LMPHY120 laboratry

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LABORATORY MANUAL

PHY120

ENGINEERING PHYSICS LABORATORY

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TABLE OF CONTENTS

S. No. Title of the Experiment Page No.

1 An introduction to units, errors, different types of graphs and

measurement of length, mass and time.

3-9

2 Determination of unknown capacitance using flashing and quenching

of neon bulb.

10 - 11

3 To find the coefficient of self-inductance of a coil by Anderson's

method.

12 - 14

4 To determine Hall Voltage and Hall Coefficient using Hall Effect. 15 - 17

5 To plot a graph between current and frequency in series and parallel

LCR circuit and find resonant frequency, quality factor and band

width.

18 - 20

6 To study the variation of magnetic field with the distance along the

axis of circular coil carrying current by plotting a graph.

21 - 22

7 To study the induced e.m.f. as the function of velocity of magnet. 23 - 25

8 To determine the refractive index of material of the prism by

calculating the angle of minimum deviation using spectrometer.

26 - 28

9 To study variation of angular acceleration with torque acting on the fly

wheel and also find out the moment of inertia of the flywheel.

29 – 30

10 Determination of acceleration due to gravity by compound pendulum. 31 – 34

Text Book:

LMPHY120.doc by Physics Dept. 1st Edition 2012

References:

B.Sc. Practical Physics by Arora C.L., S.Chand, 20th

Edition (2007)

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Experiment 1.

Aim: An introduction to units, errors, different types of graphs and measurement of length,

mass and

time.

Equipment Required: Vernier callipers, screw gauge and multimeter

Learning objective:

(1) Students learn the use of Vernier caliper, screw gauge and multimeter

(ii) Students learn to plot linear-linear and semi-log graphs

Introduction: The precision of length measurements may be increased by using a device that

uses a sliding vernier scale. Two such instruments (identify in the picture above) that are

based on a vernier scale which you will use in the laboratory to measure lengths of objects are

the vernier callipers and the micrometer screw gauge. These instruments have a main scale

(in millimetres) and a sliding or rotating vernier scale. A multimeter is an electronic

measuring instrument that combines several measurement functions in one unit. A typical

multimeter may include features such as the ability to measure (AC/DC) voltage & current,

resistance and testing of a diode.

Zero error occurs when the measuring instrument registered a reading when there should be

none.

Units.The measurement of the physical quantities should be done in the most convenient

unit e.g. mass of the body in grams, measurement using vernier calliper in cm, small

current in mA etc.All the measured quantity must be converted into SI unit while

tabulating.

Least count = (Value of one main scale division) / (Total no. divisions on the vernier

scale)Observed Reading=M.S. reading+ V.S. reading Note: find out the the least count of

the measuring instrument available in the lab e.g vernier calliper, screw gauge,

spectrometer, Michelson Interferometer, etc.

Procedure:

Part A (Measurement)

1. To find the density of the given material

You are given a rectangular block and you have to find the density of material of which the

rectangular block is made of. We know density(d) =[mass( kg)/volume ( m3

)].

To find the volume of the rectangular block measure its length, width and height by vernier

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caliper. Take at least five readings of each dimension. Also remember to check and note in

your “report sheet” the zero error and least count of the vernier caliper you are using. Even

if “zero error” is “zero” entry should be recorded in your report sheet. Next measure the

mass of the rectangular block using a balance; take at least five readings. Also note ―zero

error‖ and ― least count‖ of the balance you use for finding the mass. Tabulate the data,

calculate the density along with the possible error.

Error in density(Δd)

d=m/V or Δd/d= (Δm/m)+ (ΔV/V)

A graph is a straight or curved which shows the relative change between two quantities

out of which one varies as a result of change in the other. The quantities which is changed

at will is called independent variable while alter due to the change in the first is called

dependent variable. The point where the axes of independent and dependent variable meet

at right angle is called origin.

Following rule must be adopted while plotting a graph

1. Find the independent and dependent variables. Plot the independent variable along

X-axis and the dependent variable along the Y-axis.

2. Determine the range of each variable and count the no of divisions available on the

graph to represent the each variable along the respective axes.

3. Choose a convenient scale for both variables .It is not necessary to have the same

scale for both.The scale should neither be too narrow nor too wide.It is preferable

that 10 divisions should be represent 1,2,5, or 10 or their multiples by any +ve or –

ve power of 10. We must see that maximum portion of the graph paper is utilized

and the graph is well within it.

4. At least six observation extending over a wide range should be taken for plotting

the graph.

5. If the relation between the two variables begins from zero of if zero value of one of

one of the variables is to be found out, it is necessary to take origin as zero along

both the axes.

6. The origin need not always be represent by zero. Its value should be round number

less than the smallest given value of the independent or dependent variable.

7. It is not necessary to write all the values along the respective axes.

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8. Mark the point with a pencil. Draw a small circle or put a cross to indicate the

plotting point prominently.

9. Draw a smooth free hand curve through the plotted points. It is not necessary that

the curve should pass through every point leave as many points below it as there are

above it.

10. The title graph should be given boldly near the top of the graph paper.

11. It is always better to indicate the scale for both the variable at the top in the left or

right corner of the graph paper.

Linear graphs

Example 1

Let us consider the case of time period ‘T’ of a simple pendulum which is written as

T = (2π) (L/g)1/2

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

‘L’ is the “length” of the pendulum while ‘g’ is acceleration due to gravity. Eq. (1) can be re-

written as

T2 = (4π

2/g)L ---------(2)

Eq. (2) is an equation of straight line with slope = (4π2/g ) and intercept = 0

A student came up with the following data.

S.No T

(s)

L

(cm)

1 1.0 24.8

2 0.9 20.1

3 0.8 15.9

4 0.7 12.2

5 0.6 8.9

6 0.5 6.2

Find the value of “g” by graphical analysis.

How to draw the graph?

Step 1. From Eq. 2 we have to plot T2 vs L so our table is (L should in meters)

S.No T2

(s)

L x 10-2

(m)

1 1.0 24.8

2 0.81 20.1

3 0.64 15.9

4 0.49 12.2

5 0.36 8.9

6

6 0.25 6.2

Step 2. Choose a “linear” graph sheet which is linearly (normally in mm) graduated on both

X- as well Y- axis.

Step 3. Choose Y-axis for T2 and X-axis for L

Step 4. Max T2 is 1 and min is 0.25; choose your scale so that you can mark 0.25 clearly.

Similarly choose scale for L on X-axis.

Step 5. Mark the points on the graph with a sharp pencil

Step 6. Draw a straight line through the points so that maximum number of points are on/very

close to the line (Best fit we will not discuss presently)

Step 7. Find the slope from the graph and calculate “g”

Important:

(i) Give a title to the graph; in present case it will be T2 Vs L for a simple pendulum.

(ii) Mark scales on the graph sheet; X-axis “10mm = so many m” and Y-axis “10mm= so

many seconds”

(iii) Mark X-axis and Y-axis with quantity (along with units) you are plotting

(iv)Calculate the slope and “g” on the graph sheet so that a graph is complete and one need

not to refer to the Lab Sheets.

Interpolation: From the graph you can find the L for T=0.44 (for example, within the

present data set)) even though there is no experimental data; this process is called

interpolation.

Extrapolation: One can extend the length of the line so that one can predict L for T =0.1s

or 2.5s (outside the present data set); this is called extrapolation.

Example 2. Change in the value “g” with the distance “h” (outside the earth) is given by

gh (value of g at a height h)= g(1-2h/R) where R is the radius of earth

Data from an experiment is given in the following table

S.No gh

m/s2

h

m

1 8.8 0.05R

2 7.8 0.10R

3 6.9 0.15R

4 5.9 0.20R

5 4.9 0.25R

6 3.9 0.30R

By graphical analysis find the value of “g”. Can you find out the value of “R” from the

graph?

Semi-log graph Radioactive decay is given by N(t) = N(0) e

- , where N(t) are the observed counts at time t,

Calculate

Time ‘t’

s

No. of counts

1.0 905.0

2.0 820.0

3.0 735.0

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4.0 670.0

5.0 600.0

6.0 550.0

N(t) = N(0) e-

Or ln N(t) = ln N(o) -

Or 2.3log N(t) = 2.3 log N (0) -

Or log N(t) = log N(0) -

Plot of log N(t) with t is a straight line with log N(o) as intercept and -

one side is log so use a semi-

Log-log graph

Planetary period ‘T’ (in earth years) is related to its distance ‘R’( AU, astronomical units;

1AU is equal to average separation between earth and sun) by the relationship of the form

T = kRn

Calculate ‘k’ and ‘n’ by graphical analysis from the following data

T = kRn

or log T = log k + n log R

Plot of log T vs log R is a straight line with log k as intercept and n as slope. Since both sides

are in log form use log-log graph paper.

Error analysis

Measurement is basic to science. A measurement is meaningful only if the uncertainties

involved are specified. An operator “X” has to specify the uncertainty (error) in his final

result; the practice of comparing the result with “standard value” is unscientific as the

experimental conditions/instruments used to find out the “standard value” are different when

compared to those of X.

Please remember

The error in an experimentally

measured quantity is never

found by comparing it to

some number found in a book

or web page

These uncertainties do not include the blunders/mistakes of the person performing the

measurement. These errors are due to limitations of the measuring instruments (like zero

error, faulty calibration, error due to parallax, bias of the operator etc) and uncontrollable

changes in experimental parameters like temperature, pressure, voltage etc. The instrument

errors (systematic errors) are instrument specific, can be either +ve or –ve and are constant in

nature. On the other hand errors due to changes in experimental parameters are random in

nature; can be both +ve as well as –ve in a particular set of easements.

Estimation of systematic errors

There is no prescribed method to minimize systematic errors. An operator has to examine

various measuring instruments (scales, meters, etc) for zero-errors (zero of a meter or vernier

caliper might have shifted), take readings so as to minimize parallax error and if possible

Name of the planet T in

Earth years

R in

Astronomical units

Mercury 0.39 0.24

Venus 0.72 0.62

Earth 1.00 1.00

Mars 1.52 1.88

Jupiter 5.20 11.86

Saturan 9.54 29.46

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check the calibration of the measuring instruments. Systematic errors cannot be minimized by

taking large number of measurement (Why?).

Estimation of random errors

Random errors are both +ve as well –ve in a measurement cycle, can be handled by well-

known statistical techniques. Two basic techniques are:

(i) Arithmetic Mean or simply mean = (X1 + X2 + X3+…………………………..+XN)/N= XM

(ii) Standard deviation = (1/N) [(X1-XM)2 + (X2-XM)

2 + (X3-XM)

2 +………..+(XN-XM)

2

1/2

It shows how much deviation there is from the "average" (mean). A low standard deviation

indicates that the data points tend to be very close to the mean. whereas high standard

deviation indicates that the data are spread out over a large range of values.

Propagation of random errors

If Z is a function of X and Y so that we have Z = F(X,Y). Error in X is ΔX while for Y the

error is ΔY how to find error in Z (ΔZ) X and Y are independent that measurement in X does

not induce error in Y and vice versa; this is the case in most of your experiments.)

What will be ΔZ in case Z = X – Y ? The standard procedure is:

Contribution to the error ΔZ due to ΔX is given by (ΔF/ΔX) ΔX [(ΔF/ΔX) is partial derivative

of F with respect to X treating Y as constant) while due to ΔY the contribution is (ΔF/ΔY) ΔY.

Total ΔZ is given by

ΔZ = (ΔF/ΔX)2 (ΔX)

2 +(ΔF/ΔY)

2 (ΔY)

2

(1/2)

Example1. Z= X+Y

ΔZ/ΔX =1, ΔZ/ΔY = 1 so ΔZ = (ΔX)2 + (ΔY)

2

(1/2)

What will be ΔZ in case Z = X – Y ? What conclusion you arrive at from this example?

What will be ΔZ in case Z =a X + Y/b ? where a and b are constants?

Example2. Z = XY

ΔZ/ΔX =Y, ΔZ/ΔY =ΔX ΔZ = Y2(ΔX)

2 +X

2 (ΔY)

2

(1/2). This is absolute error in Z. Alternately

we can have ΔZ/Z =ΔZ/XY =(ΔX/X)2 + (ΔY/Y)

2

(1/2). This is relative error in Z and can be

expressed in terms of % by the relation (ΔZ/Z) x 100.

Example3. Z = X/Y

ΔZ/ΔX = 1/Y, ΔZ/ΔY = -X/Y2 ΔZ =(1/Y)

2(ΔX)

2 +[(X)

2]/Y

4 (ΔY)

2

(1/2).

Which gives ΔZ/Z =(ΔX/X)2 + (ΔY/Y)

2

(1/2).

The procedure outlined above can be used for functions with more than two independent

variables.

Significant figures

The final result of an experiment should be expressed [measured value] ± [estimated error]

units. If it is a single measurement like measurement of length your final result could be for

example, 10.28±0.05cm which means that the length could be from 10.33 to 10.23cm. All the

four digits in the result are important; your result has four significant digits. If the object

whose length was measured has breadth say 5.41±0.05cm (measured with the same scale used

for the measurement of length so that error is same). Area = (10.28±0.05cm) x (5.41±0.05cm).

(10.28) x (5.41) = 55.6148 and error in area = (0.05)2+ (0.5)

2

1/2 = 0.070710678 (calculated

on CASIO 5-VPAM). So our result will look like 55.6148±0.070710678 cm2. We know the

error in our length as well as breadth measurement is 0.05cm so the order of magnitude of the

error in area must be same which turns out to be 0.07cm when you carefully examine the final

result for area. Note that the error in area is more than that of length or breadth which is

expected(WHY?). So area = 55.6148±0.07cm2 which means that area is expressed to 1/10000

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accuracy while error is only accurate to 1/100. Hence digits 4 and 8 have no significance in

the final result which is area = 55.61±0.07 cm2.

Errors in the measurement determine the number of significant digits one should use in the

final result

How to calculate errors in your Lab experiments

1. Check for zero-errors in all your measuring instruments like scales, vernier calipers, screw

gauges, volt/amper meters etc and note them properly in your “LAB Note Book”= no rough

copy is to used in the LAB for recording of the data.

2. Check and record the least count of all the measuring instruments. Examine each

instrument carefully to determine the least count. For example a scale may be graduated so

that it has “markers’ after every one mm; least count being 0.1cm. However, if the “markers’

are distant enough so that one can read to an accuracy of o.5mm the least count is 0.05cm.

Intelligent and careful use of the measuring instruments to get best out of these instruments is

the basic experimental skill. In real world you will never get ideal instruments.

3. Make the required measurements and record these measurements directly in your “LAB

note book”. Units of all the quantities you have entered in the note book should be mentioned.

4. Compute the result

5. Calculate the error by standard deviation technique.

6. Calculate the percentage error by “partial differentiation technique”

Learning outcomes : to be written by the student

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Experiment 2: To find the unknown capacitance of a capacitor using flashing and quenching

of neon bulb

Equipment Required: A condenser of unknown capacity, 3 condensers of known Capacity

(say 32μF, 50 μF, and 100 μF), resistance of the order of few mega-ohm, a Neon flashing

bulb, stabilized DC power supply of 250V; one way keys.

Learning Objectives:

1. To learn about capacitance of a capacitor

2. To learn how capacitances behave in parallel combination

3. To learn a method to find unknown capacitance of a capacitor.

Theory: When the electrodes connected to a D.C source stray, electrons in the gas are

attracted towards the positive electrode. As voltage is increased, the speed of electrons also

increases and at particular voltage speed becomes high to ionize the gas so lamp begins to

conduct and glows. This voltage is known as flashing potential. When we place a capacitor in

parallel with lamp, due to conduction of lamp capacitor begins to discharge through it. It

continues to do this until quenching potential reached. When neon lamp ceases to conduct, the

capacitor then begins to charge again and whole process goes on repeatedly. The flashing and

quenching time can be determined by noting time taken by lamp for ‘n’ consecutive flashes

and quenches. If t1 is time taken by capacitor voltage to fall from V1 to V2 and t2 is time for

voltage to rise from V2 to V1, then V2 = V1 e (- t1/RC)

or t1 = -CR loge (V2/V1)

And V2 = V1 (1- e(- t2/RC) )

or t1 = -CR loge(1 - V2/V1)

T = t1 + t2 = C [-R loge (V2/V1)- R loge (1 - V2/V1)]

As R, V1 and V2 have constant fixed values, so we get T= k C where k is constant.

Circuit diagram:

Outline of the Procedure: (i) Draw the diagram and make the connections as in the fig.

Connect the condenser C1 in the circuit by inserting K1. Also insert the key K to connect

power supply and increase the voltage till neon lamp just begins to flash. As already

explained, the bulb starts flashing and quenching as it is connected in parallel with the

condenser. Note the flashing and quenching time for 20 flashes. Take out the key K so that the

power supply is disconnected.

(ii) Put in the key K4 for the circuit of unknown capacity C0.Since C1 and C0 are in parallel

their capacities get added up and total capacity in parallel with the lamp is (C1 + C0). Again

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insert the key K and adjust the power supply voltage to previous value. Note the time for 20

flashes. Remove the key K1 and K4.

(iii) Now repeat the experiment with the capacity C2, C3 and with all the three known

capacitor connected together in parallel with Co. Scope of result expected: By Connecting the

condensers of known capacity in parallel with lamp and with unknown condenser, time t for

20 flashes with and without unknown capacitance can be obtained.

Observations and Calculations:

Parameters and Plots:

Quenching and Flashing Time without unknown capacitor: t0

Quenching and Flashing Time with unknown capacitor: t1

Plot two graphs between values of capacitance along x-axis and flashing and quenching time t

(without and with unknown capacitance) y-axis For three different values of flashing and

quenching time draw three straight lines parallel to x-axis cutting the two graphs at A and B,

C and D, E and F respectively


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Experiment No. 3: To determine the coefficient of self-inductance of unknown coil by

Anderson’s method using a headphone.

Equipment Required: Inductance coil, Capacitor, Two variable resistances, Galvanometer,

headphone, audio oscillator


(a).Balancing point of the Wheatstone bridge.

(b). Self-inductance of the unknown coil

(c). Unknown capacity of capacitor can be determined.

Outline of the Procedure:

According to circuit diagram using a battery in place of A.C. Source and galvanometer

in place of headphone make the connections.

Make Resistance P = Q

Taking a suitable value of R adjust the value of S so as to get a null point. Note the

values of resistances P and R.

Now replace the galvanometer by a headphone and battery by A.C. source you will

hear a sound in headphone.

Reduce the sound to minimum or zero value by varying the variable resistance r by

keeping all other resistances constant out of which three are already constant. This is

the balance point for alternating current. Note the value of r for which sound in

minimum or zero.

Note the value of capacitance marked on it. Repeat it three times by changing the

value of capacitance.

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Scope of the results expected:

The self inductance of unknown coil is ------- L. This experiment can be used to calculate

the unknown capacity of capacitor.


Capacitance C =

Resistance P = Q = Ω

Resistance R = Ω

Resistance r = (i) Ω (ii) Ω (iii) Ω

Mean r = Ω

Inductance L= CR (P+2r)

Cautions:

Balancing point should be clearly noted.

Sound should be reduced to minimum value or zero before noting balancing point.

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The resistance used should be non-inductive

Error analysis:-

Probable error:-

Probable error = Standard Error

=

Where S = 2

Δ = n – mean value of frequency

m is the number of readings taken.

S.NO. Inductance of coil Δ Δ2

Percentage error:-

%age error = (actual value – measured value/ Actual value) * 100


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Experiment No. 4: - To study Hall-effect by using hall probe. (Germanium crystal).

Equipment Requirement: -Hall probe, Gauss probe, Gauss meter, electromagnet, constant

current power supply, digital voltmeter.

Material used: Ge crystal

Learning objectives:

1. To understand the concept of hall effect in materials

2. To learn to measure magnetic field produced by electromagnets

3. To learn how hall effect can be applied to know type of semiconductor

Theory: - When a magnetic field is applied perpendicular to a current carrying conductor, a

voltage is developed in a specimen in a direction perpendicular to both the current and the

magnetic field. This phenomenon is called the Hall Effect. The voltage is so produced is

called hall voltage. When the charges flow, a magnetic field directed perpendicular to the

direction of flow produces a mutually perpendicular force on the charges. Consequently the

electrons and holes get separated by opposite forces and produce an electric field. , there by

setting up a potential difference between the ends of specimen. This is called hall potential.

Outline of Procedure:-

1. Place the specimen at the centre between the pole pieces and exactly perpendicular to the

magnetic field.

2. Place the hall probe at the centre between the pole pieces, parallel to the semiconductor

sample and note the magnetic flux density from the guess meter keeping the current constant

through electromagnet.

3. Before taking the reading from the gauss meter ensure that gauss meter is showing zero

value. For this put the probe away the electromagnet and switch on the gauss meter and adjust

zero.

4. Do not change the current in the electromagnet for the first observation.

5. Vary the current in small increment. Note the current and the hall voltage.

6. For the 2nd observation keep the current constant through the specimen and vary the

current through electromagnet and note the hall voltage.

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7. Plot the graph between the hall voltage and the current through electromagnet.

Observations:

Current through the electromagnet = A(Constant)

Magnetic field (as measured by the Gaussmeter) =

Current through the specimen = mA(Constant)

S.

No

Current through

Electromagnet I’

( in )

Voltmeter reading Hall

Voltage,

V= VH’ -

VH

with magnetic

field,VH’

without magnetic

field,VH

1

Scope of Result: - The graph between the VH and I, VH and I’ is the straight line.

Parameters & Plots: -

The current density J = I / A

I = n E v A

The hall coefficient is given RH = VH b / IB,

where b = thickness of the specimen, VH = Hall Voltage, I = Current through the specimen, B =

Magnetic Field

The hall coefficient …………………m3 /

C

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Caution:-

1. The hall probe should be placed at the centre of the electromagnet.

2. The specimen should be placed at the centre of the electromagnet.

3. Zero should be ensured in the gauss meter before placing the hall probe between the centre of

electromagnet.


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Experiment No. 4- To plot a graph between current and frequency in LCR series and parallel

circuit and find resonant frequency, quality factor and band width.

Equipment Required- An audio-frequency oscillator (range 10 Hz to 10 kHz), an inductance coil,

variable capacitors, variable resistors, a non-inductive resistance box, ac milliammeter, ac

voltmeter, connecting wires etc.

Material Required: NA

Learning Objective - To experimentally study LCR series and parallel circuit.

2. To find the quality factor and resonant frequency.

3. Also calculate bandwidth from the graph.

4. Be able to explain why LCR series circuit is called acceptor and LCR parallel circuit is called

rejector circuit.

Circuit diagram:

Fig: Series LCR Circuit Fig: Parallel LCR Circuit

Procedure: 1. Connect the LCR (series/parallel) circuit.

2. With output voltage of the oscillator kept constant throughout the experiment vary the value of

A.F. and measure the corresponding value of current in millammeter for each observation.

3. Repeat the experiment for two more different values of R.

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4. Plot a graph between current (y axis) and frequency (x axis).

Observations:

Resistance R =

Capacitance C =

Inductance L =

Output voltage of audio oscillator = Input voltage for LCR Circuit , Ev =

S. No Frequency (in ) Current in the circuit (in mA) for

R1 R2 R3

Current at resonance from the graph for

(i) R1 =

(ii) R2 = (iii) R3 =

Calculated value of current at resonance for

(i) R1 = Ev /R1

(ii) R2 = Ev /R2

(iii) R3 = EV /R3

Resonant frequency, νr = 1/(2π LC )

Resonant frequency, νr (graphically) =

Quality Factor

Maximum value of current at resonance Ir =

Corresponding Frequency νr =

0.707 Ir =

Corresponding value of frequency

below νr , ν1 =

above νr, ν2 =

Band Width = ν2 - ν1 =

Quality Factor, Q = 2π

12

r

Calculated value of Q from inductance L = (ωrL)/R = R

Lr2

Calculated value of Q from inductance L = R

C r )/1( =

rCR2

1

Parallel Circuit

S. No Frequency (in ) Current in the circuit (in mA) for

R1 R2 R3

Current at (anti) resonance from the graph for

20

(i) R1 = CR

L

1

=

(ii) R2 = CR

L

2

=

Impedance at resonance Z =

Calculated value of current at (anti) resonance for

(i) R1 = Ev /Z = L

CREv 1

(ii) R2 = Ev /Z = L

CREv 2

Anti Resonant frequency, νr (graphically) =

Calculated value for R1 = 2

1

2

2

11

L

R

LC

Calculated value for R2 = 2

1

2

2

21

L

R

LC

Plots and parameters:

Current vs. frequency

Scope of the Result-

Graph between current and frequency will be Gaussian.

Resonant frequency, quality factor and band width can be calculated from the graph.

Cautions-

If the amplitude of the output voltage of the oscillator changes with frequency, it must

be adjusted.

The values of inductance and capacitance are so selected that the natural frequency of

the circuit lies almost in the middle of the available frequency range.


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Experiment No. 6 : To study the variation of magnetic field with the distance along the axis of

circular coil carrying current by plotting a graph. (Using Stewart and Gee’s apparatus.)

Equipments required: Stewart and Gee’s type tangent galvanometer, a battery, a rheostat, an

ammeter, a one-way key, a reversing key, connecting wires.

Material Used: NA


1. To understand the working of Tangent Galvanometer using Tangent Law.

2. To study the direction and magnitude of the magnetic field around the coil.

Circuit Diagram

Procedure:

1. Place the instrument in such a way that the arms of the magnetometer lie roughly east and west

and the magnetic needle lies at the centre of the vertical coil. Place the eye a little above the

coil and rotate the instrument in the horizontal plane till the coil, the needle and its image in

the mirror provided at the base of the compass box, all lie in same vertical plane. The coil is

thus set roughly in the magnetic meridian. Rotate the compass box so that the pointer lies on

the 0-0 line.

2. Connect the galvanometer to a battery, rheostat, one way key and an ammeter through a

reversing key.

3. Adjust the value of the current so that the magnetometer gives a deflection of the order of 60-

700 degrees. Reverse the current and note the deflection again.

4. Now slide the magnetometer along the axis and find the position where the maximum

deflection is obtained.

22

5. Note the position of arm against the reference mark and also the value of current. Read both

ends of the pointer in the magnetometer, reverse the current and again read both ends. Now

shift the magnetometer by 2 cm and note the reading again. Record a number of observations.

6. Similarly repeat the observation by shifting the magnetometer in the opposite direction and

keeping the current constant at the same value.

Observations.

Least count of the magnetometer =

Current I =

S. No Distance from

the centre,x

(in )

Left Side Mean θ tan θ Right Side Mean θ tan θ

Direct Reversed Direct Reversed

Scope of the result to be reported

Plots & Parameters: Plot a graph between tan θ and x, where θ is the deflection produced in a

deflection magnetometer and ‘x’ is the distance from the centre of the coil.

The intensity of magnetic field varies with distance from the centre of coil, the graph

can be plotted and variation can be known. The intensity of magnetic field is maximum at the

centre and goes on decreasing as we move away from the centre of the coil towards right or left.

The value of magnetic field at the centre of coil and radius of coil can also be

determined from this experiment. A graph showing the relation between B and the distance ‘x’ is

plotted. The curve is first concave towards O and then afterwards becomes convex. Then the

points where the curve changes its nature are called the point of inflection. The distance between

the two points of inflexion is equal to the radius of the circular coil.

Cautions: 1. There should be no magnet, magnetic substances and current carrying conductor near the

apparatus.

2. The plane of the coil should be set in the magnetic medium.

3. The current should remain constant and should be reversed for each observation.


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Experiment No. 7: To Study the induced e.m.f. as function velocity of the magnet.

Equipment Required: A small permanent magnet mounted at the middle of a semi-circular arc, a

coil consisting of number of turns, two weights, stopwatch, capacitor, diode, resistance, voltmeter

Material Required: A small strong permanent magnet, a stopwatch


T o know about Electromagnetic induction

To learn how to measure Induced e.m.f

To know the dependence of the magnitude of induced e.m.f on the velocity of the magnet.

Outline of the Procedure:

Mount the magnet at the middle point of the semi-circular arc and suspend the rigid

aluminium frame from its centre so that whole frame can oscillate freely through the coil.

Adjust the position of two weights on the diameter arm of the arc to have minimum time

period.

Connect the terminals of the coil to the diode circuit for measuring the peak value of

induced e.m.f.

Note time for about 20 oscillations with an amplitude of about say 20cm and respective

peak voltage.

Repeat thrice keeping the amplitude same and find the time period. Also note the peak

voltage each time.

Repeat the experiment after changing the amplitude and take 8-10 readings.

Now change the time period by adjusting the position of the weights on the diameter arm.

Take about three readings at this position.

Repeat the experiment after changing the time-period and take 8-10 readings.

Scope of the results expected: This experiment will help in understanding the nature and polarity

of induced e.m.f. One can apply the acquired knowledge to see the dependence of induced e.m.f.

on velocity of magnet w.r.t. the pickup coil.


(A) Time period constant, amplitude variable:

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Mean position of the centre of the magnet= cm.

Radius of the semi-circular arc R0= cm.

Sr.No. Amplitude

a = R0Ɵ0

Time for 20

Oscillations

Mean time

period(T)

eo eo/a= eo/ R0Ɵ0 Linear velocity

v = (2Π/T) R0Ɵ0

1

.

.

.

(i)

(ii)

(iii)

Mean

2

(B) Amplitude constant, time period variable:

Sr.No. Amplitude

a = R0Ɵ0

Time for 20

Oscillations

Mean time

period(T)

eo eoT Linear velocity

v = (2Π/T) R0Ɵ0

1

(i)

(ii)

(iii)

Mean

Model Plot:

25

Cautions:

The semi circular frame should oscillate freely as a whole on the knife edge.

The magnet should pass freely through the coils..

The magnet should be small and should be mounted at the middle of the semi circular arc.


26

Experiment No. 8:

AIM: To measure the refractive index of given material by using spectrometer.

Equipment required:

a) Mercury lamp (as source of white light)

b) Spectrometer

c) Prism

d) Spirit level

e) Magnifying Lens

d) Torch

Leaning Objective:

1. To study the spectrum of white light using glass prism.

2. To find out angle of minimum deviation and refractive index of given material for

different colour of light.

3. Plot the graph between refractive index and wavelength of different colours of light.

Circuit diagram: NA

Outline of Procedure:

(1) First the telescope has to be focussed distant objects i.e. infinity and

this has to be maintained until the experiment is over, so as not to refocus

again. Then, the cross-wires should be focussed by moving the eye-piece of

the telescope.

(2) Adjust the Collimator such that the image seen in the telescope is sharp

of the slit without the prism.

(3) Measuring the Angle of Prism A: Place the prism on the Prism Table

and lock the prism table in the position so the the incident beam falls on one

of the edges of the prism. Now, move the telescope and locate the images

27

of the slit and note down the angles. The difference between both the angles is 2A.

Hence, half of the difference will give us A. Angle of prism can also be calculated as

A = 2i – Dm

(4) Place the prism with the centre coinciding with the centre of the prism table and set it

approximately in the position of minimum deviation, so that light falls on the face AB

and emerges out from the face AC as shown

(5) Turn the telescope to receive the emergent light and adjust its position, so that the

image of the slit is formed on the cross-wire. Clamp the telescope and note its reading

on both vernier V1 and V2

(6) Now turn the telescope to receive the reflected light from the face AB as shown.

Adjust the position of telescope till the image of the slit falls on the vertical cross-wire.

Clamp it and note the reading on both the verniers.

(7) Bring the telescope back to receive the deviated ray. Turn the prism table without

disturbing the circular scale in the clockwise direction so that the deviated ray is

displaced by about one degree. Adjust the telescope so that the image is formed on

vertical cross-wire again. Note the reading on both the vernier scales.

(8) Turn the telescope again to receive the reflected light from the face AB. Make the

necessary adjustments and note the reading on both the vernier scales.

(9) Turn the table in clockwise direction again and take three or four observations as

explained.

(10) Rotate the prism table back to its starting position so that the prism is again in the

minimum deviation position approximately.

(11) Remove the prism and turn the telescope so that the direct light is received and the

image of slit falls on the vertical cross wire. Note the reading of both the verniers.

Plot and parameters:

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• R1-one particular line of the spectrum at the position of minimum deviation

• R2-the reflected ray coming from the prism

• R3-the image of the slit without the prism on the prism table

Angle of minimum deviation Dm = R1 - R3

Angle of incidence for minimum deviation i = 90−(R2-R3)

Angle of prism can also be calculated as A = 2i − Dm

Refractive index is μ=sin i /sin (A/2)

For example

Calculate the refractive index for other colours of the light spectrum and plot the graph

between refractive index and wavelength of different colour of light.

Cautions.

•It must be ensured that the light rays coming out of collimator are parallel.

Hence, the collimator must be focussed properly before the experiment.

•The plane on which the prism rests must be horizontal

•The slit must be as thin as possible in order to avoid diffraction


29

Experiment No.9: To study variation of angular acceleration with torque acting on the

flywheel and find out the moment of inertia of the flywheel


1. Learn to Measure the angular acceleration ‘α’, torque ‘τ’ and hence moment of

inertia of the flywheel.

2. Learn to aware of the limitations in an experiment and devise method to solve the

problems.

3. Learn to handle error estimation using sum of percent errors.

Apparatus Used: A fly wheel, slotted mass with hanger (50gm each), a strong and thin

string or fine cord, stop watch, meter rule or measuring tape and vernier callipers.

Diagram:

You will attach a mass to the axle of the flywheel and let fall. By measuring suitable

quantities, angular acceleration, torque and the moment of inertia of the flywheel can be

estimated.

Procedure:

1. Examine the wheel and see that there is the least possible friction.

2. Measure the diameter of the axle with vernier calipers at different points and find

the mean.

3. Take a strong and thin string whose length is less than the height of the axle from

the floor. Make a loop at its one end and slip it on the pin A on the axle. Tie a

suitable mass to the other end of the string. Suspend the mass by means of the

string so that the loop is just on the point of slipping from the pin A. Note the

position of the lower surface of the mass ‘m’ on a scale fixed behind on the wall.

4. Now rotate the wheel and wrap the string uniformly round the axle so that mass is

slightly below the rim of the wheel. Count the number of turns wound the axle and

let it is ‘n’. The wheel will thus make n revolutions before the thread detached.

5. With the help of stopwatch note the time taken by the mass to descend through a

height ‘h’

30

6. Repeat step-5 keeping m constant and varying the number of turns n. Take 6-7

readings.

7. Again repeat step-5 keeping the number of turns n constant and varying the mass

m. Take atleast 6 observations with different values of m. Repeat each observation

thrice and calculate the average time taken in each observation.

Scope of the result expected:

The student will learn about torque, angular acceleration produced due to torque and hence

physical importance of the moment of inertia of circular bodies like wheels.

Parameter and Plots:

Calculate Vernier constant of vernier calliper

Calculate the radius of the axle

To find angular acceleration:

Angular acceleration of the fly wheel can be calculated by calculating the time as given in

step 5 and 6. Hence draw a graph between n and t2. Slope of this graph gives us the value of

angular acceleration.

To find out torque acting on the flywheel:

Suppose the mass m, when released, starts moving downward with acceleration α. Let T

be the tension in the string. Then the torque acting on the string can be calculated by using

these parameter.

To find out moment of inertia:

Plot a graph between angular acceleration along X-axis and torque along Y-axis.

When we plot a graph between torque and angular acceleration, then slope of the straight

line gives the moment of the inertia. Also by using the values of torque and angular

acceleration, moment of inertia can be calculated.

Cautions:

1. Mass of string can be taken into account for better results.

2. Stop watch should be started and stopped with accuracy to avoid any kind of time

interval measurement error.

Learning outcomes : to be written by the student in 50-70 words

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Experiment No. 10: Determination of the acceleration due to gravity (g) by using a

compound pendulum.

Aim: To plot graph between distance of knife edges from the center of gravity and the time

period of a compound pendulum and to determine acceleration due to gravity (g) using the

graph.


1. The student will know about the Centre of Gravity and acceleration due to gravity, radius

of gyration and moment of inertia.

2. The student will learn the method to find the Centre of Gravity of the bar pendulum and

determine its acceleration due to gravity.

3. The students will also learn how to determine the radius of gyration and the moment of

inertia of the bar pendulum.

4. The students will also learn how to plot a graph between time period and distance of knife

edges from the centre of gravity.

5. The skill of handing the apparatus will also be inculcated in the student by using the

telescope and stop watch.

Equipment Required:

Bar Pendulum, Small metal wedge, Spirit level, Telescope, Stop watch, Meter rod, Graph

paper

Theory:

A bar pendulum is the simplest form of compound pendulum. It is in the form of a rectangular

bar (with its length much larger than the breadth and the thickness) with holes (for fixing the

knife edges) drilled along its length at equal separation. Two knife-edges are placed

symmetrically with respect to C.G as at A and B. The time period of the compound pendulum

about a horizontal axis through Centre of Oscillation is the same as about Centre of

Suspension, given by the formula:

Where L is the length of an Equivalent Bar pendulum

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Procedure:

1. Balance the bar on a sharp wedge and mark the position of its C.G. Also mark one side of

the bar of C.G. as A and other side as B.

2. Fix the knife edges in the outermost holes at either end of the bar pendulum. The knife

edges should be horizontal and lie symmetrically with respect to centre of gravity of the

bar, so that the sharp edge points towards the centre of gravity.

3. Place a spirit level on the glass plates fixed on the bracket in the wall meant for suspending

the pendulum and see that the upper surfaces of the glass plates are at the same level.

4. Suspend the pendulum from the knife-edge on the side A so that the knife edge is

perpendicular to the edge of the slot and the pendulum is hanging parallel to the wall.

5. Adjust the eye-piece of the telescope so that the cross wires are clearly visible through it.

Focus the telescope on the lower end of the bar and put a reference mark on the wall

behind the bar to denote its equilibrium position.

6. Set the pendulum into vibration with small amplitude of about 5˚ and allow it to make a few

vibrations so that these become regular. Make sure that there is no air current in the vicinity

of the pendulum.

7. Look through the telescope and when the image of the reference mark is passed by the bar,

start the stop –watch and count zero. Count one when the pendulum is passing through the

same position in the same direction and so on. Note the time taken for 20 vibrations.

Repeat again and take the mean.

8. Measure the distance between the C.G. and the inner edge of the knife edge.

9. Now suspend it on the knife-edge on the side B and repeat the observations.

10. Repeat the observations with the knife-edges in the 2nd, 3rd, 4th etc. holes on either side

of the centre of gravity.

Note: See that the knife edges are always placed symmetrically with respect to C.G.

Observations:

S.No. Side A Side B

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Time for 20

Vibrations

Time

Period t

(Mean/20)

Distance

from

C.G.

Time for 20

vibrations

Time

Period t

(Mean/20)

Distance

from

C.G. 1 2 Mean 1 2 Mean

1.

2.

3.

To Plot the graph:

1. Take the Y-axis in the middle of the graph paper .Represent the distance from the C.G.

along the X-axis and the “Time-Period” along the Y- axis.

2. Plot the distance on the side A to the right and the distance on the side B to the left of the

origin.

3. Draw smooth curves on the either side of the Y-axis passing through the plotted points

taking care that the two curves are exactly symmetrical as shown in graph.

To find the value of ‘g’:

1. Draw two lines parallel to the X-axis cutting the curves at the points CAGBD and

C`A`G`B`D` respectively (from A side to B side). Also draw the line MON touching

the two portions of the graph at M and N respectively.

2. Select points like C and B, A and D etc on the graph on the two sides of the C.G., not

equidistant from it, having the same time period. Measure the distance AD and CB.

3. Similarly measure the distance A`D` and C`B`.

4. Similarly more lines can be drawn parallel to the x-axis.

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Calculations:

For the line CAGBD, L1 = (AD + CB)/2 = ........ cm

t1 (Time period for line CAGBD) = ...... sec.

For the line C’A’G’B’D’, L2 = (A`D` + C`B`) /2 = ........ cm.

t2 (Time period for line C`A`G`B`D`) = ....... sec.

Similarly calculate L3, L4 and so on for other lines on the graph and corresponding t3, t4

Find the mean of all lengths and time periods, using

L = (L1 +L2 + L3)/3 and t = (t1 +t2 + t3)/3

And hence find L/t2

= .......

Now, Calculate ‘g’ using the formula

Error Analysis:

Actual value of g is 9.8 m/s2

Cautions:

1. The knife -edges should be horizontal and the bar pendulum parallel to the wall.

2. Amplitude should be small.

3. The time period should be noted after the pendulum has made a few vibrations and the

vibrations have become regular.

4. The two knife-edges should always lie symmetrically with respect to the C.G.

5. The distance should be measured from the knife-edges.

6. The graph drawn should be a free hand curve.

Learning outcomes: To be written by the students in 50-70 words.

LMPHY120 laboratry

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