (D/2)/ Nn

= 2 x 2.54 x Sin (D/2)/ 15,000----------(2)

Where D is the angle of minimum deviation and n is the order of the spectrum. Equation (2) isused for the minimum deviation method to calculate the wavelength of the light radiation.PROCEDURE: -

a. Normal incidence method: -Preliminary adjustments of the spectrometer are made, focusing and adjusting the eyepiece of the telescope to a distant object. The grating table is levelled with a spirit level. Thegrating is mounted on the grating table for the normal incidence. The slit of collimator isilluminated with sodium light. The direct reading is taken, the telescope is turned from the positionthrough 90 and fixed in this position, as shown in the fig 1. The grating is mounted vertically onthe grating platform, the rulings on it being parallel to the slit in the collimator. The platform isnow rotated until the image of the slit as reflected by the glass surface is seen in the telescope.

The vertically cross wire is made to coincide with the fixed edge of the image. The platform is fixedin this position. The vernier table is now rotated in the appropriate direction through 45, so thatthe rays of light from the collimator fall normally, on the grating.

Grating set for normal incident lightThe telescope is now released and rotated it so as to catch the first order-diffracted image

on one side, say right (or left) as shown in the fig 2. With sodium light two images of the slit, veryclose to each other are seen. These are the D and D lines of sodium light. The point of intersectionof the cross wires is set on the D line and the reading in the vernier I & II is noted. Similarly, thereading corresponding to the D line is noted. The telescope is now focused to the direct raypassing through the grating and the point of intersection of the crosswire is set on the direct ray.

The reading in the vernier I& II is noted. The difference in the readings corresponding to any onegives the angle of diffraction for that line in the first order spectrum.

Diffracted ImageThe experiment is repeated for the second order spectrum and the results are tabulated in

table 1. The number of lines per inch as marked on the grating is noted and the number of lines Nper cm is given by:

N =Number of lines per inch/2.54(b) Minimum deviation method: -

The direct image of the slit is observed through the telescope. The point of intersection ofthe cross wire is set on the sharp image of the slit. The vernier table is fixed and the reading onthe circular scale is noted. The prism table is released from the vernier table. The telescope isturned to one side, (say right) And the first order-diffracted image is observed. The prism table isslowly rotated to the right. As it is slowly rotated to the right side, the image first moves towardsleft, reaches a limiting position and then retraces its path. In this limiting position, the telescope isfixed such that the point of intersection of the cross wire is on the D line and the reading on the

circular scale is taken. The difference between the direct reading and this reading gives the angleof minimum deviation for the D line in the first order spectrum. Similarly the angle of deviation forthe D line of the first order noted. Next, the angle of minimum deviation for the D and D lines inthe second order spectrum is found similarly. The results are tabulated in table 2.


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Table 1OBSERVATIONS: -Number of lines (as marked on the grating) per inch = ------------Number of lines per cm = N = ------------

Order of

theSpectrum

Line Reading on the

circularscale whenthe telescopeis onthe right handside

Direct reading Difference

vernier1 vernier2

1

1

Sin

FirstOrder

D1

D2

Vernier1 Vernier2

SecondOrder

D1

D2

Knowing , n and N, the wavelength ( ) of the given source of radiation for D1& D2 lines are calculated using equation (1).

Table 2

OBSERVATIONS: -Direct reading: Vernier 1 =

Vernier 2 =

Order of theSpectrum

Line Telescope inminimumdeviation position

Angle ofminimumdeviation

Wavelengthlight

First Order

D1

D2

Second Order

D1

D2

3. DISPERSION OF LIGHT{Prism Spectrometer method}

AIM: -To determine the dispersive power of the material of the given prism by thespectrometer.

APPARATUS: -Spectrometer, Mercury Vapour Lamp & Prism

THEORY: - The essential parts of the spectrometer are :(a) The telescope, ( b)The collimator & (c) prism table.


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(a) The Telescope: -The telescope is an astronomical type .At one end of a brasstube is an objective, at the other end a (Rams dens) eye piece and in between, across wire screen .The eye piece may be focused on the cross wires and thelength of the telescope may be adjusted by means of a rack and pinion screw. Thetelescope is attached to a circular disc, which rotates symmetrically about avertical axis and carries a main scale, divided in half degrees along its edges. Thetelescope may be fixed in any desired position by means of a screw &fineadjustments made by a tangential screw.

(b)The Collimator: -The collimator consists of a convex lens fitted at one end of abrass tube and an adjustable slit at the other end. The distance between the twomay be adjusted by means of a rack and pinion screw .The collimator is rigidlyattached to the base of the instrument.

(c) The Prism Table: -The prism table consists of a two circular brass discs with threeleveling screws between them. A short vertical brass rod is attached to the center of thelower disc & this is fitted into a tube attached to another circular disc moving above themain scale. The prism table may be fixed on the tube by means of a screw. The second

circular disc moving over the main scale carries two verniers at diametrically opposite.The vernier disc also revolves about the vertical axis passing through the center of themain scale and may be fixed in any position with the help of a screw. A tangential screw isprovided for fine movements of the vernier scale.

Most Spectrometers have 29 main scale divisions (half degrees) divided on thevernier into thirty equal parts .Hence , the least count of the vernier is one sixteenth of adegree or one minute .

Preliminary Adjustments: -

The following adjustments are to be made before the commencement of an experimentwith spectrometer.Eyepiece Adjustment: -The telescope is turned towards a bright object, say a white wallabout 2 to 3 meters way and the eyepiece is adjusted so that cross - wires are veryclearly seen. This ensures that whenever an image is clearly seen on the cross wires, theeye is an unstrained condition.Telescope Adjustment: -The telescope is now turned towards a bright object, and its length isadjusted until the distant objects is clearly seen in the plane of the cross wires: that isthe image suffers no lateral displacement, with the cross wire of the eye shifted slightlyto and fro. In this position the telescope is capable of receiving parallel rays. This meansthat whenever any image is seen clearly on the cross wires, it may be taken that therays entering the telescope constitute a parallel bundle.

In case the experiment is to be performed in a dark room from which a view of

distant object is difficult to obtain, the method suggested by Schewster may be adopted.A prism is placed on the prism table and a refracted image of the slit is viewed.The prism is adjusted to be almost at minimum deviation .At this stage, it will be foundthat the image is fixed telescope for two positions of the prism ,which may be obtained byturning the prism table one way or other. The prism table alone is adjusted so that theimage leaves the field of vision (traveling towards the direct ray) and returns again. Nowthe collimator alone is adjusted for clarity of image. This is repeated a few times until theimage is quite clear.(iii) Collimator Adjustment: -The slit of collimator is illuminated with light. The telescope isturned to view the image of the slit and the collimator screws are adjusted such that aclear image of the slit is obtained without parallax in the plane of the cross wires. The

slit of the collimator is also adjusted to the vertical & narrow.The refractive index of the material of the prism is given by

Sin(A+D/2)


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= ------------------ ------------------------- (1)Sin(A/2)

Where A is the angle of the equilateral prism andD is the angle of minimum deviation

When the angle of incidence is small, the angle of deviation is large .As theangle incidence is slowly increased, the angle of deviation begins to diminishprogressively, till for one particular value of the angle of incidence, the angle of deviationattains a least value. This angle is known as the angle of minimum deviation D

The dispersive power ( ) of thematerial of the prism is given by

B -R = ---------- --------------------- (2)

(-1)

Where B = the refractive index of the blue rays; R = the refractive index ofthe red ray and

( B + R)

= -------------- ; the mean of Band R2

Noting the angle of minimum deviation D . for blue & red raysB and R arecalculated using equation (1 ) and using equation ( 2 ) the dispersive power of thematerial of the prism is calculated .

PROCEDURE: -The prism is placed on the prism table with the ground surface of the prismon to the left or right side of the collimator. Care is to be taken to see that the groundsurface of the prism does not face either the collimator or the telescope. The vernier table

is then fixed with the help of vernier screw.The ray of light passing through the collimator strikes the polished surface BC of theprism at Q and undergoes deviation along QR and emerges out of the prism from the faceAC. The deviated ray (continuous spectrum) is seen through the telescope in position T2.Looking at the spectrum the prism table is now slowly moved on to the one side, so thatthe spectrum moves towards undeviated path of the beam. The deviated ray (spectrum)also moves on to the same side for some time and then the ray starts turning back eventhough the prism table is moved in the same direction. The point at which the ray startsturning back is called minimum deviation position. In the spectrum, it is sufficient if onecolour is adjusted for minimum deviation position. In this limiting position of the spectrum,deviation is minimum. The telescope is now fixed on the blue colour and the tangent

screw is slowly operated until the point of intersection of the cross wire is exactly on theimage. The reading for the blue colour is noted in vernier I and vernier II and tabulated.The reading is called the minimum deviation reading for the blue colour. The telescope isnow moved on the red colour and the readings are taken as explained for blue colour.Next, the telescope is released and the prism is removed from the prism table. Thetelescope is now focused on to the direct ray (undeviated path) and the reading in vernierI and vernier II are noted.

The difference of readings between the deviated reading for blue colour and the directreading gives the angle of minimum deviation, reading for the blue colour (DB). Similarly, the difference of readings between the deviated reading for the red colour andthe direct reading gives the angle of minimum deviation for the red colour (DR). therefractive indices for the blue and red rays are calculated using equation (1) (Assumingthe angle of the equilateral prism, A = 60O , the values of Band R are substituted inequation (2) and the dispersive power of the material of the prism is calculated.


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CIRCUIT DIAGRAM:-

Arrangement of prism for dispersive power

OBSERVATION TABLE:-

Least count of the vernier of the spectrometer, LC=Angle of prism A=

Direct reading Vernier I =Vernier II =

Colour of the line Position of minimum deviation Angle of minimum deviation

Vernier I Vernier II Vernier I Vernier II

Blue

Red

4. DETERMINATION OF LASER RADIATION

AIM: -To determine the wave length of a given source of He-Ne laser using a planetransmission grating by normal incident method.APPARATUS:- Plane diffraction grating, laser beam of He- Ne source, a scale and prismtable.DESCRIPTION:-

A plane diffraction grating consists of parallel sides glass plates with equidistantfine parallel lines drown very closely upon it by means of a diamond point. The number oflines drown per inch are written on the diffraction grating by the manufacturers. The He-Ne laser consists of a mixture of he-Ne in the ration of about 10:1, placed inside a longnarrow discharge tube. The pressure inside the tube is about 1 mm of Hg. The gas system

is enclosed between a pair of plane mirror or pair of concave mirror so that a resonatorsystem is formed. One of the mirrors is of very high reflectivity while the other is partiallytransparent so that energy may be coupled out of the system. The 6328 A transition of


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beam corresponding to the well known red light of He-Ne laser. Lasers are lightamplification by stimulated emission of radiations.THEORY:-

An arrangement consisting of large number of parallel slits of the same width (e)and separated by equal opaque space (d) is known as the Diffraction Grating (e+d) isknown as the grating element. A grating is constructed by rubbing equidistant parallellines N ruled on the grating per inch are written over it.

Hence (e+d) = l = 2.54 cmi.e. the grating element (e+d)= 2.54 cm.

The normal critical incidence the condition for obtaining principle maxima is-(e+d) sin = + = (2.54 sin )/(nN) Where is wavelength of light, N is Lines per inch on

the plane diffraction grating and n is order of diffraction light .

PROCEDURE:-

Keep the grating in front of the laser beam such that light is incident normally on it.When light of laser falls on the grating the central maxima along with four other lights areseen on the screen. The light next to central maxima and light next to first order is secondorder maxima. Now measure the distance between the grating and the screen andtabulate it as d1 and the distance between central maxima to first order and thencentral maxima and second order is d2and it is also tabulated.OBSERVATION TABLE:-Number of lines on the grating N=The distance between grating and the screen D= cm

Order No Left side d1 Right side d2 Mean d Sin =

d / d2+ D

2q = Sin /nN

PRECAUTIONS:-1) Do not look at the laser beam directly.

2) The prism table should be perpendicular to the laser and laser beam and the gratingshould be horizontal.

RESULT:-


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The wave length of He-Ne laser beam= nm.

5. C-R CIRCUIT

AIM:- To study the decay of current in a C-R circuit and to determine RC timeconstant.

MICRO BOARD CONSISTS OF:- Fixed Power supply, Switch, Ammeter, Combinations ofResistor & Capacitors.THEORY:- When a condenser C is charged through a resistance R then chargeincreases exponentially in accordance with the formula.

Q = Qo (1-e t/RC) Where Q is the charge in time t; and Qo is themaximum charge.

The product CR is called time constant. It is the time taken to establish ( l e )part of the maximum charge in the condenser. It is equal to the time taken to establish

0.632 part of the total charge.When a condenser is discharged through a resistance, the charge falls in

accordance with the formula.Q = Qo e t/RC

The time constant in this case is equal to the time, taken to decrease the charge ofe part of the maximum charge. It is equal to the time taken to discharge to a value of0.368 part of maximum charge.i.e. we can say that I = dq / dt

= -to e-t/RCWhere C = capacitor in farad; R = resistance in ohm; I = current in the circuit. When I= 0.36 Io then t = RC

PROCEDURE:-1. Rig up the circuit as per the circuit diagram. Clinching2. Flip the switch towards push to charge, the capacitor start charging towards the

power supply. The switch is in this position for short interval of time until theammeter shows maximum deflection, but within the limit. Note down the maximumcurrent as Io.

3. Now flip the switch to other side and start the stop clock. The current start falling.4. Note the ammeter reading at a regular time interval.5. Plot the graph of current (l) on Y-axis and time (t) on X-axis.

CIRCUIT DIAGRAM:-

OBSERVATION TABLE:-C1 = farad, C2 = farad & C3 = farad.

Sr.No Time in sec Time in sec Time in sec


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Current inAmp

For R1 =

For R2 = For R3 =

C1 C2 C3 C1 C2 C3 C1 C2 C3

Sr.No. R in C inFarad

Time constant (t) texp / ttheTheoretical

Experimental

GRAPH:-

Draw an intercept to the X-axis as shown in the graph the corresponding t gives the timeconstant.

6. L C R CIRCUIT

AIM: -The aim of this experiment is to study the characteristics of LCR series circuitand to determine 1. Resonant frequency, 2. Quality factor and 3. Band width.

APPARATUS: L C R circuit board with a set of inductor(s), capacitor(s) and resistor(s), an

ammeter; signal generator and connecting wires etc.THEORY & PRINCIPLE: When an alternating e.m.f. of frequency, fis applied to a circuithaving an inductor(L), capacitor(C) and a resistor(R) in series as shown in fig.1. themaximum value of a.c.current flowing in the circuit is given by

Io = Eo / R2

+ XL

@Xcb c2F Guu

t

Where Eo = maximum value of applied e.m.f.; R = resistance applied; XL= L = inductivereactance i.e. effective resistance offered by inductor in an a.c.circuit.; Xc = 1/ C =capacitive reactance i.e. effective resistance offered by a capacitor in an a.c.circuit.

Hence R2+ XL @Xc

b c2F Guut plays the same role in the a.c.circuit as a resistance in d.c. circuit.

This isknown as impedance, Z of the circuit. Thus,


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Z = R2+ XL @Xc

b c2F Guut

1. Resonant frequency:From eq.2. it is obvious that for a given L and C inductive and capacitive reactances

depends on the frequency of applied e.m.f..XL increases as frequency increases where asXc decreases and at a particular frequency both become equal. Hence, the effective

reactance (XL Xc) in the circuit becomes zero, and the resultant impedance of the circuitis a minimum (=R). The particular frequency at which impedance of a series L-C-R circuitbecomes minimum or the current becomes maximum is called the resontant frequency(fo) and the circuit is called series resontant circuit.Expression for fo:

At resonant frequency, fo we knowL = 1/ C or = 1/ LCp or 2fo = 1/ LCp

or fo = 1/ 2 LCp ------------------------------(3)

Eq. (3) shows that the resonant frequency depends on the values of L and C but does not

on R.Following figure shows the variation of the peak value of current with frequency of applieda.c.e.m.f. for different resistances.

The curves are plotted at three different resistances R, R, R (R


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At the instant of maximum current Io, through the inductor, the energy stored =1

2

ff LIo and

the power loss per period is equal to1

2ff

Lo2R.

Q = 2 foL/R = L/R =XL/RSimilarly, it can be shown thatQ = 1/ CR = Xc/R

Hence, Quality factor can also be defined as the ratio of reactance of either inductance orcapacitance. Since at the resonant frequency both reactances are equal, Q will remainsame.3. Band width:The difference of two half power frequencies is called as Band Width of a resontantcurve.

Band Width (B.W.) = f2-f1= f0/ Q = f0R/ L = R/2LThe half power frequencies (f1 and f2) corresponding to the frequencies at whichinstantaneous current becomes 1/ 2p or 0.707 times its maximum value (Io).PROCEDURE:

(1) Make the necessary connections as shown in fig.1 . See the voltage of 10V isapplied.(2) Calculate the frequency for the given L&C to set required frequency range at thesignal generator.(3) Vary the frequency in equal steps till the ammeter record a sharp rise and fall,

adjust the signal such that the ammeter deflection is maximum possible. This is theresonant frequency of the connected combination of the circuit. And note down thereadings in table.1.

(4) Adjust the signal generator amplitude such that to get full scale deflection. Nowreduce the frequency till the deflection falls considerably, by increasing thefrequency in regular intervals and note down the ammeter readings

(5) Repeat the above steps second time and find the average.(6) Find the resonant frequency from the graph, this value should be close to thecalculated value.(7) Repeat above steps using different combinations of Rs to study how fo, Q, B.W. areaffected.

OBSERVATIONS:-Table.1.

S.

N

o.

Applied

frequency

( )

Deflection of Ammeter

( )

R1( ) R2 ( ) R3( )Trail 1 Trail 2 Avg. Trail 1 Trail 2 Avg. Trail 1 Trail 2 Avg.

CALCULATIONS:-

1. Resonant frequency (fo):a. Theoretical:

b. Experimental:2. Quality factor (Q):


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3. Band Width (B.W.):Table.2.L = ; C =

Resistance (R)

( )

Peak current(Io)

( )

Resontant freq.(fo)

( )

Q factor (Q)

( )

Band Width(B.W)

( )

From the values tabulated following conclusions can be drawn:1. Resonant frequency, band widths are independent of resistances used where as

Q factor and peak value of current does.2. Q factor and peak current decreases as R increases.3. Lower R, Sharper is resonance.

Series Resonant Circuit: Parallel Resonant Circuit:

RESULT:-

Resonant frequency, quality factor and bandwidth are calculated for variouscombinations of L, C and R. The results are tabulated (table.2)

7. ENERGY GAP OF A SEMI CONDUCTOR

AIM: -To determine the energy gap of a semi conductor diode.MICRO BOARD CONSISTS OF:- Germanium diode (OA 79), Thermometer, Copper Vessel,

Regulated DC power supply, Micro ammeter, Heater & Bakelite lid.PROCEDURE: -Connections are made as per the circuit diagram. Pour some oil in the copper vessel. Fix the

diode to the bakelite lid such that it is reversed biased. Bakelite lid is fixed to the copper vessel, ahole is provided on the lid such that it is reversed biased. Bakelite lid is fixed to the copper vessel,a hole is provided on the lid through which the thermometer is inserted into the vessel. With thehelp of heater, heat the copper vessel till temperature reaches upto 80oC. Note the current readingat 80oC apply suitable voltage say 1.5v (which is kept constant) & note the corresponding currentwith every 5oC fall of temperature, till the temperature reaches the room temperature. A graph isplotted between l /T (K) on x-axis and log 10 R on y-axis is a straight line. Slope is measured bytaking the values of two points where each one of them intersects on the straight line as shown inthe fig. The energy gap = slope x Boltzmanns constant / log 10 e. The energy gap Eg = 1.9833 X slope X 10-4 evNOTE: -Do not allow the temperature to rise 100oC if you switch off the heater at 80oC it willkeep on rising for few minutes and may go upto 85/90 degress before stabilizing/falling.


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AB X Scale on Y-axis

CIRCUIT DIAGRAM: - Slope= ------------------------------ BC X Scale on X-axis

Depending upon the doping level of the diode the energy gap may vary between0.5ev to 0.7ev.TABULAR FORMAT: -

V= 1.5 VoltTemp in Co T= t + 273

in K

Current in A

I

R=V/I in

Log10R 1 / T in K

8. DETERMINATION OF RIGIDITY MODULUS OF THE MATERIAL OF A WIRE

(Torsional pendulum)

AIM:To determine the rigidity modulus (n) of the material of the given wire using torsionalpendulum.APPARATUS: -Torsion pendulum, Stop clock, meter scale, and vernier caliper, Screw Gauge Roughbalance.THEORY:

A torsional pendulum is a flat disk, suspended horizontally by a wire attached at the top ofthe fixed support. When the disk is tuned through a small angle, the wire is twisted .On beingreleased the disk performs torsional oscillations about the axis performs torsional oscillationsabout the axis of the support .The twist wire will exert a torque on the disk tending to return it tothe original position. This is restoring torque. For small twist the restoring torque is found to beproportional to the amount of twist, or the angular displacement, so that

Here k is proportionality constant that depends on the properties of the wire is called torsionalconstant. The minus sign shows that the torque is directly opposite to the angular displacement.Eq n 1, isthe condition for angular simple harmonic motion. The equation of motion for such a

system is

-----------------(2)So that, on using the equation (1) we get


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---------------(3)

The solution of the equation 3 is, therefore, a simple harmonic oscillation in the angle co-ordinate, namely

= m

cos ( t + ) Here m is the maximum angular displacement i.e. the amplitude of the angular oscillation. Theperiod off oscillation is given by

T = 2 (I /k)Where I = rotational inertia of the pendulumK= torsional constantIf k and I are known, T can be calculated.PROCEDURE:

Torsional pendulum consists of a uniform circular metal (brass or iron) disc of diameterabout 10cm and thickness of 1 cm. Suspended by a metal wire (whose n is to be determined) atthe center of the disc .The other end of the wire is griped into another chuck, which is fixed to awall bracket. The length (l) of wire between the two chucks can be adjusted and measured using

meter scale .An ink mark is made on the curved edge of the disc. A vertical pointer is kept in frontof the disc such that the pointer screens the mark when straight. The disc is set into oscillations inthe horizontal plane, by tuning through a small angle .Now stopwatch is started and time (t) for 20oscillations is noted. This procedure is repeated for two times and the average value is Taken. Thetime period T (=t/20) is calculated. The experiment is performed for five different lengths of thewire And observations are tabulated in table. The diameter and hence the radius (a) of the wire isdetermined accurately at least at five different places of the wire using screw gauge, since theradius of the wire is small in magnitude and appears with forth power in the formula of rigiditymodulus. The mass (M) and the radius (R) of the circular disc are determine by using roughbalance and vernier respectively.

A graph is drowning between l on x-axis and T2 on Y-axis.Rigidity modulus (n) of given wire is determine using the formula

OBSERVATION TABLE:-

Mass of the disc m = gmRadius of the disc R = cmRadius of the wire, a

Sr.no PSR HSR L.C PSR + (HSR*LC) Diameter (cm) Radius ,a(cm)

Sr. No Length of thewirel between

Time taken for 20Oscillations (sec)

time periodT (sec)

Trial 1 Trial 2 Mean


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chucks (cm)

Result:-

9. STUDY OF NORMAL MODES ON A STRING USING FORCED VIBRATIONS IN RODS(MELDES APPARATUS)

AIM: -To determine the frequency of a vibrating bar, or tuning fork using Meldesarrangement.APPARATUS: - Smooth pulley fixed to a stand, tuning fork, Connecting wires, Weight box,Pan, Thread & Power supply.THEORY: -

(a) Transverse arrangement:The fork is placed in the transverse vibrations position and by adjusting the length

of the string and weights in the pan; the string starts vibrating & forms many well-definedloops. This is due to the stationary vibrations set up as results of the superposition of theprogressive waveform the prong and the reflected wave from the pulley. Well-definedloops are formed when the frequency of each segment coincides with the frequency of thefork. The frequency of the transverse vibrations of the stretched string by the tension of T dynes is given by:

Where m = mass per unit length of the string; l = length of a single loop.(b) Longitudinal arrangement:

When the fork is placed in the longitudinal position and the string makeslongitudinal vibrations, the frequency of the stretched string will be half of the frequency( ) of the tuning fork. That is, when well-defined loops are formed on the string, the frequency of each vibrating segment of the string is exactly half the frequency of the fork.During longitudinal vibrations, when the prong is in its right extreme position the stringcorresponding to a loop gets slackened string moves upto its initial horizontal position &becomes light. But when the prong is again in its right extreme position, therebycompleting one vibration, the string goes up; its inertia carrying it onwards and therebycompletes only a half vibration. Hence, the frequency of each loop is:


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PROCEDURE: -

The apparatus (tuning fork) is first arranged for transverse vibrations, with thelength of the string3 or 4 meters & passing over the pulley. The circuit is closed vary the pot till the forkvibrates steadily. The load in the pan is adjusted slowly, till a convenient number of loops(say between 4 and 10) with well-defined nodes & maximum amplitude at the antinodesare formed, the vibrations of the string being in the vertical plane. The number of loops

(X) formed in the string between the pulley and the forks are noted. The length of thestring between the pulley and the fork (d) is noted. The length (l) of a single loop iscalculated by:

l = d/X -------Cm.

Let: m = mass of the pan. M = load added into the pan.Therefore, Tension, T = (M + m)g dynesWhere g = acceleration due to gravity at the place.Increasing or decreasing the load M repeats the experiment, so that the number of loopsincreases or decreases by one. The experiment is repeated till the whole string vibrates inone or two loops & the observations are recorded. Next the tuning fork is arranged for thelongitudinal vibrations. The experiment is repeated as was done for the longitudinalvibrations & the observations are recorded. At the end of the experiment, the mass m ofthe pan, the mass of the string (w) and the length (Y) of the strings are noted.OBSERVATIONS: -

1. Mass of the string (thread) = W = -------gm (correct to a mg)2. Length of the (thread) string = Y = -----cm3. Linear density of the thread = (W/Y) = --------gm/cm4. Mass of the pan = m = --------gm (correct to a mg)TABULAR COLUMN:-

For transverse and longitudinal arrangementS.No

.

Load applied

in to the panM gm

Tension

T=(M+m)gdynes

No. of

loopsX

Length of

X loops=dcm

Length

of eachloopl=d/xcm

T

T /l

RESULT:Frequency of a vibrating tuning fork using Meldes arrangement is __________________-- Hz


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10. LOSSES IN OPTICAL FIBERS AT 660NM & 850NM

1.1 Aim of the Experiment:To study various types of losses that occurs in optical fibers and measure losses in

dB of two optical fiber patch cords at two wavelengths, namely, 660nm and 850nm. Thecoefficients of attenuation per meter at these wavelengths are to be computed from theresults.

1.2 Basic Definitions:Attenuation in an optical fiber is a result of a number of effects .We will confine our

study to measurement of attenuation in two cables (cable 1 and cable 2)employing anSMA SMA in -line adapter .We will also compute loss per meter of fiber in dB. We willalso study the spectral response of the fiber at 2 wavelengths, 660nm and 850nm.

The optical power at a distance, L, in an optical fiber is given by where

Po is the launched power and is the attenuation coefficient in decibels per unit length.The typical attenuation coefficient value for the fiber under consideration here is 0.3dBper meter at a wavelength of 660nm .Loss in fibers expressed in decibels is given by 10log (Po/Pf) where, Po is the launched power and Pf is power at the far end of the fiber.Typical losses at connector junctions may vary from 0.3 dB to 0.6 dB.Losses in fibers occur at fiber-fiber joints or splices due to axial displacement, angulardisplacement, separation (air core), mismatch of cores diameters, mismatch of coresdiameters, mismatch of numerical apertures, improper cleaving and cleaning at the ends.The loss equation for a simple Fiber-optic link is given as:Pin (dBm)-Pout (dBm)= LJ1+LFIB1+LJ2+LFIB2+LJ3 (JB): where, L J1 (dB) is the loss at the LED-connector junction, L FIB1 (dB) is the loss in cable1, LJ2 (dB) is the insertion loss at a splice or

in-line adapter, L FIB2 (dB) is the loss in cable2 and LJ3 (dB) is the loss at the connector-detector junction.1.2Procedure with Block SchematicThe schematic diagram of the optical fiber loss measurement system is shown below andis self explanatory.

The step by step Procedure is given here:

Step1: Connect one end ofCable 1 to the LED1 port of the PHY 148-TX and the otherend to the FO PIN port (power meter) of PHY 149-RX unit.Step2: Set the DMM to the 2000 mV range. Turn the DMM on. The power meter is nowready for use.

Step3: Plug the AC mains for both units. Connect the optical fiber Patchcord, Cable1securely, as shown, after relieving all twists and strains on the fiber.While connectingthe cable please note that minimum force should be applied. At the same timeensure that the connector is not loosely coupled to the receptable. After


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closer to the true values, if we take the average of many readings. The attenuationcoefficient of aprrox 0.3dB per meter at 660nm is normally well defined, as per thespecifications of the manufacturers. Deviation, if any, will be due to connector losses notbeing identical for the two cables. Also the assumed value of lose in the In-line-adapter(1.0dB) may be off the mark in some cases.The loss per meter of cable at 850nm is not specified by the manufacturers. The range ofloss 2.5dB+/-1.0 dB is acceptable.

11. NUMERICAL APERTURE

AIM:To determine the numerical aperture (NA) of the given optical fiber.

APPARATUS:One or two meters of the step index fiber, Fiber optics kit, and scale.THEORY:The numerical aperture of an optical fiber is a measure of the light collectedby it. It is defined as the product of the refractive index of the surrounding medium andthe Sine of the maximum ray angle (acceptance angle)

Numerical aperture (NA) = n0 Sina .............(1)For air as surrounding medium n o = 1

And NA -Sin . (2)For a step index fiber, NA is given by

NA = [n 1- n2]1/2 .. (3)

Where n1 and n2 are refractive indices of core and cladding materials.

Light from the fiber end ' A ' falls on the screen BD. Let the diameter of the light falling onthe screen BD = w (Fig. 1)Let the distance between the fiber and the screen AO = L From the triangle AOB

Sin a = OB/AB

= OB / (OA2 + OB2 )1/2

=(w/2) / (L2 + w2 / 4) 1/2

Sin a = w/ (4L2 + w2) 1/2

NA = Sin a = w/ (4L2 + w2) 1/2 (4)

Knowing w and L, the NA can be calculated and substituting this NA value in

equation (2) the acceptance angle

acan be calculated.PROCEDURE:-To determine the NA of a optic fiber (OF) make the connection as shown in the fig.2

Connect one end of the OF cable to Po and another end to the NA fig(i.e. Landing o/p of LED into OF cable).

Connect power adapter into socket Vin and plug the AC mains. Red light should appear


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at the end of the fiber on the NA jig. To set maximum output turn the SET Po/IF Knobclockwise. The red light intensity should increase. Hold the acrylic white screen whichhas printed scale at a distance of 10 mm (L) from the emitting fiber end and you will viewthe red spot on the screen.Measure the diameter w of the spot. If the intensity within thespot is not evenly distributed, wind three turns of the fiber on the mandrel. Substitutethe measured values L and w in the formula,

NA = Sin a = w/ (4L2 + w2) 1/2

And calculate the value of the numerical aperture of the fiber.Repeat the experiment for the distances of 15mm, 20 mm, 25 mm and 30 mmAnd note the readings in table (1)OBSERVATIONS AND RESULTS

Table 1

Sl NoL

(mm)W

(mm)NA

a

(Degrees)

RESULT:

Numerical Aperture (NA) =

12. STUDY OF MAGNETIC FIELD ALONG THE AXIS OF A CIRCULARCOIL STEWART AND GEES USER MANUAL

AIM: -To study the variation of magnetic field along of a circular coil carrying current.

APPARATUS: - Stewart and Gees type of tangent galvanometer, Rheostat, Ammeter, DeflectionMagnetometer, Battery eliminator, 4way & 2 way key.

THEORY:The magnetic field (B) at a point on the axis of a circular coil carrying current i isgiven by the expression

onia2

B = -------------- Tesla.

2(x2+a2)3/2

Where n is the number of turns, a the mean radius of the coil and x is the distance ofthe point from the center of the coil along the axis. To measure this field the stewart and Gees

type of tangent galvanometer is convenient. The apparatus consists of a circular frame c madeup of non-magnetic substance. An insulated Copper wire is wounded on the frame. The ends of thewire are connected to the other two terminals. By selecting a pair of terminals the number of turnsused can be changed. The frame is fixed to a long base B at the middle in a vertical plane alongthe breadth side. The base has leveling screws. A rectangular non-magnetic metal frame issupported on the uprights. The plane of the frame contains the axis of the coil and this frame issupported on a movable platform. This platform can be moved on the frame along the axis of thecoil. The compass is so arranged that the center of the magnetic needle always lie on the axis ofthe coil. The apparatus is arranged so that the plane of coil is in the magnetic meridian. The framewith compass is kept at the center of the coil and the base is rotated so that the plane of the coil isparallel to the magnetic needle in the compass. The compass is rotated so that the aluminumpointer reads zero zero. Now the rectangular frame is along East-West directions. When a current

i flows through the coil the magnetic field produced is in the perpendicular direction to the planeof the coil. The magnetic needle in the compass is under the influence of two magnetic fields. Bdue to coil carrying current and the earths magnetic fields Be which are mutually perpendicular.

The needle deflects through an anglesatisfying the tangent law.


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B/ Be =Tan ----------------------- (1)

Thus B= Be Tan

The value of B is given by.. onia

2

B = -------------- Tesla.

2(x2+a2)3/2

PROCEDURE: -With the help of the deflection magnetometer and a chalk. A long line of about one meter is

drawn on the working table, to represent the magnetic meridian. Another line perpendicular to theline is also drawn. The Stewart and Gees galvanometer is set with its coil in the magnetic meridianas shown in the fig. The external circuit is connected as shown in the fig. keeping the ammeter,rheostat away from the deflection magnetometer. This precaution is very much required because,the magnetic fields produced by the current passing through the rheostat and the permanentmagnetic fields due to the magnet inside the ammeter affect the magnetometer reading, if theyare close to it. The magnetometer is set at the center of the coil and rotated to make thealuminum pointer reads, (0,0) in the magnetometer. The key K, is closed and the adjusted so as

the deflection in the magnetometer is about 60

0

. The current in the magnetometer before andafter reversal of current should not differ much. In case of sufficient difference say above 20 or 30

necessary adjustments are to be made. The deflections before and after reversal of current arenoted when d = 0. The readings are noted in Table 1.The magnetometer is moved towards Eastalong in steps of 5cm at a time. At each position, the key is closed and the deflections before andafter reversal of current are noted. The mean deflection be denoted as E The magnetometer isfurther moved towards east in steps of 5cm each time and the deflections before and afterreversal of current be noted, until the deflection falls to 300. The experiment is repeated byshifting the magnetometer towards West from the center of the coil in steps of 2 cm, each timeand deflections are noted before and after reversal of current. The mean deflection is denoted asW.

It will be found that for each distance (x) the value in the last two columns of the second table

are found equal verifying equation (1) & (2). A graph is drawn between x (the distance of thedeflection magnetometer from the center of the coil) along x=axis and the corresponding TanEand TanW along Y-axis. The shape of the curve is shown in the fig. The point A and B marked onthe curve lie at distance equal to half of radius of the coil (a/2) on either side of the coil.

CIRCUIT DIAGRAM:-


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MODEL GRAPH:-

OBSERVATION TABLE:-Horizontal component of earths magnetic field Be = 0.38 X 10 -4 Tesla (or Wb/m2)

Radius of coil (a) = meter (diameter of coil /2)Current carrying in the ammeter= Amp

0 = 4 X 10-7DistanceFrom the

Center of coil

Deflection in Eastdirection Mean

Deflection in Westdirection Mean W

=(+W)/2 Tan

1 2 3 4 1 2 3 4

Distance X in meter Theoretical B Practical B

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