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Engineering Physics Lab Manual Dept of H&S

ENGINEERING PHYSICS LAB MANUAL

DEPARTMENT OF H&S

Document No:

MLRIT/H&S/I/OGRIS/I.5/

ASUCF/LAB MANUAL/

ENG PHY/2014-2015/VERSION 1.4

Date of Issue

August -2014

Date of Revision

August-2014

Compiled by

Dr.V.Radhika Devi

Verified by

Ms.HariniChandra, Ms.Jyothi, Ms.Hari kamala sree, N. Noel, G. Prashanthi, M. Lakshmi Nadh

Authorized by

HOD(H&S)

Name of the student :

Name of the Branch :

Roll no :

Academic Year :


Instructions for Laboratory …03

Bibliography ...04

EXPERIMENTS

1: Study the characteristics of solar cell ...05

2: Determination of wavelength of a laser source-Diffraction Grating ...10

3: Newton’s Rings-Radius of curvature of Plano convex lens …14

4: Melde’s Experiment – Transverse and Longitudinal Modes …19

5: Time Constant of RC Circuit …23

6: Resonance in LCR circuit ...26

7: Magnetic field along the axis of current carrying coil (Stewart & Gees method) ...33

8: Study the Characteristics of LED ...37

9: Bending Losses in Optical fiber and Evaluation of Numerical Aperture of a given fiber …39

10: Energy gap of a material of p-n junction …45

11: Torsional pendulum …48

CONTENTS


Instructions for Laboratory

The objective of the laboratory is learning. The experiments are designed to illustrate

phenomena in different areas of Physics and to expose you to measuring instruments.

Conduct the experiments with interest and an attitude of learning.

You need to come well prepared for the experiment

Work quietly and carefully (the whole purpose of experimentation is to make reliable

measurements!) and equally share the work with your partners.

Be honest in recording and representing your data. Never make up readings or doctor

them to get a better fit for a graph. If a particular reading appears wrong repeat the

measurement carefully. In any event all the data recorded in the tables have to be

faithfully displayed on the graph.

All presentations of data, tables and graphs calculations should be neatly and carefully

done.

Bring necessary graph papers for each of experiment. Learn to optimize on usage of

graph papers.

Graphs should be neatly drawn with pencil. Always label graphs and the axes and

display units.

If you finish early, spend the remaining time to complete the calculations and drawing

graphs. Come equipped with calculator, scales, pencils etc.

Do not fiddle idly with apparatus. Handle instruments with care. Report any breakage

to the Instructor. Return all the equipment you have signed out for the purpose of your

experiment.


Bibliography

Here is a short list of references to books which may be useful for further reading

in Physics or instrumentation relevant to the experiments. Also included are some

references to books of general interest with regard to science and experimentation.

1. "Fundamentals of Physics", 6th Ed., D. Halliday, R. Resnick and J. Walker, John

Wiley and Sons, Inc., New York, 2001.

2. "Physics", M. Alonso and E.J. Finn, Addison Wesley, .1992.

3. "The Feynman Lectures in Physics (Vols. 1, 11 and 111)", R.P. Feynman, R.B.

Leighton and M.Sands, Addison Wesley, 1963.

4. "Fundamentals of Optics", 4th Ed., F.A. Jenkins and H.E. White, McGraw-Hill

BookCo., 1981.

5. "Optics", A Ghatak, Tata-McGraw Hill, New Delhi, 1992

6. "Vibration and Waves", A.P. French, Arnold-Heinemann, New Delhi, 1972.

7. "Students Reference Manual for Electronic Instrumentation Laboratories", S.E.

Wolf and R.F.M. Smith, PHI, 1990.

8. "Basic Electronic Instrument Handbook", C.F. Coombs, McGraw-Hill Book Co.,

1972.

9. "Laboratory Experiments in College Physics", C.H. Bernard and C.D. Epp, John

Wiley and Sons, Inc., New York, 1995.

10."Practical Physics", G.L. Squires, Cambridge University Press, Cambridge,

1985.

11."Great Experiments in Physics", M.H. Shamos, Holt, Rinehart and Winston Inc.,

1959.

12."Experiments in Modern Physics", A.C. Melissinos, Academic Press, N.Y., 1966.

13."Reliable Knowledge", J.Ziman, Cambridge University Press, Cambridge, 1978.

14."Introductory Readings in the Philosophy of Science", Edited by E.D. Klenke, R. Hollinger, A.D. Kline, Prometheous Books, Buffalo, New York, 1988


Experiment-1

LASER-Diffraction Grating

Aim:- To determine the wavelength of laser light using Diffraction

Grating.

Apparatus Required:

He- Ne Laser, a diffraction grating, scale, stand and a screen.

Theory And Formula Used: A diffraction grating is an optical device which

produces spectra to diffraction. It has a large no. of lines grooved on it. The

spectra consisting of different orders is governed by the relation-

d.Sin n.The no. of lines on the grating is-

d 2.54

15000

Wavelength of the laser light is –

d.Sin

n

Where d= grating constant

n=1, 2… (Order of spectra)


Procedure:

1. Diode laser is mounted on its saddle.

2. A plane transmitting grating is mounted on an upright next to laser.

3. The position of x of the spot of 1st order on either side of central

Maxima is marked.

4. The distance D between the grating and screen.

Observation Table:

S. No.

D in cm. Order

Distance x cm. Mean

x cm. x2 D

2 Sin x

x2D

2L.H.S R.H.S

1.

2.

3.

CALCULATION:

d.Sin n

Where d= grating constant

n=1, 2… (Order of spectra)

Percentage Error:-

(Standard value ~ observed Value) *100

% ERROR =

Standard Value

Precautions:

1. Direct viewing of laser light should be avoided.

2. Proper alignment of the laser diode must be done.

3. Before switching any other source, switch on the laser diode.

Result:

1. The wavelength of the given LASER beam is …………………

Engineering Physics/Chemistry Lab H & S Dept

M L R I n s t i t u t e o f T e c h n o l o g yL L E G E

Experiment -2 V-I Characteristics of Solar Cell

AIM: Study of V-I characteristics of photo voltaic cell.

APPRATUSREQUIRED: Powersupply, PVC characteristic Kit, connectingleads,Voltmeter, Ammeter.

THEORY: The silicon solar cell converts the radiant energy of the sun into electricalpower.Thesolarcell consist of a thin slice of single crystal p-type silicon, unto 2cmsquare, into which a very thin(0.5micron) layer of n-type material is diffused. Theconversion efficiency depends on the spectral content & the intensity of the illumination.

PROCEDURE:1. Connect the circuit as shown in figure.

2. Switch on the power supply.

3. Vary the value of input dc supply in steps.

4. Note down the ammeter & voltmeter readings for step.

5. Plot the graph of Voltage Vs Current

6. Plot the graph of Power Vs Current

CIRCUITDIGRAM:



OBSERVATION TABLE:

S.No Voltage(Volts) Current(mA) Power(watts)

GRAPH:



RESULT: The V-I characteristics of photo– voltaic cell has been plotted.

PRECAUTIONS:

1. Always connect the voltmeter in parallel & ammeter in series as showing fig.2. Connection should be proper &tight.3. Switch ‘ON’ the supply after completing the ckt.4. DC supply should be increased slowly in steps5. Reading of voltmeter & Ammeter should be accurate.

Viva voce questions:

Q1: What are photo voltaic cells?A. These cells are semiconductor junction devices used for convertingradiation energy into electrical energy.Q2: Which material is most commonly used for these cells?A. Selenium &Silicon.Q3: What are advantages of these cells?A. They have ability to generate voltage without any bias & have fastresponse.



Experiment 3Newton’s Rings

Aim:

To observe Newton rings formed by the interference produced by a thin air film and to determine

the radius of curvature of a plano-convex lens.

Apparatus:

Traveling microscope, sodium vapour lamp, Plano-convex lens, plane glass plate, magnifying

lens.

I. Introduction:

I.1 The phenomenon of Newton’s rings is an illustration of the interference of light waves reflected from

the opposite surfaces of a thin film of variable thickness. The two interfering beams, derived from a

monochromatic source satisfy the coherence condition for interference. Ring shaped fringes are produced

by the air film existing between a convex surface of a long focus plano-convex lens and a plane of glass

plate.

I.2. Basic Theory:

When a Plano-convex lens (L) of long focal length is placed on a plane glass plate (G) , a thin film of air

I enclosed between the lower surface of the lens and upper surface of the glass plate.(see fig 1). The

thickness of the air film is very small at the point of contact and gradually increases from the center

outwards. The fringes produced are concentric circles. With monochromatic light, bright and dark

circular fringes are produced in the air film. When viewed with the white light, the fringes are coloured.

A horizontal beam of light falls on the glass plate B at an angle of 450. The plate B reflects a part of

incident light towards the air film enclosed by the lens L and plate G. The reflected beam (see fig 1) from

the air film is viewed with a microscope. Interference takes place

and dark and bright circular fringes are produced. This is due to

the interference between the light reflected at the lower surface

of the lens and the upper surface of the plate G.



For the normal incidence the optical path difference

Between\ the two waves is nearly 2µt, where µ is the refractive

index of the film and t is the thickness of the air film. Here an extra phase difference π occurs for the ray

which got reflected from upper surface of the plate G because the incident beam in this reflection goes

from a rarer medium to a denser medium. Thus the conditions for constructive and destructive

interference are (using µ = 1 for air)

2 t = n for minima; n = 0, 1, 2, 3… … … … (1)

and 1

22

t n

for maxima; ; m = 0,1,2,3… … …(2)

Then the air film enclosed between the spherical surfaces

Of R and a plane surface glass plate, gives circular rings

such that (see fig 2)

rn2 = (2R-t)t

where rn is the radius of the nth order dark ring . Fig.2

(Note: The dark ring is the nth dark ring excluding the central dark spot).

Now R is the order of 100 cm and t is at most 1 cm. Therefore R>>t. Hence (neglecting the t2 term),

giving

2

2 nrtR

Putting the value of “ 2 t” in equn(1) gives 2

2 nr

R

With the help of a traveling microscope we can measure the diameter of the nth ring order dark ring = Dn

Then2

mn

Dr and hence,

2 1

4nD

Rn

The value of 2nD

nis calculated from the slope of the graph drawn in between n Vs

R = (Dm2-Dn

2)/4 (n-m) or 4

SlopeR

So if we know the wavelength , we can calculate R(radius of curvature of the lens).



II. Setup and Procedure:

1. Clean the plate G and lens L thoroughly and put the lens over the plate with the curved surface

below B making angle with G(see fig 1).

2. Switch in the monochromatic light source. This sends a parallel beam of light. This beam of light

gets reflected by plate B falls on lens L.

3. Look down vertically from above the lens and see whether the center is well illuminated. On

looking through the microscope, a spot with rings around it can be seen on properly focusing the

microscope.

4. Once good rings are in focus, rotate the eyepiece such that out of the two perpendicular cross

wires, one has its length parallel to the direction of travel of the microscope. Let this cross wire

also passes through the center of the ring system.

5. Now move the microscope to focus on a ring (say, the 20th order dark ring). On one side of the

center. Set the crosswire tangential to one ring as shown in fig 3. Note down the microscope

reading .

fig 3 _

(Make sure that you correctly read the least count of the vernier in mm units)

6. Move the microscope to make the crosswire tangential to the next ring nearer to the center and

note the reading. Continue with this purpose till you pass through the center. Take readings for an

equal number of rings on the both sides of the center.

Observations and results:

1. Least count of vernier of traveling microscope = ___________________mm



2. Wave length of light = _______________________ m

Table 1: Measurement of diameter of the ring

S.No Order of the

ring (n)

Microscope reading DiameterLeft side Right side

MS VS Net(cm) MS VS Net(cm) D(cm) D2 (cm2)12345678910

Precautions:Notice that as you go away from the central dark spot the fringe width decreases. In order to minimize the

errors in measurement of the diameter of the rings the following precautions should be taken:

i) The microscope should be parallel to the edge of the glass plate.

ii) If you place the cross wire tangential to the outer side of a perpendicular ring on one side of the

central spot then the cross wire should be placed tangential to the inner side of the same ring on

the other side of the central spot.(See fig 3)

iii) The traveling microscope should move only in one direction

Calculations:

Plot the graph of D2 Vs n and draw the straight line of best fit.

Give the calculation of the best fit analysis below. Attach extra sheets if necessary.

From the slope of the graph, calculate the radius of curvature R of the plano convex lens as

4

SlopeR

= ____________________________ cm.

Results: The radius of curvature of the given plano-convex lens = cm

(One graph paper required).




1. What is meant by radius of curvature?

2. What is the principle behind the formation of Newton’s rings?

3. What is meant by phase shift?

4. What is the relation between phase difference and path difference?

5. What happens if the lower glass plate is replaced by another convex lens?

6. What is meant by reflection and refraction?

7. What is the nature of central fringe?

8. Under what conditions the central fringe will be bright or dark?

9. What is the purpose of inclined glass plate?

10. What is meant by back lash error?

11. What is coherence?



EXPERIMENT 4

Melde’s Experiment

Aim:

To determine the frequency of AC mains by Melde’s experiment.

Apparatus:

• Electrically maintained tuning fork, A stand with clamp and pulley, A light weight pan, A weight box,

Analytical Balance, A battery with eliminator and connecting wires etc.

Theory:

STANDING WAVES IN STRINGS AND NORMAL MODES OF VIBRATION:

When a string under tension is set into vibrations, transverse harmonic waves propagate along its

length. When the length of string is fixed, reflected waves will also exist. The incident and reflected

waves will superimpose to produce transverse stationary waves in the string.

The string will vibrate in such a way that the clamped points of the string are nodes and the point

of plucking is the antinode.

Figure 2. The Envelope of a standing waves

A string can be set into vibrations by means of an electrically maintained tuning fork, thereby

producing stationary waves due to reflection of waves at the pulley. The loops are formed from the end of

the pulley where it touches the pulley to the position where it is fixed to the prong of tuning fork.

(i) For the transverse arrangement, the frequency is given by



1

2

Tn

L m

where ‘L’ is the length of thread in fundamental modes of vibrations, ‘ T ’ is the tension applied to the

thread and ‘m’ is the mass per unit length of thread. If ‘p’ loops are formed in the length ‘L’ of the thread,

then

2

P Tn

L m

(ii) For the longitudinal arrangement, when ‘p’ loops are formed, the frequency is given by

P Tn

L m

Procedure:

Find the weight of pan P and arrange the apparatus as shown in figure.

Place a load of 4 To 5 gm in the pan attached to the end of the string

Passing over the pulley. Excite the tuning fork by switching on the power supply.

Adjust the position of the pulley so that the string is set into resonant

Vibrations and well defined loops are obtained. If necessary, adjust

The tensions by adding weights in the pan slowly and gradually. For finer adjustment, add

milligram weight so that nodes are reduced to points.

Measure the length of say 4 loops formed in the middle part of the string. If ‘L’ is the distance in

which 4 loops are formed, then distance between two consecutive nodes is L/4.

Note down the weight placed in the pan and calculate the tension T.

Tension, T= (wt. in the pan + wt. of pan) g

Repeat the experiment twine by changing the weight in the pan in steps of one gram and altering

the position of the pulley each time to get well defined loops.

Measure one meter length of the thread and find its mass to find the value of m, the mass

produced per unit length.

OBSERVATIONS AND CALCULATIONS::::

For longitudinal arrangementMass of the pan, w =……… gm

Mass per meter of thread, m =……… gm/cm



Frequency P T

nL m

S.No. Weight (W) gms

No. of loops (p)

Length of thread (L) cms

Length of each loop (L/P) cms

Tension (T) (W+w) gms

Frequency (n) Hzs

123456

Mean frequency= ---------------- Hzs

For transverse arrangement

Mass of the pan, w =……… gm

Mass per meter of thread, m =……… gm/cm

Frequency 2

P Tn

L m

S.No. Weight (W) gms

No. of loops (p)

Length of thread (L) cms

Length of each loop (L/P) cms

Tension (T) (W+w) gms

Frequency (n) Hzs

123456

Mean frequency= ---------------- Hzs

PRECAUTIONS: The thread should be uniform and inextensible. Well defined loops should be obtained by adjusting the tension with milligram weights. Frictions in the pulley should be least possible.



RESULT

The frequency of given Electrical Tuning fork in

Transverse Mode = Hz

Longitudinal Mode = Hz


1. What are stationary waves? Give some examples

2. What are different modes of vibration?

3. What are nodes and antinodes?

4. What is the relation between frequency and length of the string?

5. What happens to the frequency if the tension ‘T’ increases?

6. What is meant by linear mass?

7. What is the frequency of A.C. mains?

8. If the mass is increased, what happens to the number of loops formed?

9. What is the importance of pulley in this experiment?

10. What is the nature of the thread in this experiment?



EXPERIMENT NO.5

TIME CONSTANT OF AN R-C CIRCUIT

AIM : To study the growth and decay of charge in an RC circuit and determine the value of time constant.

Apparatus: Battery, High resistance, Condenser, Voltmeter, Stopclock etc.

THEORY: A resistor capacitor circuit or RC filter or RC network, is an electric circuit composed of resistors and capacitors driven by a voltage or current source. Consider a circuit having a d.c. source and a capacitance in series with a resistance. When the source is switched on, the process of energy storage starts and the circuit voltage and current builds up gradually rather than instantly. When the capacitor has stored the energy to its full value, the circuit voltage and current do not change with time any more and the circuit is said to have acquired steady state response. When the source is switched off, the energy stored in the capacitor releases gradually and it does not permit the circuit voltage and current to fall abruptly to zero, but takes a finite time. During the process of storage or decay of energy, the circuit is said to be in a transient state. During transient state variation of voltage and current depends on circuit parameters.

A R.C. circuit with resistance R and capacity C is shown in the fig. When the condenser is receiving charge from the battery through the resistance R, the charge of the condenser increases with time as an exponential function. If q is the charge at time t,

Q = Q0 ( 1 – )

The product RC is the time constant of the circuit. It is time taken by the charge to grow to (1-e-

1) i.e. 0.638 times the final value.

The decay of charge of the condenser in RC circuit is given by Q = Q0

The time constant is equal to the time taken by the charge to decrease to e-1 of the maximum charge.Charge Q = capacity x potential difference = CV



PROCEDURE : RC board is used in this experiment as shown in fig. The experiment is performed in two parts i) charging and ii) discharging.

Charging

1. Rig up the circuit as per fig.

2. Press the switch ‘S’ and start the clock simultaneously. The interval of time can be selected according to convenience from 0.5 sec to 10 sec.

3. Note the voltmeter reading at regular intervals of time and also note the maximum voltage Vo (at which voltage becomes constant).

4. Plot the graph between time (t) and voltage (v).

5. From the graph identify the time constant, the time corresponding to 0.638

Discharging

1. Release the switch ‘S’ after attaining Vo.

2. Start the stop clock and note the voltmeter readings at regular intervals of time.

3. Plot the graph between time (t) and voltage (v).

4. From the graph identify the time constant, the time corresponding to 0.367 Vo voltage

Value

TABULAR FORM

R=_________; C=-----------------------

S

No.Time ‘t’ sec

Voltage(v)

Charging Discharging



The experiment can be repeated for different sets of resistors and capacitors at different time intervals.

PRECAUTIONS

1. There should not be any leakage of charge.

2. The readings should be note down so carefully.

RESULT

The growth and decay of charge in RC circuit is studied and the time constant while charging is -------------- and that of discharging is …………


1. What is meant by time constant?

2. What is the relation between charge ’Q’ and capacitance ‘C’?

3. What is transient state?

4. What is the expression for energy stored in a capacitor?

5. Physically how can we identify the value of resistance of a resistor?

6. What is unit of resistance, capacitance?

7. What is the relation between voltage and current?

8. What happens to time constant if the resistance value is doubled?

9. How is the time constant determined in this experiment?



EXPERIMENT NO.6

LCR CIRCUIT

AIM : To study the frequency response characteristics of LCR series and parallel circuits and to determine the quality factor.

Apparatus: Resistors, Capacitors, Inductors, AC ammeter etc.

L1 = 40 mH , L2= 70 mH , L3=100 mH, C1= 0.0047F, C2=0.33 F, C3 = 0.1F R1 = 680KΩ , R2 = 1KΩ , R3 = 2.2KΩ

THEORY: An RLC circuit (also known as a resonant circuit, tuned circuit, or LCR circuit) is an electrical circuit consisting of a resistor (R), an inductor (L) and a capacitor (C) connected in series or in parallel. This configuration forms a harmonic oscillator.

Tuned circuits have many applications particularly for oscillating circuits and in radio and communication engineering. They can be used to select a certain narrow range of frequency from total spectrum of ambient radio waves.

There are two fundamental parameters that describe the behavior of RLC circuits. The resonant frequency and attenuation (or, alternatively, damping factor).

Resonance : A circuit is said to be resonant when a sinusoidal e.m.f. with a frequency equal to the natural frequency of the circuit is applied to it. In A.C. circuits, however, the voltage and current are usually out of phase. Under certain conditions, however, the current and voltage may be in phase and the circuit behaves as a pure resistance. This phenomenon is called resonance.

The un damped resonant frequency of an RLC series or parallel circuit is given by

fo = ω0 /2π =1/2π

Attenuation is defined as = for series RLC circuit and = for parallel circuit.

Damping factor is the ratio of the attenuation to the resonant frequency o.

Bandwidth : The RLC circuit may be used as band pass or band stop filter by replacing R with a receiving device with the same input resistance. In the series case bandwidth is



f =ω/2π = α/ π = ω0 /π = R/2π L

The bandwidth is a measure of the width of the frequency response at the two half power frequencies. As a result, this measure of bandwidth is sometimes called the full width at half power. Since electrical power is proportional to the square of the circuit voltage (or current), the frequency response will drop to

at the half power frequencies.

Quality factor Q : The degree of selectivity or the sharpness of resonance is expressed in terms of the symbol Q, known as quality factor, which is defined by

Q = ω0 / (ω2 - ω 1)= ω0/ω=f0/f

SERIES RESONANCE

Fig 1. Shows the circuit of series resonance consisting of capacitor in series with the coil.

Fig1. Series resonant circuit Fig2. Parallel resonant circuit.

Following points about the circuit are worth noting

The circuit current is maximum and is given by Im = V/R

The circuit offers minimum impedance Zmin = R

The circuit behaves like a pure resistive circuit and has a power factor of unity. Voltage drop VL and Vc are maximum and equal in magnitude but cancel out since they are 1800 out of phase with each other.

Resonant frequency is given by fo =



PARALLEL RESONANCE: Fig 2. Shows the circuit consisting of a capacitor in parallel with a coil of negligible small resistance. When fed from an ac voltage, the capacitor draws a leading current whereas coil draws a lagging current. This circuit resonates to a frequency which makes XL = XC, so that the two branches are equal but opposite. Hence, they cancel out with the result that current drawn from the supply is zero. In practice however line current drawn is not zero but has minimum value due to small resistance R of the coil. Since current drawn by the circuit is minimum, it means it offers maximum impedance to the applied voltage under resonant condition.

PROCEDURE

SERIES RESONACE

1. Rig up the circuit as per fig1.

2. Apply the input signal from a reliable signal generator. Adjust the output voltage of the signal generator to 10v.

3. Feed the output of the circuit to the input sockets of the AC ammeter.

4. Vary the frequency of the signal generator till the deflection is the maximum possible. This is the resonant frequency of the connected combination of the circuit.

5. Adjust the amplitude of the signal generator to get full-scale deflection. Now reduce the frequency till the deflection falls considerably. Then increase the frequency in regular intervals and note down the deflection.

6. Repeat the procedure using different values of frequency and study how Q is affected. Also study how resonant frequency depends upon different combinations of L.C.R.

PARALLEL RESONANCE

1. Rig up the circuit as per fig2.

2. Apply the input signal from a reliable signal generator. Adjust the output of the signal generator to 10v.

3. Take the output across the tank circuit and feed to the input sockets of the AC ammeter.

4. Vary the frequency till the ammeter records sharp rise. Adjust the signal such that the deflection falls down considerably. Then increase the frequency in regular intervals and note down the deflection.

5. Adjust the amplitude of the signal generator to get full-scale deflection. Now reduce the frequency till the deflection falls considerably. Then increase the frequency in regular intervals and note down the deflection.



6. Repeat the procedure using different values of L-C-R and study how Q is affected. Also study how resonant frequency depends on different combinations of L.C.R.

7. Plot the graph for ammeter deflection vs frequency.

TABULAR COLUMN

Series circuit : L = henries C = farads

Table1

S.No. Frequency F

Output current ( Iout)

R1 = 680K R2 = 1 K R3 = 2.2 K

Table2

S.No. Resistance Resonant frequency fo

from graph

Band width Q = fo / Lo/R

Average fo =

Calculated value of fo from the formula fo = = Hz

Parallel circuit : L = Henries C = farads R = ohms



Table 3

S.No. Frequency (f) Output current Iout

CALCULATIONS

Series resonance parallel resonance

Im = V\R Io =

Zmin = R fo =

fo = Q0 = 2π foL/R

B.W. = f = f2 –f1 = fo/Qo



PRECAUTIONS

1. The output voltage of the signal generator should be kept constant for every frequency.

2. The readings should be taken on either side of fo.

3. R should be less in series circuit and it should be very large in parallel circuit.

4. R should be 10 times the output impedance of the signal generator.

MODAL GRAPHS:

Graph 1. Series resonance Graph2. Parallel resonance

RESULT :

The resonant frequency = Hz




1. What is meant by series and parallel combination of LCR circuit?

2. What is meant by resonance?

3. What is Q factor?

4. What is band-width?

5. What is meant by attenuation?

6. What is damping factor?

7. What is meant by lower cut off frequency and upper cut off frequency?

8. What happens to the resonant frequency if the values of L, C, and R are doubled?

9. At resonant frequency, what is the nature of current in series and in parallel combination?

10. What is impedance and acceptance?

11. What is the phase relationship between voltage and current?



EXPERIMENT NO.7

MAGNETIC FIELD ALONG THE AXIS OF CURRENT CARRYING COIL –STEWART AND GEES APPARATUS.

AIM: To study the variation of magnetic field with distance on the axis of a circular coil carrying current.

Apparatus: Stewart Gee type Galvanometer, Battery, Plug key, Commutator, Rheostat, Ammeter etc.

THEORY: There was a time when magnetism was regarded as a separate branch of science having no connection with electricity. In 1820, Oersted discovered that a compass needle suffers a deflection when brought near a current carrying wire. According to Oersted’s experiment, a current conductor produces a magnetic field around it. Biot and Savart performed a series of experiments to study the magnetic field produced by various current carrying conductors. They obtained a relation by means of which B can be calculated at any point of space around a conductor in which a current is passing. The relation is called as Biot and Savart law.

Fig1. Shows a circular coil of radius ‘a’ and carrying current ‘i’ . P is a point on the axis of the coil distant ‘x’ from the centre. The magnetic field dB at point P due to current element AB of length dl is given by

dB = µ0i dl

4πr2

Fig .1 Fig.2 Fig.3

If there are N turns in the coil, then



B = µ0Nia2 / 2(a2+x2)3/2 weber/metre2

At the centre of the coil x = 0. Thus at the centre of the coil B = µ0Ni / 2a

The variation of the field B along the axis of the coil is represented in fig2.

The Stewart and Gee galvanometer is shown in fig3. Its construction resembles that of a tangent galvanometer and deflection magnetometer. It consists of a circular coil in a vertical plane fixed to a horizontal bench at its middle point. The ends of the coil are connected to binding screws.

A magnetic compass box is arranged such that it can slide along the horizontal scale passing through the centre of the coil. The length of the scale is perpendicular to the plane of the coil. The compass box consists of a short magnetic needle and a long aluminium pointer attached at its mid point at the centre of a horizontal circular scale. The circular scale consists of four quadrants each of which measures angles from 00 to 900 . A plane mirror is provided below the pointer so that deflections can be observed without parallax.

PROCEDURE : The circuit is constructed as shown in Fig.3

1. The primary adjustments of the instrument are made. The coil of the instrument is set along the magnetic meridian. The aluminium pointer is made to read 00-00 with no current.

2. The ends of the coil are connected to the commutator and through it to a battery rheostat and ammeter. When the circuit is closed with plug key, a current flows through the circular coil.

3. A magnetic field is produced on the axis of the coil. The magnetic needle in the compass is subjected to the horizontal component of earth’s magnetic field (H) and magnetic field (B) due to the circular coil carrying current. Those two magnetic fields are acting at right angles to each other. The magnetic needle dings along the direction of resultant magnetic field. The magnetic

needle is deflected through an angle from the direction of (H) the horizontal component of

earth’s magnetic field. F = tan.

4. The current in the circuit is adjusted such that the deflection lies between 300 and 600 using rheostat.

5. The compass box is displaced by 5 cm or 10 cm along the horizontal seal and the deflection of the needle is measured at every distance by reading both the ends of the pointer. Let the readings be

1 and 2.

6. The readings 3 and 4 are observed after reversing the direction of the current.

7. The experiment is repeated on the other side of the coil.



8. A graph is drawn with tan along Y-axis and distance ‘x’ from the centre of the coil along X-axis. This graph shows the variation of magnetic field on the axis of a circular coil with distance. It is symmetrical about Y-axis and magnetic field is maximum at the centre of the coil.

Table:

H=30.23μ0 N/A.m ,Where μ0=4π*10-7 N/A2

S.No

Position Magnetomain

Distance ‘x’

Deflection Average

Tan F = H tan F= µ0Nia2

2(a2+x2)3/21 2 3 4

Left( ----)West of the coil

Right( +)East of the coil



MODEL GRAPH

PRECAUTIONS

1. Galvanometer should not be disturbed after making primary adjustments.

2. The deflection should be observed without parallax.

3. The current measured in amperes is converted into e.m.u. and used in the formula.

RESULT

The variation of magnetic field with distance along the axis of a circular coil carrying current is studied and is found that B is greatest at the centre of the coil where x=0 and decreases on both sides as we move away from the centre.


1. What is Faraday’s law?

2. What is Biot Savart’s Law?

3. What is magnetic permeability?

4. What happens to the value of magnetic field at a point ‘P’ if the radius of the coil is halved?

5. What is the purpose of a plane mirror in the deflection magnetometer?

6. What is the value of ‘B’ at the centre of the coil i.e. at x=0?



7. What is the unit of ‘B’?

8. What happens to the value of ‘B’ if the current value is doubled?

9. What is magnetic filed?

10. What is the purpose of using a rheostat in this experiment?



EXPERIMENT NO.8

STUDY OF CHARACTERISTICS OF LED SOURCE

AIM: To study the characteristics of LED (Light Emitting Diode).

Apparatus: LED characteristic apparatus consisting of two meters to measure voltage and current , Connecting wire etc.

THEORY: The Light Emitting Diode (LED) is a solid state source. LED’s have replaced incandescent lamps in many applications because they have the following advantages.

1. Low voltage

2. Long life ( more than 2 yrs)

3. Fast ON-OFF switching ( nanoseconds)

In a forward biased rectifier diode, free electrons and holes recombine at the junction. When a free electron falls into a hole, it drops from a higher energy level to a lower one. As the electron falls, it radiates energy in the form of heat and light. Because silicon is opaque (not transparent) none of the light escapes to the environment. A LED is different. To begin with, semitransparent materials are used instead of silicon. In a forward-biased LED, heat and light again are radiated when free electrons and holes recombine at the junction. Because the material is semitransparent, some of the light escapes to the surroundings. By using elements like gallium, arsenic, and phosphorous, a manufacturer can produce LED’s that radiate red, green, yellow, amber, or infrared light. LEDs that produce visible radiations are used in instrument displays, calculators, digital clocks, etc. The infrared LED finds application in burglar-alarm and other area requiring invisible radiation. LED’s have a typical voltage drop from 1.5V to 2.5V for currents between 10 and 50mA. Incidentally, LED’s have low reverse voltage ratings. For instance, the TIL 221, a red LED has a maximum reverse voltage rating 3V. This means accidentally applying a reverse voltage greater than 3V may destroy or degrade the LED characteristics.

PROCEDURE

1. Connect the 0-3V DC supply to input sockets. (Red terminal to Red terminal & Black terminal to Black terminal).

2. Connect the voltmeter and current meter to the circuit as shown in fig.



3. Switch ON the instrument using ON/OFF toggle switch provided on front panel.

4. Keep output potentiometer fully anticlockwise. 5. Vary the input voltage in small steps and note down the observations. 6. Plot a graph between voltage and current.

TABULAR COLUMN and CIRCUIT

PRECAUTIONS: 1.We have to increase the LED voltage gradually.

2. Readings should be note down without parallax error.

RESULT: The characteristics of LED are studied. And Knee Voltage = V


1. What is a LED?

2. How is a LED different from other light sources?

3. What is the difference between a rectifier diode and a LED?

4. What are the applications of LED’s?

5. What are the materials used in the manufacture of LED’s?

6. What is the precaution regarding applied voltage?

7. What is the principle involved behind the emission of light from LEDs?

8. If we increase the LED voltage what happened to LED current?

9. How can we classify the LEDs?

10.What is meant by Breakdown Voltage?

S.No. LED Voltage(V)

LED Current(µamp)



EXPERIMENT NO.9

BENDING LOSSES OF FIBER

AIM: To study various types of losses that occur in optical fibers and measure the loss in dB of two optical fiber patch cards.

Apparatus: Optical fibre trainer kit, Fiber patch cards,etc.

THEORY: Attenuation in an optical fibre is a result of a number of effects. Here attenuation in a fibre due to macro bending and losses in two patch cords is estimated.

The optical power at a distance L, in an optical fibre is given by PL = Po 10(-L/10) where Po is the

launched power and is the attenuation coefficient in decibels per unit length. The typical attenuation coefficient value for the fibre under consideration here is 0.3 dB per 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 fibre.

Typical losses at connector junctions may vary from 0.3dB to 0.5dB. Losses in fibers occur at fibre-fibre joints or splices due to axial displacement, angular displacement, separation (air gap), mismatch of core diameters, mismatch of numerical aperture, improper cleaving and polishing at the ends. The loss equation for a simple fibre optic link is given as

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 a splice or in-line adaptor

LF1B2 (db) is the loss in cable 2

LJ3 (db) is the loss at the connector-detector junction.

PROCEDURE

1. Connect one end of FO cable1 (1 meter) to the FO LED of the TNS20A and the other end to the FO PIN.



2. Set the DMM to the 2000mV range. Connect the DMM Vdc to P1 and the DMM common P2. Turn the DMM on. The power meter is now ready for use.

3. Plug the AC mains. Connect the optical fibre patch cord securely, as shown, after relieving all twists and strains on the fibre. Adjust the set Pout knob to set Po to a suitable value, say -15.0 dBm (the DMM will read 150mV). Note this as Po1.

4. Wind one turn of the fibre on the mandrel and note the new reading of power meter Po2. Now the loss due to bending and strain on the plastic fibre is Po1-Po2 dB. For more accurate readout set the DMM to the 200.0mV range and take the measurement. Typically the loss due to the strain and bending the fibre is 0.3 to 0.8 db.

5. Next remove the mandrel and relieve the cable of all twists and strains. Note the reading Po1 for cable1 (1meter cable). Repeat the measurement with cable2 (5 meter cable) and note the reading Po2. Use the in-line SMA adaptor and connect the cables in series. Note down the measurement Po3.

Po3-Po1 gives the loss in cable 2 + Loss in ILPo3-Po2 gives the loss in cable 1 + Loss in ILAssuming a loss of 1.0dB in the in-line adaptor we obtain the loss in each cable. The experiment may be repeated in the higher sensitivity range of 200.0mV.

TABULAR FORM

S.No. Po1 (dBm) Po2 (dBm) Po3 (dBm) Loss in cable1(dB)

Loss in cable 2(B)

Loss/meter(db)

1.

2.



3.

4.

PRECAUTIONS

1. Optical fiber cables should be connected appropriately.

2. Power meter values should be increased gradually.

RESULT

The loss in the fibre optic patch cards = dB


1. What is an optical fibre? What are the applications?

2. What is the principle of working of optical fibre?

3. What is meant by optical power of a fibre and how is it determined?

4. What is meant by attenuation? What is it’s unit?

5. What are the types of losses in fibers?

6. What is meant by bending loss?

7. What is numerical aperture?

8. What is the use of in-line adaptor in this experiment?

9. How can we classify the Optical fibers?



10. Which type of cable is used in this experiment?

EVALUATION OF NUMERICAL APERTURE OF GIVEN FIBER

AIM: To determine the numerical aperture of the PMMA fibre cables included in TNS20A.

Apparatus: Optical fiber kit, AC power adaptor, Numerical measurement jig, Scaled screen

THEORY: Fiber optics deals with the light propagation through thin glass fibers. The optical fibers are use as dielectric waveguides for guiding the electromagnetic waves at optical frequencies. The light is guided through transparent glass fibers by total internal reflection.

Numerical aperture (N.A.) of the fiber is the light collecting efficiency of the fiber and is the measure of the amount of light rays that can be accepted by the fiber.

Mathematically N.A. = (n1- n2)1/2

Where n1 is the refractive index of medium 1(core) and

n2 is the refractive index of medium 2(cladding

N.A. is the product of the refractive index of the incident medium and maximum ray angle and is given b

N.A. = ni Sinmax =

Where ni is the refractive index of the incident medium ( ni = 1 for air)

max is the maximum angle at which light can be sent into the fiber.

W is the width of the output beam

L is the distance of the screen from the end of the fiber.

PROCEDURE

1. Connect one end of the cable1 (1meter FO cable) to FO LED of TNS20A and the other end to the NA Jig.

2. Connect power adaptor into the socket Vin and plug the AC mains. Red light should appear at end of the fiber on the NA jig. Turn the set Pout knob clockwise to set to maximum Po. The light intensity should increase.



3. Hold the white screen with concentric circles (10, 15, 20, and 25mm diameter) vertically at a suitable distance to make the red spot from the emitting fibre cable coincide with the 10mm circle. Note that the circumference of the spot (outer most) must coincide with the circle. A dark room will facilitate good contrast. Record L, the distance of the screen from the fibre end and note the diameter (W) of the spot.

4. Substitute the measured values (L) and (W) in equation(1) and determine the value of N.A.

5. Repeat the experiment for the distances 10mm, 12mm, 14mm and note the readings.

TABULAR FORM

PRECAUTIONS

1. All the connections have to be made properly and checked once before switching on the power.

2. Do not focus light from fiber into eyes.

3. The screen has to be held normal to the output beam.

4. The readings have to taken without parallax error.

RESULT

S.No. L (mm)

W (mm)

N.A. max

( degrees)



Numerical aperture of the given fiber =


1. What is the type of fibre used in this experiment?

2. Which type of waves is carried out in fibers?

3. What change in NA is observed if the distance between the screen from the end of the fibre varies?

4. What is core and cladding of a fiber?

5. If the refractive index of the incident medium increases, what will happen to the numerical aperture?

6. Define total internal reflection?

7. Define critical angle?

8. What is meant by wave guide?

9. Which type of light source is used in this experiment?

10. What is the significance of numerical aperture?



EXPERIMENT NO.10

ENERGY GAP OF A MATERIAL OF PN JUNCTION

AIM: To determine the energy gap of a given semi-conductor.

Apparatus: Semiconductor, Ammeter, Thermometer, Copper vessel etc.

THEORY: The energy gap (EG) of a material is defined as the minimum amount of energy required by an electron to get excited from the top of the valence band to the bottom of the conduction band. According to the band theory of solids, insulators and semiconductors are materials which posses a band gap (i.e. a range of forbidden energy values) at the Fermi level. Thus, these materials have a completely filled energy band below the gap and empty band above the gap. The width of this band gap is small enough (< 2ev) that at finite temperatures thermal excitation of electrons across the gap, into the empty “conduction” band, is possible leading to a small but measurable conductivity. The band gap in insulators is simply too large to have any appreciable concentration of charge carriers excited into the conduction band. The temperature dependence of the resistivity of a pure semi-conductor is given by

i = B(T) exp (Eg/2KBT)

Where Eg is the width of the gap and the function B(T) is only very weakly dependent on temperature. To a good approximation we can take B(T) = constant. Thus, we can easily measure the gap energy of semi-conductor of a sample over a range of temperatures.

The resistance of a semi-conductor varies with temperature as R = Ro exp(EG\KT)

Where Ro is the resistance of a semiconductor at absolute zero,

K is Boltzman constant and

T is the temperature of the material.

Applying logarithm log10 R = log10Ro+ (EG\KT) log10e

Slope = and

EG = (slope)K\log10e or

EG = (1.9833 x 10- 4 x slope) eV



PROCEDURE

1. Make connections as shown in fig. Pour some oil in the copper vessel and fix the diode to the Bakelite lid.

2. The lid is fixed to the copper vessel, a hole is provided to the lid through which the thermometer is inserted in the vessel. Apply constant voltage (say 0.5v) across the semi-conductor and switch on the heater.

3. Measure the current as the temperature is increasing at a regular interval till the temperature is reached to 800C.

4. Switch off the heater. Tabulate the values of current and temperature correspondingly.

5. Find the resistance for each value of current. Repeat the experiment for two or more different voltages.

6. Draw a graph between 1\T and log10R by taking i\T on X- axis and log10 R on the Y-axis. Find the slope of the straight line. Substitute in the equation to find the value of energy gap.

TABULAR FORM and CIRCUIT

S.No. T ( K )(Temp )

I(current)

R= V/I Log10R 1/T (K-

1)



PRECAUTIONS

1. The applied voltage should be minimum.

2. The tip of the thermometer should be dipped in oil.

RESULT

The energy gap of the given semiconductor = eV


1. What is a semiconductor? Types of semiconductor.

2. How is a pn junction formed?

3. What is energy gap?

4. What is meant by conduction band and valence band?

5. What is Fermi level? How is it in case of semiconductors, conductors and insulators?

6. What is the main purpose of oil in the copper vessel?

7. If temperature increases, what happens to the energy gap?

8. How can we measure the energy gap from the graph?

9. What are the applications of Semiconductors?

10. Give examples for semiconductors.

11. What is meant by doping?



EXPERIMENT 11

TORSIONAL PEDULUM RIGIDITY MODULUS

Aim: To determine the rigidity Modulus of the given wire by dynamical method.

Apparatus: Torsional pendulum, stop watch, screw guage, vernier calipers, scale etc.

Experimental Arrangement:

Theory: A heavy cylindrical disc suspended from one end of a fine wire whose upper end is fixed

constitutes a Torsional pendulum. The disc is turned in its old plane to twist the wire, so

that on being released, it executes torsional vibrations about the wire as axis.

Let be the angle through which the wire is twisted.

Then the restoring couple set up in it is equal to



4. . .

2

n ac

l

Where 4( . . )

2

a nc

l

-------- is the twisting couple

per unit (radian) twist of the wire.

This produces an angular acceleration (dw/dt) in the disc

Therefore if “I” is the moment of inertia of the disc about the

wire we have

I. .dw

cdt

dw c

dt I

i.e the angular acceleration (dw

dt) of the angular displacement() and therefore its motion

is simple harmonic hence time period is given by

T= 2πI

c -----------------------

From & 4 2

8 I ln

a T

In case of a circular disc whose geometric axes coincide with the axis of rotation. The

moment of inertia “I” is given by

I= 2

2

MR

where M is the mass of disc and “R” is the radius of the disc.

Plot a curve for l Vs T2 and calculate the slope.

4

8n

a

2

2

MR × Slope dynes/cm2

1

2

1 2



Table :

Sl.NoLength of Wire

l ( cm)

Time for 20 oscillation Time Per one oscillation

2

l

TTrial1 Trail2 Mean (t) T T2

1

2

3

4

5

Table :

Radius of the wire using screw gauge

L.C. = Error = Correction =

S.No. Pitch scale reading

Head scale reading HSR x LC PSR + (HSRxLC)Observed Corrected

GRAPH :

A graph is drawn between L and T2 by taking the values of L on X-axis and corresponding T2 on Y-axis. It is a straight line passing through origin. L\T2 value is determined from the graph and by substituting it in the formula the value of rigidity modulus is calculated.



Precautions:

1. while using vernier calipers see that the readings must be taken without any parallax error

2. Measure the thickness of wire using screw guage

3. Note the disc should be rotated along with its own axis.

Result: The rigidity modulus of the given wire using dynamical method is n = dynes/cm2


1. What is meant by torsion?

2. Define rigidity modulus?

3. What is moment of inertia?

4. Mention the factors on which the rigidity modulus of a material depends?

5. What is meant by mechanical deformation?

6. Define restoring force?

7. Define stress and mention its units?

8. Define strain and mention its units?

9. If we increase the diameter of the wire, what happened to rigidity modulus?

10. Differentiate simple pendulum and torsional pendulum?

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