1

2

Sriramajayam SASTRA UNIVERSITY

Thanjavur – 613 401

ENGINEERING PHYSICS LABORATORY

Code: BCCCPY109/MCCCPY109/BCCCPY209/MCCCPY209

List of Experiments

1. Spectrometer - Diffraction Grating.

2. Newton’s Rings Method - Radius of Curvature of Lens.

3. Measurement of dielectric constant using parallel plate capacitor.

4. Lee’s Disc method - Thermal Conductivity of Bad Conductor.

5. Transistor Characteristics - Common Emitter Configuration.

6. Optical Fibers - Numerical Aperture and Measurement of Attenuation.

7. Calibration of Ammeter using Potentiometer.

8. Laser Grating - Determination of wavelength of He-Ne Laser.

and Non-Destructive Testing.

9. Hall effect – Measurement of carrier concentration and mobility of

semiconductor

10. Variation of Resistance with Temperature of a Thermistor.

11. Logic Gates - OR, AND, NOT, NOR and NAND using Discrete

Components.

12. Velocity of Ultrasonic waves in Liquids and Compressibility of the

liquid using Ultrasonic Interferometer.

13. Four Probe Method – Measurement of Resistivity of material

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1. SPECTROMETER – GRATING

Aim:

To standardize the grating and to find the wavelength of prominent lines of mercury spectrum by the method of normal incidence. Apparatus Required:

Spectrometer, plane transmission grating, sodium vapour lamp, Hg vapour lamp etc., Formula:

.Sin

nmm Nθλ =

Where θ is the angle of diffraction in degrees

m is the order of spectrum N is the number of lines per meter in the grating λ is the wavelength of the prominent lines in the Hg spectrum. Procedure: 1. Adjustment of the grating for normal incidence:

The initial adjustment of the spectrometer is made as usual. The plane

transmission grating is mounted on the prism table. The telescope is released and placed in front of the collimator. The direct reading is taken after making the vertical cross-wire to coincide with the fixed edge of the image of the slit, which is illuminated, by a monochromatic source of light. The telescope is then rotated by an angle 90o (either left or right side) and fixed. The grating table is rotate until on seeing through the telescope the reflected image of the slit coincides with the vertical cross-wire. This is possible only the reflected image of the slit coincides with the vertical cross-wire. This is possible only when a light emerging out from the collimator is incident at an angle 45o to the normal to the grating. The vernier table is now released and rotated by an angle 45o towards the collimator. Now light coming out from the collimator will be incident normally on the grating. (Fig 1).

3

T

C

Fig. 1 Fig. 2 2. Standardization of the grating:

The slit is illuminated by sodium light. The telescope is released to catch the different image of the first order on the left side of the central direct image. The readings in the two vernier are noted. It is then rotated to the right side to catch the different image of the first order, the readings are noted. (Fig 2). The difference between the positions of the right and left sides given twice the angle of diffraction 2θo. The number of lines per meter of the grating (N) is calculated by using the given formula assuming the wavelength of the sodium light as 589.3 nm. Wavelengths of the spectral lines of the mercury spectrum:

The sodium light is removed and the slit is now illuminated by white light

from mercury vapour lamp. The telescope is moved to either side of the central direct image, the diffraction pattern of the spectrum of the first order and second order are seen.

The reading are taken by coinciding the prominent lines namely violet, blue, bluish – green, yellow1 , yellow2 and red with the vertical wire. The readings are tabulated and from this, the angle of diffraction for different colours are determined. The values are tabulated in table. The wavelengths for different lines are calculated by using the given formula.

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Tab

le.

Det

erm

inat

ion

of w

avel

engt

h of

var

ious

spe

ctra

l lin

es o

f H

g sp

ectr

um

L.C

= 1

’

N =

6 X

105

lines

/met

re

m =

1

Res

ult:

The

wav

elen

gths

of p

rom

inen

t lin

es o

f mer

cury

spe

ctru

m h

ave

been

foun

d an

d ar

e ta

bula

ted.

Col

or

Tel

esco

pe R

eadi

ng (

degr

ees)

D

iffe

renc

e

Mea

n 2θ

de

g

θ deg

λ

nm

Lef

t R

ight

V

erni

er A

A

1 V

erni

erB

B

1 V

erni

erA

A

2 V

erni

er B

B

2 2

θ A

1~A

2

deg

2 θ

B1~

B2

deg

MSR

VSC

CR

MSR

VSC

CR

MSR

VSC

CR

MSR

VSC

CR

5

C

S

G

M

Y X

2. NEWTON’S RINGS Aim:

To find the radius of curvature of the convex surface of the given long focus convex lens. Apparatus Required:

Optically plane glass plate, sodium vapour lamp, microscope etc., Formula:

Radius of curvature of convex lens 2 2

4n m nD D

R metremλ

+ −=

where 2 2

n m nD D+ − is the mean value of the difference between squares of diameters of nth and (n+m)th ring.

λ is the wavelength of the sodium vapour lamp = 5893 Å and m is the order

Diagram:

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Procedure:

A plano-convex lens L is placed on an optically plane glass plate XY. Now a thin film of airwedge is formed between the glass plate and the lens. Monochromatic light is allowed to fall on the thin film of air with the help of lens C and glass plate G inclined at 45o. Due to multiple reflections of light between the glass plate XY and lens L with plano-concave air film, a system of concentric alternate bright and dark rings known as Newton’s rings are seen with the help of a microscope above the glass plate G. Leaving the first few rings from the centre (say 3), the cross-wire of the microscope is placed tangentially on n+27th ring on the left side of the centre (taking care to note that the microscope is capable of moving from n+27th ring on the extreme left to n+27th ring on the extreme right without any obstruction). The reading is noted from the horizontal scale of microscope. Similarly the cross-wire is placed on n+24, n+21, n+18…etc., upto the nth ring and the corresponding readings are noted. Now the cross-wire is placed tangentially on the nth ring at the right side of the centre leaving symmetrically the same few rings as above and the readings of the microscope scale is noted. Similar readings are noted when the cross-wire is placed on n+3, n+6….. n+27 rings. The observations are tabulated as in table 1. The difference between the corresponding readings on the left and right will give the diameter of nth, n+3th, n+6th….. etc rings. The squares of diameters are also found. The squares of diameters are also found. The difference of above square for m rings (say 15) are found successively and the mean of consistent values is taken from the last column of the table. Radius of curvature of lens is found using then above formula.

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Tab

le 1

L

.C=0

.001

cm

Ord

er o

f ri

ngs

Mic

rosc

opic

sca

le r

eadi

ngs

Dia

met

er

of th

e ri

ng

D

10-2

m

D2

10-4

m

D2 n+

m-D

2 n

10-4

m

Lef

t R

ight

MSR

10

-2m

V

SC

CR

=MSR

+ (V

SCxL

C)

10-2

m

MSR

10

-2m

V

SC

CR

=MSR

+ (V

SCxL

C)

10-2

m

n n+3

n+6

n+9

n+12

n+15

n+18

n+21

n+24

n+27

Res

ult :

The

radi

us o

f cur

vatu

re o

f the

con

vex

surf

ace

of th

e gi

ven

long

focu

s co

nvex

lens

is …

……

…..

m.

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3. MEASUREMENT OF DIELECTRIC CONSTANT USING

PARALLEL PLATE CAPACITOR

Aim:

To determine the dielectric constant of the dielectric material of the given capacitor by the method of charging and discharging.

Apparatus Required :

1. Digital volt meter 2. Dielectric cell-1 having two Gold plated discs( 75mm. each) 3. Dielectric cell-2 having two Gold plated brass discs(25 mm. each)

4. Given samples

Theory: In this experiment an LC circuit is used to determine the capacitance of the dielectric cell and hence the dielectric constant. The circuit is given the figure 1

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The audio oscillator is incorporated inside the instrument. If Csc and Cdc represents the capacitances of the standard capacitor and dielectric cell respectively and if Vsc and Vdc are the voltages across SC and DC then Vsc/I =1 / ωCsc (1) I = ω Vsc Csc (2) The same current I passes through the dielectric cell. Vdc / I = 1 / ω Cdc (3)

Cdc = I / ωVc

= ω Csc Vsc / ω Vdc

= Csc Vsc / Vdc (4) By measuring Vsc & Vdc and using the value of Csc we can determine the capacitance of the dielectric cell containing the sample. If Co represents the capacitance of the dielectric cell without the sample and the plates separated by air gap whose thickness is the same as the thickness of the sample, then Co is given by

Co =εoA / d = r2 / 36d nf (5) Where r represents the radius of the gold plated discs and d represents thickness of the sample in meters. The dielectric constant of the sample is given by εr = C/ Co (6) Procedure :

1) Connect CRO to the terminals provided on the front panel of main unit. If no sinusoidal waveform appears on CRO, then adjust ‘CAL’ such that waveform appear.

2) Connect the dielectric cell assembly to the main unit and insert the sample in between the SS plates.

IMPORTANT: Do not put extra pressure, as PZT sample and Glass samples are brittle and may be damaged.

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3) Switch ON the unit. 4) Choose the standard capacitor (with the help of switch S2) SC1 for materials

having low dielectric constants(like Bakelite, Glass,Plywood samples or SC2 for material having high dielectric constant(PZT sample).

5) Thro S1 towards DC to measure the voltage across dielectric cell, say Vdc and

towards SC to measure voltage across standard capacitor, say Vsc. Calculate the capacitance C using relation

C =( Vsc / Vdc) x Csc

6) Measure thickness of the sample using the cell holder and calculate the value of Co(air) using relation (5) 7) Determine the dielectric constant or the sample using the relation

εr = C / Co(air) Result: The dielectric constant of the given sample =

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4. THERMAL CONDUCTIVITY OF A BAD CONDUCTOR (LEE’S DISC METHOD)

Aim:

To determine the thermal conductivity of a bad conductor (cardboard) by Lee’s disc method. Apparatus Required:

Lee’s Disc, Cardboard disc of uniform thickness, two 100º C thermometers, stop

clock, etc. Formula:

1 2

(2 )(2 2 ) ( )

d h r dK Ms

dt h r Aθ

θ θ+ = + −

W m-1 K-1

Where θ1 θ2 are the steady temperatures of stream chamber and brass disc A is the area of the cardboard d is the thickness of the board s is the specific heat capacity of material of disc M is the mass of the disc

ddtθ

is the mean value of the rate of temperature

h is the thickness of the disc r is the radius of the disc and K is the thermal conductivity of the cardboard to be determined Procedure:

To begin with the mean thickness ‘d ‘of the cardboard disc is determined with a

screw gauge, measuring its thickness at least in six different places. Its diameter (which is the same as that of the lower metallic disc), is found by finding the diameter of the lower metallic disc with a vernier calipers. The mean thickness h of the lower metallic disc is also determined with a screw gauge. The mass M of this disc is found approximately with a trip scale balance. The apparatus is arranged as shown in Fig 1. Steam from the boiler is then passed through the steam-chest. The temperature indicated by the thermometers begins to rise. After the steam has been passed for about an hour, the reading of the thermometers become steady. The steady temperatures θand θ2 respectively recorded by the thermometers are noted.

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The cardboard is then removed, and the steam chest is placed in direct contact

with the metallic disc. The temperature of the disc rapidly rises. When the temperature of the disc rises by 8 to 10° C above the steady temperature θ2 the steam chest is taken away. The metallic disc is now allowed to cool. A stop clock is started and its temperature is noted every one degree fall, until it falls by 8 to 10° C below θ2. A cooling curve is drawn with time along the X-axis and the temperature along the Y-axis, Fig 2. From this graph a rate of cooling dθ/dt at temperature θ2 is determined by finding slope of the curve at the point corresponding toθ2. From these reading the thermal conductivity of the cardboard is calculated.

θ1= θ2 =

Temperature

οοοο C

Time

t Sec

Range R

οοοο C

Time

t Sec

Rate of fall of Temperature

dθθθθ/dt = R/t οοοο C S-1

S

B

D

Steam

T1

T2

13

To Find the Thickness ‘d’ of the cardboard and brass disc ‘h’ - Screw gauge L.C: Z.C:

Thickness of the Cardboard ‘d’ = _______________________x10-3m Thickness of the brass disc ‘h’ = _______________________x10-3m

Using the radius of the cardboard ‘r’ area of the cardboard ‘A’ = π.r2 is found . The Mass ‘M’ of the disc is found using ordinary balance. Specific heat capacity of the material disc ‘s’ is taken from the standard table. The value of the dθ/dt can also be found from the slope of time temperature graph at the temperature θ2. Using all these values, thermal conductivity of the given bad conductor (cardboard) is calculated using the formula given above.

Sl.No.

Pitch Scale Reading(PSR)

mm

Head Scale Coincidence

(HSC) div

Observed Reading(OR) OR= PSR+(HSCXLC)

mm

Correct Reading(CR) CR= OR-ZE

mm

Car

dboa

rd (d

)

Mean Thickness ‘d’=

Bra

ss d

isc(

h)

Mean Thickness ‘h’=

14

To Find the radius ‘r’ of the brass disc – Vernier Caliper

L.C: Z.C:

Sl.No. Main Scale

Reading (MSR)

cm

Vernier Scale Coincidence(VSC)

div

Observed Reading (OR)

OR=MSR+(VSCXLC) cm

Correct Reading(CR) CR=OR-ZE

cm

Mean diameter =

Result: Thermal conductivity of the given bad conductor ( cardboard) = ……………..Wm-1K-1

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5. TRANSISTOR CHARACTERISTICS – CE CONFIGURATION

Aim:

To draw the characteristics curves of NPN transistor in common emitter configuration, and calculate its constants. Apparatus required:

BC 547 transistor, potential divider arrangement, milliammeter, microammeter, and millivoltmeter etc. FORMULA:

1. BE

B

dVZi ohm

dI=

Where dVBE is the small change in base to emitter voltage dIB is the small change in base current Zi is the input impedance to be determined

2. C

B

dIdI

β =

Where dIC is the small change in collector current dIB is the small change in base current β is the current amplification factor to be determined CIRCUIT DIAGRAM: 0-50mA - + C IC 0-500 µA 1K + - B NPN + 0-10V + 0-2V E - VBE VCE -

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PROCEDURE:

The collector and emitter of the NPN transistor are connected to 10V power supply through a potential divider. Base and emitter are included in the 2V supply through another potential divider, observing proper polarities as shown by the circuit diagram.

The voltmeters VBC and VBE will measure the voltages of collector and base respectively. The micro and milliammeter will measure the base and collector currents IB and IC respectively. To investigate the input Characteristics VCE is kept as +2V. By varying the base current IB from 20 to 100 microamperes in-steps of 20 the corresponding collector current IC and base to emitter voltage VBE variations are noted. The experiment is repeated by changing 2V to 4V and 6V respectively. The observations are tabulated as follows. I B µA

VCE = +2V VCE = +4V VCE = +6V

IC mA

VBE (V)

IC mA

VBE (V)

IC mA

VBE (V)

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A graph is plotted taking VBE on the X-axis and IB on Y-axis. Another graph is plotted taking IB on X-axis and IC on the Y-axis.

I B IC IB VBE

From the above graph input impedance and current amplification found using the formula given. RESULT: The input characteristics curves of a NPN transistor are drawn and the transistor parameters are found to be 1. Input Impedance Zi = 2.Current amplification factor β =

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6(a). OPTICAL FIBER – MEASUREMENT OF ATTENUATION Aim: To study various types of losses occur in optical fibers and measure the loss in dB of two optical fiber patch cords. Apparatus Required: TNS 20 A fiber optic testing kit, two fiber optic cables of different lengths, LED source, power meter, cable connections, mandrel, in-line adapter, etc., Formula: The attenuation of loss equation for a simple fiber optic link is given as L = Pin (dBm) - Pout (dBm) = Lj1 + LF1B1 + Lj2 + LF1B2 + Lj3(dB) Where Lj1(dB) is the loss at the LED connector junction LF1B1(dB) is the loss in cable 1 Lj2(dB) is the insertion loss at in-line adapter LF1B2(dB) is the loss in cable 2 and Lj3(dB) is the loss at the connector – detector junction. Procedure: Attenuation in an optical fiber is due to various reasons. Losses in fibers occur at fiber-fiber joints or splices due to the axial displacement, angular displacement, separation (air gap), mismatch of cores diameters. This experiment deals with the attenuation in a fiber due mainly due to macro bending and to estimate the losses in patch cords of two different lengths. The loss is measured as a function of the length of the fiber optic cable. The schematic diagram of the optic fiber loss measurement system is shown in the figure.

Power meter

Fibre Optic LED

PSet P

OF

AC

P0 P0 P0 P0

P0 P0

Cable 1 ( 1 m ) Cable 1 ( 4 m )

Cable 1 Cable 2

In-line adopter

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The source for the optic fiber is derived from LED operation at the wave length of 660nm. Initially, one end of the 1 meter fiber cable is connected to ‘P0’ of the source and the other end is connected to the ‘Pin’ of the power meter. Plug the AC mains. Connect the optical fiber patch cord securely after relieving all twists and strains on the fiber. Adjust the set P0 knob to set ‘P0’ to a suitable value say – 15.0 dBm. Note this as P01. Wind one turn of the fiber on the mandrel and note the new reading of the power meter as P’01. Now the loss due to bending and strain on the plastic fiber is the difference between P01 and P’01. Typically, the loss due to strain and bending the fiber is 0.3 to 0.8 dB. Next remove the mandrel and relieve the cable of all twists and strains. Note the reading P01 for 1 meter cable. Repeat the measurement with the 4 meter cable and note the reading P02. Use the in-line SMA adapter and connect the cables in series as shown in figure. Note the reading as P03. The difference in values of P03 and P01 gives loss in second cable plus the loss due to the in line adopter. Assuming a loss of 1.0 dB in the in-line adapter we obtain the loss in each cable. The experiment is repeated by setting the ‘Set P0’ value at different positions. The values are tabulated as follows.

S.No.

P01

dBm

P02

dBm

P03

dBm

Loss in cable 1

dBm

Loss in cable 2

dBm

Loss/meter

dB

Result: Transmission loss (attenuation) in the given fiber optic cable = ___________dB.

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6(b). OPTICAL FIBER – MEASUREMENT OF NUMERICAL APERTURE Aim: To determine the numerical aperture of the PMMA fiber cables and also the acceptance angle. Apparatus Required: TNS 20A fiber testing kit, fiber optic cable wire, numerical aperture jig, screen etc., Formula:

1. ( )

12 2 24

WNA

L W=

+

where W is the diameter of the spot, L is the distance of the screen from the fiber end, NA is the numerical aperture to be found.

2. ( )1Sin NAθ −= where θ is the acceptance angle of the given fiber to be found. Procedure: Numerical aperture of any optical system is a measure of how much light can be collected by the optical system. It is a measure of the amount of light rays that can be accepted by the fiber. It is the product of the refractive index of the medium and sine of the maximum ray angle. Acceptance angle is the light gathering power of the optic fiber. The schematic diagram of the numerical aperture measurement system is shown in the figure.

Fibre Optic LED (660mm) P0 Set P0

OF Cable AC

Mai

n

W

L

1 meter cable

21

One end of the 1 meter fiber optic cable is connected to Po of source and the other end to the NA Jig, as shown in the figure. The AC main is switched on. Light should appear at the end of the fiber on the NA Jig. Turn the ‘Set Po’ knob clockwise to set to maximum Po. The light intensity should increase. Hold the while screen with the 4 concentric circles (each of 10,15,20, and 25 mm in diameter) vertically at a suitable distance to make the red spot from the emitting fiber coincide with the smallest (10mm) circle. Note that the circumference of the spot (outermost) must coincide with the circle. A dark room will facilitate good contrast. Record L, the distance of the screen form the fiber end and the diameter W of the spot. The diameter of the circle is measured with accurately with a suitable scale. The experiment is repeated for 15mm, 20mm, 25mm diameter in the same way. In case ensure even distribution of the light in the fiber, first remove twists on the fiber and then wind 5 turns of the fiber on the mandrel as shown below. Use an adhesive tape to hold the windings in position. Now the intensity will be more evenly distributed within core. Then using the formula given the numerical aperture of the optical fiber is computed. The readings are tabulated as follows.

From the mean value of NA the acceptance angle (the light gathering power of the optic fiber) is also computed using the formula given. Result:

1. Numerical aperture of the given fiber optic cable = 2. Acceptance angle of the given fiber optic cable =

S.No. Distance of the screen from the

fiber end (L)

10-3 m

Diameter of the spot

(W)

10-3 m

Numerical Aperture

(NA)

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7. CALIBRATION OF AMMETER USING POTENTIOMETER Aim:

To calibrate the given low range ammeter using potentiometer. Apparatus Required:

Potentiometer, accumulator, Daniel cell, ammeter, galvanometer, rheostat, plug keys, one ohm standard resistance, high resistance, etc., Formula:

2

1

1.08 li

Rl×′ = amp

where l1 is the primary balancing length l2 is the secondary balancing length R is the standard resistance = 1 ohm And i’ is the current in the secondary circuit to be determined. Circuit Diagram: Fig1 Fig2

HR

A B

K2V

1.08V G

HR

A B

K2V

A1Ω

-

G

+

6V

23

Procedure: The experiment consists of two parts. First part is to standardize the given potentiometer by finding the balancing length (l1) for a known e.m.f. of Daniel cell. The circuit connection is made as shown by fig1. The positive terminal of an accumulator is connected to one end ‘A’ of the potentiometer and the negative terminal to the other end ‘B’ through a plug key. The Daniel cell, high resistance box, galvanometer and jockey are connected as shown by the fig 1. The jockey is moved and pressed along the 10 meter potentiometer wire till the position for null deflection is found in the galvanometer i.e., there will be no current flow through the galvanometer. The balancing length AJ(l1) for the potential difference of the Daniel cell is determined. In the second part of the experiment the Daniel cell is removed and a new circuit is made with a 6V battery, a standard resistance ‘R’ ohm, a rheostat, plug-key and the given ammeter all in series as shown by the fig2. The rheostat of the ammeter circuit is adjusted till the ammeter reads 0.1 A. Now the jockey is moved and pressed to get null deflection. The second balancing length ‘l2’ is determined. By adjusting the rheostat, the ammeter is made to read 0.1, 0.2, 0.3….. 1 A Covering the required range and in each case the balancing length l2 is determined. The readings are tabulated. The first balancing length l1 = ________________ metre

SL. No.

Ammeter reading

(i) ampere

Second balancing length

(l2) metre

Calculated Current

(i΄) ampere

Correction

(i-i΄) ampere

24

The calculated current is calculated using the formula given. Also the correction (ammeter reading - calculated current) is also found. If the calculated value is less than the ammeter reading, the correction is positive; if greater than the ammeter reading, the correction is negative. A graph is drawn between ammeter reading (i) and calculated reading(i’). Another graph is drawn between ammeter reading (i) and correction (i-i’). Result:

The given ammeter is calibrated.

The graphs were drawn for i vs i΄ and i vs (i-i΄).

i '

i

Cor

rect

ion

i

25

8. a LASER GRATING-DETERMINATION OF WAVELENGTH

Aim: To determine the wavelength of laser by normal incidence method. Instruments Required: Diffraction Grating, Laser source, screen etc., Diagram: Experimental Procedure:

• Diffraction Grating with a known number of lines per meter N is mounted on a stand and placed on the table normal to the laser source.

• Place a screen on the other side of the grating to view the diffraction pattern of the source as a series of bright spots on the either side of central maximum O.

• The average distance of the first order and second order spot is noted from the left and right side of the center O as “Y”.

• The distance between the grating and the screen is noted as “X”. • Using the value of X & Y wavelength of the source is measured.

Tabulation: To calculate the wavelength N= 6x 105 lines / meter

S.No Distance (X)in m

Left Side Right side Mean

θ Order

λ in nm Yx10-2m tan θ

=Y/X θ Yx10-2

m tan θ =Y/X θ

x

y

o He-Ne Laser θ

26

Formula: Tan θ = Y/X θ = tan-1 Y/X Where Y = average distance between the order of spots X = Distance Between screen and the grating

.Sin

nmm Nθλ =

Where θ is the angle of diffraction in degrees m is the order of spectrum N is the number of lines per meter in the grating λ is the wavelength of the Laser source Result: The wavelength of the given laser source is found to be = ……………nm.

27

8 b. NON – DESTRUCTIVE TESTING (NDT) OF MATERIALS Aim: To detect the defects in the internal structure of solids and also to determine the depth of the flaw in the specimen using ultrasonic waves. Apparatus Required:

Ultrasonic flaw detector, Ultrasonic transducer, specimen etc., Formula: d = (v x t)/2 metre where v is the velocity of the sound in the specimen

t is the time interval between incident pulse and pulse reflected from the flaw

d is the depth of the flaw to be determined. Principle:

Whenever there is a change in medium, the ultrasonic waves will be reflected from the medium this is the principle used in the NDT. Since the flaws can be detected without destroying the material, it is called as Non-Destructive Testing. Description:

It consists of a piezoelectric transducer ( a transducer is a device which converts a non electrical signals to an electrical signals and vice-versa) coupled to the upper surface of the specimen (metal) without any air gap between the specimen and the transducer. A frequency generator is connected to the transducer to generate high frequency pulses. The total setup is connected to the amplifier and to a CRO as shown in the block diagram.,

Frequency generator

Specimen

Transducer (Receiver)

CRO

Amplifier

Transducer (Transmitter

)

28

• The pulse generator generates a high potential difference and is applied to the piezo electric transducer and it produces ultrasonic waves. Ultrasonic testing of materials is based on pulse echo system.

• These waves are recorded (pulse A) in CRO and is transmitted through the specimen. They travel through the specimen and is reflected back by the other end. The transducer receives the reflected waves (pulse B).

• These reflected signals are amplified and are found to be almost the same as that of the transmitted signal, which shows that there is no defect in the specimen.

• On the other hand, if there is any defect on the specimen (flaw) then the ultrasonic waves will be reflected by the flaw due to the change in medium and they give rise to another signal (pulse C) in between pulses A and B. If we have many such flaws many C pulses will be seen over the screen of CRO.

• From the time delay between the transmitted and received pulses the position of the flaw, and from the height of the pulse the depth of the flaw can be found.

Pulse generator Amplifier

Transducer

Specimen Flaw

CRO

29

Procedure:

The transducer is placed on the surface of the object that is going to be tested. A couplant ( a thin layer of fluid) is used to make the contact between the transducer and the surface of the material. The couplant performs two major functions such as, (i) it removes the air between the transducer and the test specimen and (ii) it provides a medium for the transfer of the sound vibrations.

Scan A display presents the information, the presentation in the CRT is

based on time Vs amplitude. From the pulses the position and depth of the flaw are detected. The transducer is moved through the entire specimen and all the flaws with their positions are recorded.

Knowing the velocity of sound in that medium, we can find the depth of

the flaw using the formula given.

Result:

The given specimen may be tested for the defects in the internal structure.

The depth of the flaw in the specimen = ___________ metre.

30

9 . HALL EFFECT – MEASUREMENT OF CARRIER

CONCENTRATION AND MOBILITY OF SEMICONDUCTOR

Aim: To determine the Hall coefficient, Hall voltage and charge carrier density of a semiconductor crystal Apparatus Required :

Electromagnet, Electromagnet constant power supply, Hall probe, Gauss meter, semiconductor crystal mounted on PCB, multimeter

Theory and Formulae

When a current carrying conductor is placed in a magnetic field perpendicular to the direction of current then an electro motive force is developed perpendicular to both the current and magnetic field applied. This effect is known as Hall Effect and the voltage developed is known as Hall voltage

Figure 1: Hall effect

Suppose an electric current (Ix) flows in the x direction and the magnetic field (Bz) is applied normal to this electric field in the z direction. Each electron is then subjected to a force called Lorentz force perpendicular to the direction of flow of electron as well as perpendicular to the magnetic field. It causes the accumulation of electrons on one side of the crystal and is deficient on the other side. Thus an electric field is developed in Y direction, which is called Hall field (EH). Under the equilibrium the Lorentz force on the electrons and hall force (the force on the electron due to hall field) balance each other, i.e.

q EH =q vx Bz

Where v x is the velocity of electrons in x direction

EH = vx Bz

The magnitude of current density Jx=nqvx, where n is the number of charge carriers per unit volume

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xx x H

Jv J R

nq= =

Here 1

HRnq

= is known as Hall Coefficient.

H x H zE J R B=

tH

HV

E = and xI x

xI

JA bt

= =

Substitute the values of EH and Jx

HH

x z

V bR

I B=

Here ‘t’ is the dimension of the crystal in y direction and ‘b’ is the dimension

of the crystal in z direction.

The number of charge carriers per unit volume i.e., charge carrier density is given by

1H

neR

=

If the conduction is primarily due to one type of charge carriers, then conductivity is related to mobility µm as

µm =σ RH

Precautions 1. The Hall probe should be placed between the pole pieces such that

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maximum Hall voltage is generated. 2. Current through the Hall probe should be strictly within the limits. 3. Hall voltage developed should be measured very accurately Procedure 1. Mount PCB (with crystal) and hall probe on pillars and complete all the connections. 2. Switch on the Gauss meter and place hall probe away from the electromagnet. Adjust the reading of the Gauss meter as zero (do not switch on the electromagnet power supply at this moment). 3. Switch on the constant current source and set the current, say 5 mA. Keep the magnetic field at zero as recorded by Gauss meter (do not switch on the electromagnet power supply at this moment). 4. Set the voltage range of the multimeter at 0-200 mV. When a current of 5mA is passed through the crystal without application of magnetic field the hall voltage recorded by the multimeter should be zero (do not switch on the electromagnet power supply at this moment). 5. Bring the current reading of the constant current source to zero by adjusting the knob of the constant current source. 6. Now switch on the electromagnet and select the range of the Gauss meter as ×10 and measure the magnetic flux density at the center between the pole pieces. The tip of Hall probe and the crystal should be placed between the center of the pole pieces. For carrying out the experiment the magnetic flux density should be maximum i.e. between 2000 to 3500 Gauss. 7. Vary the current through the constant current source in small increments. Note the value of current passing through the sample and the Hall voltage as recorded by the multimeter (do not change the current in the electromagnet). 8. Reverse the direction of magnetic field by interchanging the ‘+’ and ‘-‘ connections of the coils and repeat the step 10. Observations Width of the specimen, b:………………… Length of the specimen, l:………………. Thickness of the specimen, t:……………. Magnetic flux density, Bz:……………….. Gauss

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Tabulation

S.No Current Ix (mA)

Reading of millivoltmeter(mV) Mean

Value of VH(mV)

VH/Ix (Ohms) Bz and I

in one direction

Bz and I in reverse direction

Calculations 1. Draw a graph between VH and Ix and Find the slope of the curve

H

x

VI

∆∆

2. Calculate the value of Hall coefficient using the formula

H

Hx z

V bR

I B∆ = ∆

3. Calculate the carrier charge density using the formula

H

1eR

n =

Results The value of Hall coefficient for the given semiconductor crystal is -------------. The obtained value of carrier charge density is----------------------.

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10. VARIATION OF RESISTANCE OF THERMISTOR WITH

TEMPERATURE Aim:

To draw the resistance temperature characteristic of a thermistor and also to find the Energy gap of the given material of the semiconductor..

Apparatus Required:

Thermistor, resistance boxes, Power supply, heater coil, table galvanometer etc., Theory:

Thermistor is a temperature sensitive semiconductor with high negative temperature coefficient (NTC) of resistance. The active material in it is mixture of metallic oxides such as manganese, nickel, cobalt, copper etc., The resistance of a thermistor will vary from 0.5 ohms to several kilo-ohms.

The resistance of a thermistor varies with temperature according to the relation R = A e B/T where A and B are the constants and T is the absolute temperature. The constants A and B are the characteristics of the thermistor used.

Taking logarithm on both sides log e R = log e A + B/T (or) 2.303 log10 R = 2.303 log10A + B/T log10R = log10A + 0.4343 B/T

A graph is drawn between log10R and 1/T. It is a straight line graph as shown.

The slope gives the voltage of 0.4343B. Hence B can be calculated. Knowing the value of B, constant A can be calculated from the formula Log10A = log10R – 0.4343B/T If R is unknown at temperature (T), substituting the value of B in the above equation A can be calculated.

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Procedure: The thermistor is connected in the fourth arms of the wheatstone bridge as shown in the figure. In the two arms of P and Q, resistance 1k each is placed and in the third arm R a variable resistance box is connected. The thermistor is placed inside the test tube, which contains a dielectric liquid and is placed in a water bath as shown in the fig.,

The bridge is balanced by adjusting the variable resistance box. The resistance in the third arm R gives the resistance of the thermistor at room temperature. Similarly the resistance is found at various temperatures in steps of 50C of the water bath. After that the water bath is cooled and resistance of the thermistor is found again at the temperature at which the resistance are found while heating. The average resistance at each step is calculated. The values are tabulated as follows:

Formula for Energy gap Eg=(2.303 x 2 KB (dy/dx) )/1.6 x 10 -19 eV KB =Boltzmann’s constant(1.38 x 10 -23) JK-1 dy/dx = Slope Value

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Tabular column.

S.No Temp.ºC. Resistance Mean

Resistance (R) Ω

Log10R 1/T ºK-1 Increasing Temp (Ω)

Decreasing Temp (Ω)

Result: The resistance temperature characteristics of the thermistor is studied and a graph is also drawn.

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11. LOGIC GATES (Using Discrete Components)

Aim :

To verify the truth tables of logic gates OR, AND, NOT, NAND, and NOR gates using Discrete Components(Diode, Transistor and Resistance). Apparatus required:

1. Diode IN4001, Transistor (BC507), Resistances 1 K and 2.2 K 2. Bread Board 3. 5 volts Power Supply.

Procedure

• Connect the components to 5 volts power supply as per the circuit. • Implement the logic as per the truth table . • Record the readings

OR – Gate

Input Output Output Voltage(V)

A B Y = A + B Y = A + B

0 0 0 0 1 1 1 0 1 1 1 1

AND – Gate

Input Output Output Voltage(V)

A B Y = A.B Y = A .B

0 0 0 0 1 0 1 0 0 1 1 1

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NOT – Gate

Input Output Output Voltage(V)

A Y = A Y A= 0 1 1 0

NAND – Gate

Input Output Output Voltage

(V) A B Y = A.B Y = A.B

0 0 1 0 1 1 1 0 1 1 1 0

NOR – Gate

Input Output Output Voltage(V)

A B Y A B= + Y A B= +

0 0 1 0 1 0 1 0 0 1 1 0

Result:

The truth tables of the gates OR, AND, NOT, NAND and NOR are Constructed using Discrete components and the outputs are verified.

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12. ULTRASONIC INTERFEROMETER - ULTRASONIC VELOCITY IN LIQUIDS

Aim

To determine the velocity of Ultrasonic Waves in water and in the given liquids using Ultrasonic interferometer and to calculate the adiabatic compressibility. Instruments Required

Ultrasonic Interferometer arrangement, measuring cell, given liquid etc.

Fig. Micrometer with cell

Procedure The measuring cell is cleaned and then filled with experimental liquid up to the brim and micrometer is fitted into the cell. The RF oscillator is switched on and allowed to warmup for sometime to achieve the thermal equilibrium for the electronic components. When the micrometer screw is operated (move either upwards or downwards), the pointer in the micrometer of the interferometer shoots up to a maximum and falls to minimum repeatedly. This is due to the reflected wave falling on the crystal in phase or out of phase. The micrometer reading for first maximum is noted as ‘n’. The micrometer is moved in the same direction and after 10th maxima reading is noted as ‘n + 10’. This procedure is repeated at intervals of 10 maxima up to n + 60 and the readings are tabulated. A

Micrometer

Reflecto

Crystal

Transduc

Outlet

Inlet

To the output of the generator

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shift for 20 maxima is also calculated using the same procedure and the average distance ‘d’ is calculated. Then the ultrasonic velocity and the adiabatic compressibility of the liquid is calculated using the formula given below: Formula (i). Wavelength λ = 2d/n m. where d is the distance moved for ‘n’ maxima. (ii). Velocity v = ν λ m/sec where ν is the frequency of the oscillator in MHz.( 2 MHz) (iii). Adiabatic compressibility β = 1 / (v2ρ) m2/N Where ρ is the density of the liquid in Kg/m3.

Liquid Order of maxima

Micrometer Reading (mm)

Distance for each

Maxima (d) (mm)

Wavelength (λ) mm

Velocity (v) m/s

Water

n

n+1

n+2

n+3

n+4

n+5

n+6

Mean =

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Liquid Order of maxima

Micrometer Reading (mm)

Distance for each

Maxima (d) (mm)

Wavelength (λ) mm

Velocity (v) m/s

Toluene

n

n+1

n+2

n+3

n+4

n+5

n+6

Mean =

Result

The Ultrasonic velocity and adiabatic compressibility of the given liquids are calculated. 1. (a). Ultrasonic velocity in water =……………….m/s (b). Ultrasonic velocity in =……………….m/s 2. (c). The adiabatic compressibility of water =……………….m2/N (d). The adiabatic compressibility of =……………….m2/N

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13. FOUR PROBE METHOD – MEASUREMENT OF RESISTIVITY OF MATERIAL

Aim:

To study the variation of resistivity with temperature and determine the energy band gap of a semiconductor using four probe method Apparatus Required

Four probe arrangement, oven, thermometer, sample semiconductor crystal,voltmeter, ammeter, connecting leads. Theory The Ohm's law in terms of the electric field and current density is given by the relation

E = ρ J where ρ is electrical resistivity of the material. For a long thin wire-like geometry of uniform cross-section or for a long parellelopiped shaped sample of uniform cross-section, the resistivity ρ can be measured by measuring the voltage drop across the sample due to flow of known (constant) current through the sample. This simple method has following drawbacks: • The major problem in such method is error due to contact resistance of measuring leads. • The above method can not be used for materials having irregular shapes. • For some type of materials, soldering the test leads would be difficult. • In case of semiconductors, the heating of sample due to soldering results in injection of impurities into the material thereby affecting the intrinsic electrical resistivity. Moreover, certain metallic contacts form schottky barrier on semiconductors. To overcome first two problems, a collinear equidistant four-probe method is used. This method provides the measurement of the resistivity of the specimen having wide variety of shapes but with uniform cross-section. The soldering contacts are replaced by pressure contacts to eliminate the last problem discussed above.

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In this method, four pointed, collinear, equi- spaced probes are placed on the plane surface of the specimen (Figure 1). A small pressure is applied using springs to make the electrical contacts. The diameter of the contact (which is assumed to be hemispherical) between each probe and the specimen surface is small compared to the spacing between the probes. Assume that the thickness of the sample d is small compared to the spacing between the probes s (i.e., d << s). Then the current streamlines inside the sample due to a probe carrying current I will have radial symmetry, so that

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Figure 2: Four probe circuit

Formulae The resistivity of the semiconductor crystal is given by

Where

d is the thickness of the crystal V is the voltage across the crystal I is the current through the crystal

The energy gap is Eg of semiconductor crystal is given by

where k is Boltzmann constant = 8.6 × 10−5 J / K and T is temperature in Kelvin. Precautions 1. All four probes should be in contact with crystal surface. 2. Current through the crystal should remain constant through out the experiment. 3. Temperature of oven should not be increased beyond 130 0 C.

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Procedure 1. Connect the outer pair of probes leads to the constant current power supply and inner pair to the voltage terminals. 2. Place the four probe arrangement in the oven and fix the thermometer in the oven through the hole provided. 3. Switch on the power supply and keep the digital panel meter in the current measuring mode through the selector switch. In this position the LED facing mA would glow. Adjust the current to a desired value. 4. Now change the digital panel meter in the voltage measuring mode. In this position the LED facing mV would glow and the meter would read the voltage between inner probes. 5. Connect the oven supply, the rate of heating may be selected with the help of a switch. 6. Increase temperature of the oven upto 1300C and then switch off the oven. 7. The temperature of the oven will decrease automatically. Now, measure the voltage in the digital panel meter four various values of temperatures with a difference of 500C. 8. Record the observations till the temperature of the oven reaches to the room temperature. Observations Distance between the probes (S): 2.5 mm Thickness of the crystal (d): 0.05 mm Current through the crystal (I)=-----------------------mA Table S.No Temp

(C) Temp (K)

1000/T Voltage V (mV)

Log 10 ρ

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Calculations 1. Draw a graph between 1000/T versus log 10 ρ . 2. Find the slope of the curve plotted in step 1 i.e. obtain the value of

3. The energy band gap Eg of semiconductor crystal is calculated by

Result : The bandgap of the given semiconductor is Eg=………………….eV