Dr Giasuddin Ahmed And Md Shahabuddin

74 Pages·2011·8.05 MB·English

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I
PRACTICAL PITTSICS
for degree students
(8. Sc. Pass, Honours and Engineering Students)
Dr. Giasuddin Ahmad.
B. Sc. Hons. M. Sc. (Dhaka), Ph. D. (Glasgow)
Professor, Department of Physics
Bangladesh University of
Engineering and Technology, Dhaka.
and
Md. Shahabuddin, M. Sc. M. A-
Librarian, Bangladesh University of Engineering and
Technologr, Dhaka.
Formerly of the Department of Physics.
Ahsanullah Engineering College and Bangladesh University
of Engineering and Technology, Dhaka.
FOURTH EDITION
ThoroughLg reuised bg
ProJ. Giasuddin Ahmad Ph. D.
Department of PhUsics, Bangtadesh Uniuersitg
oJ Engineering and" Technologg. Dhcrka
IrIAF.IZ BOOK CENTRE
PREFACE TO FIRST EDITION CIIAPTER I. INTRODUCTION
The "Practic-al Physis5 for Degree Students" is designed to co\rer ArL 1.1 Importance of laboratory work I
the syllabi of the B.Sc. Pass and Subsidiary and B. Scl@ngineering) Art. 1.2 Errors in measurements I
examinations of the different Unlrrersities of pakistan. our long Art. 1.3 Degree of accuracy in measurement
experience in teaching physics and conducting practical classes 4
has acquainted us with the various difficulties=that the students Art. 1.4 Drawing of graphs 5
face in performing experiments. In this textbook attempts have Art. 1.5 Experimental guidelines I
breeceonr dm daadeta tosy gstueidmea ttihcael lsy tuadnedn ttsh esno cthoarrte ltahteey thmeamy ptoro cgeeetd t hteo Art. 1.6 A few general instructions t2
rmesaunlntse. rs strobj ethcta mt tahftee r sotuf dtheen tbso omk ahya sin bdeeepne nprdeesnetnlyte dp einrf oi'srmim pthlee CHAPTER II. GENERAL PROPERTIES OF MATTPR
eexxppeerrimimeenntst wreiltehvoeunt tt hqeu ehsetlipo nosf tahne dte tahceheirr sa. nAstw theers ehnadr roef beeaecnh Art. 2.1 The slide callipers 13
provided, thus clarilying the theoretical aspect of the experiment. Expt. l. To measure the length of a rod with a
lables are provided at the end of each eiperiment. Hor,vever, it vernier callipers. l5
should be remembered that they are purely suggestive and there is ArL 2.2 The screw gauge 18
nothing special about any particular form of tl-bulation. Tables of Expt. 2. To measure the diameter of a piece of
physical constants and logarithmic and trigonometrical tables have wire with a screw gauge and to find its
bIpMneho eyownsre ircp,i tsrSlo n svDgpid aeettchtdaiai ,sal l Kytb .t tohGhoeo.k sMe ewna dbjeu yo mc fW odthanaerst,s u boRltonoeo.yd k W C dfhooiforrfs uernderoehapnud rtya y b,nr eodGfoe aFrkenslngi ncuoetl,in. , A Hpll.re aSnci ntaigcnhad,l AEIxLpt. 2J..3 TTavohe edr aesgtpeehr mcerrioonsmes -etshteeecr ttiohnickness of a glass 2203
J Chatterjee and K. Din. Various theoretical books hive also been plate wlth a spherometer 24
consulted. Art- 2.4 The balance 30
We like to thank Professor K. M. Saha, M.Sc. Head of the Art. 2.5 Travellins microscoDe 32
Department of Physics, E. P. University of Engineering and Art" 2.6 Cathetometer 34
Techonlogr, Dacca, for hts keen interest in the 6ook an? his Expt. 4. To weigh a body by the method of
constant encouragefirent and guidance. We also like to thank our oscillation 37
colleagues Mr. T. Hossain. M. Si. and Mr. Asadullah Khan. M. Sc. for Expt. 5. To draw a graph showing the sensitivity of
their various helps rendered during the preparation of this book. a balance with loads 39
WMe. Sgcr.a t(eDfaucll)y, Mac. kAn.o w(Cleodlugme btihae) fdoerb mt awney ovwaelu atob lMe ra.n Nd ucrounl sMtroumcteivne. Expt. 6. Tmoa tdeertiaelr mofi nae w thiree Ybyo uSnega'srl em'so aduplpusa froart tuhse 43
suggestions.
Wfoer halisso a lciktiev eto c oth-oapnekr aMtior.n Hians sbarinn gZionbge roi uotf tMhi/sS .b oZookb.e rTi haanndk sp eaarrel Expt. 7. Tfleox duerete romf ian eb ethaem Y (obuenngd'isn gm modeultuhs obdy )t he 50
also due to Mr. Anwar Ali of the Department of physics rvho helped Expt. 8. To determine Young's modulus (Y),
us in getting the manuscript typed within a short time. rigidity modulus (n) and Poisson's ratio
The book has been hurried through the press and as such some (o) of a short wire by Searle's dynamic
printing mistakes might have crept in inspite of our best efforts. method 55
We shall -gratefully welcome any suggestion which may help to Expt. 9. To determine the modulus of rigidity of a
improve the book. wire b1r statical method. 59
to. To determine the modulus of rigidity of a
E. P. University of Engineering and
wire by the method of oscillations
Technologr. Dhaka.
IstJanuary, 1969 a/@yfintic method) 65
Expt. l\lt\. ,/ T{debrmine the spring constant and
Giasuddin Ahmad '.-.v{ /effective mass of a given spiral spring and
Md. Shahabuddin hence to calculate the rigidity modulus of
l-he material of the spring 68
\
TTflyoo- wddheeetteeerrlmm ailbnnoeeu ttthh ieets vm aaoxluimse e oonf ft r goo,tf a altnciocener.tleiara otifo na 73 Expt. 29. Tcoon ddeutcetrivmttlyn eo ft hae m ceota-el fuficsiienngt Soefa rthlee'srmal
apparatus t62
due to gravity, by means of a compound Expt.
pendulum 30. To determine the thermal conductivitv of
EEExxxpppttt... 11t465... TvTbTreeoyoovr icdeddffaeree sptJtteieeiublrrrllrammmeinr ilyinpn'ns eeeet u n l atttbdhhwheueee. l u mvssmauuelr.truhffaeaoc cdoee f at'tgene,ndn bs shyiiooe nKnn acooeteff rtw'osater 88794A EExxpptt.. 31. DTc(amYo oe eb=n satdso hdectroa mtodcen/eortcm 'nsrpd. ir)nmue efcseo tsttrohhu raore ebdi r y.r aab Lntyiedo eC csole ofam nnssedptn eaCtc nhiatf olncvrd lotholuenma'stes at 1t6727
Qmueirnccukrey sa nmde tthhoed a.ngle of contact by 95 32. vTsaionr kidoeeurtse rtmeminpee rthaetu rdee bnys itmy eoafn ws aotfe ar galtass
Expt. 17. To determine the surface tension of a 177
liquid by the method of ripples (Rayleigh's CHAPTER IV - SOUND
method)
99
Expt. t8. To determine the co-efficient of viscosity ArL
4.1. Some terms connected with experlments
of a liqutd by its flow ilrrough a capillary 105 on sound l8t
tube. tuL
Expt. 19. To show tle variation of viscosity of water 4.2. wIntaevrfeersen ce of sound and stationary
with temperature. llo ArL l g4
Expt. 20. Tdeo tevremriifnt eS ttohkee v'si slcaows iatyn do fh ae nlicqeu itdo Expt. 43.33.. VToib friantdio tnh eo fv aa rsiatrtilnogn foixf etdh ea tf rbeoquthe necny dosf a l g4
(glycerine) tt4 tuning fork with the length of a
sonometer (n-l curve) under given tension
CIIAPTER III . HEAT and hence to determine the unknown
frequency of a tuning fork
Expt. 186
Expt. 21. To determine the pressure co-efficient of 34. To veriff the laws of transverse vibratlon
a g.as at constant volume by constant of a stretched string by sonometer I92
Expt.
volume air thermometer 120 35. To veriff the laws of transverse vibration
Expt. 22. To determine the co-efficient of of strings and to determlne the frequency
expansion ofair at constant pressure by of a tuning fork by Melde's experimlnt i96
constant pressure air thermometer r28 Expt. 36. To determine the velocity of sound in air
Expt. 23- To determine the true temperature of a by Kundt's tube
Expt. 24. Tbmyoi x tdthueertee mr mbeyitnh reoa ddt hioaeft imsopniex tccuiofrirecr e hwcetiitaohtn oraf daia sUoolind 134 Expt. 37. Theoa dt eatte rcmoninseta tnht ep rreastslou roef othf ea irs ptoe ctihfiact at 2Ag
correction constant volume 1y= CO/C) by Kundt's
140
Expt. 25. To determine the specific heat of a liquid tube. 208
by the method o[ mixture
Expt. 26. To determine the specific heat of a liquid 144 CIIAPTER V - LIGHT
by the method of cooling 146 Art.
Expt. 27. To determine the latent heat of fusion of Art. 5.1 Parallax 2to
ice by applying the method of radiation Art. 5.2 The optical bench and its uses. 2r2
correction 5.3 kns 2t4
152 Expt.
Expt. 28. To determine the latent heat of steam by ,:7 To determine the focal length and hence
applying the method of radtailon the power of a convex lens by
correction displacement method wlth the help of an
157 optical bench
221
-/
Expt. ^-W v z/ )" determine the focal length and hence CHAPTER VII . ELPCTRICITY
I the power of a concan e lens by using an
arxiliary convex lens 227 Art.
.10. 7.1 Sonre electrical accessories 330
Ex1.lt. fvf-/ ,rTlioqu dide lebrym pinine mtheeth roedfr atrcstiinrrge ain pdleaxn eo fm airror AArrtt.. 7.2 Electrical cells and their uses 340
7.3 Galvanometers and their uses 346
and a convex lens 232 Art.
Expt. 4l To determine the refractive index of the ArL 7.4 Shunts 349
7.5 Ammeters 350
material oF a convex lens by a telescope Art. 7.6 Voltmeter 352
arrd splrerometer 237 Afl.
Expt. 42 To determine by Boy's method Art. 7.7 Polarity tests 353
7.8 General rules to be observed in electrical
a. the radius of curvature of a lens and
experiments 354
b. the refractir,e index of the material of Art. 7.9 Principle of Wheatstone's network: metre
the lens 241
Art. 5.4 Experiments rr,,ith the spectrometer 245 E-xpt. bridge; post office box 355
Expt. 43. 'l-o foctts the spectrometer for parallel 53. To determine the end-corrections o[ a
metre bridge 359
rays 255 Expt.
Expt. 44. To determine the angle of a prism (by Expt. 54. To calibrate a metre bridge wire 364
55. To determine the specific resistance of a
rotation of the telescope) 260
.dpt. 4s. To determine the refractive index of the grq{- wire using a metre bridge 367
sa To determine the value of unknown
material of a prism 264
Art 5.5 lnterference of light 270 resistence and to verify the laws of series
Expt. 46. To determine the radius of curvature of a and parallel resistances by means of a
Post Office Box 371
u*^/ lens by Newton's rings 274 Art. 7.1O Uses of suspended coil type galiranometer 378
To determine the wavelength of Expt. ..57 To determine the figure of merit of a
nronochromatic light by Newton's rings 284 ,/
Art. 5.6 Essential discussions for diffraction --gx{t. E8 Tgaol vdaentoemrrneitneer the resistance of a 379
experiments 285
Expt. 44. To determine the wavelengths of various Expt. galvanometer by half-deflection method. gB2
59. To determine a high resistance by the
spectral lines by a spectrometer using a method of deflection 385
plane diffraction grating 29r Expt.
Art. 5.7 Polarization of light 294 60. To determine the value of low resistance
Expt. 49. To calibrate a polarimeter and hence to b(My atthheie mseent haodn do Hf foapllk oinf 'sp omteentthiaold of
determine the specific rotation of a sugar projection)
389
solution by means of a polarimeter 306 Expt. 6l To determine the electro-chemical
CIIAPTER VI . MAGNETISM eqrrivalent of copper by using an ammeter
and copper voltameter 394
tut. Expt. 62 Determination of electro-chemical
6.1 Magnetometers 314
Expt. equivalent of silver using an ampere
50. To deterrnine the horizontal component
balance 396
of the earth's magnetic field and the Art. 7 .l I Potentiometer and its action 403
magnetic moment of a magnet by Art.
7.12. Precautions to be taken in performing
Expt. 51. Tenor pcloomyipnagr em thaeg nn-reagtnoemtice mteomrse nts of two 317 Expt. experiments with a potentiometer 406
63. To determine the'e.m.f. of a cell rvith a
nlagnets 324
Expt. 52. To measure the magnetic dip at a place. JZi) pao mteinllitaiommmeeteter rof known resistance using 408
Expt. -9d To compare the e.m.f. of two cells with a
potentiometer
4lO
/
Expt. CONTENTS
65. To measure the current flowlng through a
resistance, by measuring the drop of OF
ppootteennttiiaolm aectreorss it, wlth the help of a ADVANCED PRACTICAL PHYSICS
417
K(
66 To determlne the internal resistance of a
Expt. cell by a potentiometer 421 * To determine the thermal conductivity of rubber.
67 To calibrate an ammeter by potential drop *
method with the help of a potentiometer 424 To determine Stefan's constant.
Expt.
68 To calibrate a voltmeter by a {. To determine the angle of prism by rotation of the prism table.
Expt. 69 Tpoo tdeentteiormmientee rthe value of J, the 429 * To determine the refractive index of the material of a prism.
*
mechanical equivalent of heat, by To determine the refractive index of the material of the thin
Expt. electrical method +JJ prism by the method of normal incidence.
7O Tamnoe dcd heBataenrricnmaeilsn eeeq lteuhclevt raviclaealnul te mo foe fth heJoa,d tt hbey Callendar 439 Tano dd eate rgmivineen t hlieq ureidfra bctyiv eto intadle xin otefr tnhael mreaftleerciatilo no f uas pinrigs ma
ArL 7.13 Carey Foster's bridge 443 spectrometer.
Expt.
71 To determine the resistance per unit To measure the dispersive power of the material of a prism by
Expt. length of metre bridge wire 443 spectrometer using a discharge tube.
72 To compare two nearly equal low *
resistances by Carey Foster's bridge 447 To calibrate a spectrometer.
Expt. J3-' To determine the temperature co- * To determine the Cauchy's constants and the resolving power
l efficient of the reslstance of the material
of a wire 450 of the prism using a spectrometer.
Expt. 7 4 To determine boiling point of a liquid by To determine the wavelength of monochromatic light by
platlnum reslstance thermometer 454 Fresnel's bi-prism.
Expt.
75 To construct an one ohm coil 464
Art. 7.14 Thermo-couple 467 To determine the thickness (or refractive index) of a very thin
Expt. 76 To plot the thermo-electromotive force- transparent plate.
ttehmerpmeora-ctouurep le(c aalinbdra htieonnc ec utrov ed)e ftoerr ma tgieiven To determine the refractive index of a liquid (available in
its thermo-electric power 470 minute quantities) by Newton's rings.
Expt.
77 To determine the melting point of a solid To determine the separation between D1 and D2 lines of
by means of a thermo-coupte with the
sodium by Michelson interferometer.
help of a calibration curye. 481
AErxtp. t. 7.15 The triode val.se-tts descrtption and action 447 To determine refractive index (or thickness) of a film by
7a. To draw the characteristic curves of a Michelson intOrferometer.
tcroiondstea natnsd hence to determtne its 489 To determine wavelength of monochromatic light by
Art.
7.16 Semiconductor diode 499 Michelson interferometer.
Expt.
79 jTuon cdtriaornv t(hsee mchi acroancdteurcistotirc)s doiof dae .pn 505 To determine the melting point of a solid by means of a
Expt. 80 To determine e/m of electron using thermo-couple with the help of a calibration curve.
Art. 7.17 HPheolmtoh-oelltezc ctroicil effect 551116 To determine the logarithmic decrement of a ballistic
Expt. 8l To determine the threshold frequency for galvanometer and hence to determine its critical damping
photo-electric effect of a photo-iathode resistance.
and the value of the Planck's constant by
using a photo-electric cell 519
CIIAPTER T
INTRODUCTION
r.T IMPORTANCE OT LIIBORATORY WORK
A student of physics should realise that the laboratory
work, popularly known as practical classes, is no less
important than the theoretical lectures. In performing an
experiment in the laboratory, one is required to revise
thororrghly t.he ideas and the principles involved in the
experin)ent which were explained by the teachers in the
t.heoretical classes, possibly long ago. Thus practical classes
serve as a sor[ of revision exercises of the theoretical
lectures. Moreorrer, laboratory work n-lakes a student
methodical, accurate, diligent and trained to rules of -
discipline.
The overall aims of the physics practical programme are
to help the students learn
a to experiment i.e. measure unknown quantities and draw
conclusion from them.
b. to write scientific (or technical) reports and papers and
c. to use specialized methods of experimental measu_
rement.
r.2 ERRORS IN MEASUREMENTS
In detemining a physical consta,t in Lhe raboratory, it is
necessary to measure certain quantities which are related to
the constanL in a formula. Measurement of these quantities
involves various errors which are enumerated below.
(a) Personal Errors: When recording an event, the same
person at different times and different persons at the szune
tinre record it clifferenily. This is due to the personal
qualities of the workers. For example, different time keepers
in a sport are found to record different times o[ start ancl
finish. Inexperienced observers or observers not in a normal
state of health make errors of varying magnitude. Such
errors may be eliminated by taking mean o[ several
observations.
\_
3
for Degree Students
Practical Physics
(b) Constant or Systematic Errors: Errors which affect (d)ErrorsofMethod:Theformulawithwhichtheresult
the result of a series of experiments by the same amount is is calculated may not be exact and hence inaccuracy creeps
called the constant error. Faulty graduation of an instrument, in the calculated result. care should be taken to see that the
which is used in veri$ring certain physical laws, introduces a basis of calculation is exact and accurate'
constant error. In determining the value of g by simple (e) Pq4lqx E11gls: When a reading is taken along a scale'
tpheen dvaulluuem .o bthtaei nleendg ftrho mof wa hsiecrhie iss omf eoabssuerrevda tbioyn as fwaouultlyd sdciafflee,r stotr atitgretr t-sourr fcaicrcei toafr Jthhee slicnael eo.f Dsiugeh tt om ucsatr eblee sastn reigssh ti nan tghleiss
by a constant amount from the true value. Such errors are respect an error in reading is inevitable' This error in
eliminated by different methods. ."uitng due to looking at wrong direction is called error due
(i) In some experiments errors are previously to parallax. In order to avoid such errors the scale' straight
determined and correcti.ons in the readings are made or circular, is often placed over a mirror' An image of the
accordingly. Thus, these e.-rors cannot affect the final resul. objecL is formed in the mirror by reflection and the reading
Exanrples of these errors are the zero-error in measuring of the object is taken wi[hout ditticulty'
(0 Level Errors: Instruments like a balance'
instruments such as screw gauge, slide callipers, end-errors
in a meter bridge etc. spectrorfrEGr,-difficle etc, require levelling before use.
(ii) In some experiments error is allowed to occur and These instruments are generally provided with levelling
then eliminated with the help of the data recorded during screws. Using a spirit level and by adjusting the screws'
the experiment. In determining specific heat of solid or levelling is done.
Iiquid by the method of mixture, the loss of heat by radiation (g) Back-lash Error: It occurs when one part of a
is allwed to occur and then this loss is corrected for. connected machinery can be moved without moving the
(iii) There are cases in which errors are elimina[ed by other parts, resulting from looseness of fittlng or wear'
repeating the experiment under different conditions. Thus Generallythiserrordevelopsininstrumentspossessingnut
in an experiment with meter bridge in finding the null and screw arrangements. With continued use, the screw and
point, a tapping error is introduced owing to the fact that the nut wear away due to friction and the space within the
the pointer which indicates the position is not exactly nut for the play of the screw increases more and more' The
situated above the fine edge of the jockey which makes result is that when the screw is turned continuously in one
contact with the bridge wire. This is eliminated by obtaining direction, the stud at the end of the screw moves as usual;
two balance points after interchanging the resistance coils. but when rotated in the opposite direction the stud does not
wor(kc)e Ar chcaidse nnota lc oEnrrtroorl:. TInhesrpei tear eo fe rarollr sc oovrreerc wtihoincsh athned move fpr a while. The error introduced on reversing the
precautions taken against all possible known causes, some direction of turning is called back-Lash error. This is avoided
errors due to unknown causes occur which affect the by turning the instrument, before taking any reading' always
observations. Such errors are called accidental errors. Errors in the same direction.
in such cases are reduced by taking a number of observations (h) Probable Error: Probable error means the limit rvithin
and finding their mean. By applying the theory of which the true value of the constant probably lies. If x be the
probabilities, it can be shown that if the mean of four arithmetic mean of a set of obsewations and o the probable
observations instead of a single observation be taken, the error, then the true value is as likely to lie within the range
accidental error is reduced to * or I of the error that x 1 a as outside it. If the observed values of the same quantity
,{+z u be x1 , xz .....xn, then m, the arithmetic mean of these
comes in with single observation. values, may be taken to be the nearest approach to the
Practical PhYsics
for Degree Students
correct value of u. Let us now determine the limits within
which the errors of u may lie. tf d be the arithmetic mean of maximum value of f ," glven bY
the numerical values of the deviations of individual
observations given by dr =@ym), d2=@2-m), .... dn=@n-m), (T)'""-= u * * 4 . "\ """""' t't
then d will give the mean error and for all practical
In equation (21 a, b, c are numerical values of the powers
t
purposes, tr-m d.
and are taken as Positive.
The probable error may be calculated as follows: 6u 5x &t 6z
(i) Calculate the arithmetic mean. The quantities f;, ;,i, V are the proportional errors
(ii) Find the difference between the observed values in nleasrrrernent ot the respeCtive quantities. When each is
and the arithmetic mean. It is called the deviationd' nrtrll-iplied by lOO, the corresponding percentage o[ error is
(iii) calculate the average value of the deviation without given. As the errors in x,U and z may not be in the same
taking their signs in consideration' Call this value 6 direction, the errors in u may be less tltan that given in
the average deviation. relalion (2). The error in the quantities to be measured is
(iv) Divide 6 by {n- f where n is the number of multiplied by l-he numerical value of the power to which
observations. o= 6l16-t is the average deviation o[ each quantity is raised as shown in the expression for
the mean. The probable error is O'B times this maximum error. It is, therefore. obvious that the quantitg
value. tmrtng the higl'rcst pouer slwuld be measured uith a ligher
Example: Suppose that in determining the resistance of precision Lhon the rest.
a wire with a meter brid$e the following vales are obtained For example, in determining the rigidity modulus (n) of a
in ohms. wire o[ length I and radius r, we use the formula
(i) 8.9, (ii) 9.3, (iii) 8.2' (iv) 9.1, (v) 8.8' (vi) 9"I'he Q99E
arithmetic mean is 8.9. The deviations are O'+O'4, -O'7, +O'2' ., = xzr4 /E\........ (sr
-thOe.1ir. saignnds , +thOe. 1v arelusep eisc t1iv.5e layn, dO tnhe aird advinerga gaen vda lduies r6e gisa rld'5in/g6 The power[ qis / 4 lor r, 2 for n and I for all other
quantities. The value of n is known. The value of r is to be
= O.25
The probable error is o.8 6/ rE--r = o.2 / ^[5-o'l' The measured. If r be measured with an error not exceeding O'OI
final value may. lherefore, be written as 8.9 + O' l ohms' mm, and if Lhe value obtained for r is O,5O mm' then the
percentage of error ,. + x IOO = 2o/o.lts contribution to the
1.3. DEGREE OF ACCURACY IN MEASUREMENT
maximum error in n will be 4 times this value i. e. 80/o' This
When several quantities are to be measured in an shows that the radius of the wire should be nreasured with
experiment, it is pertinent to examine the degree of high precision.
u""r.u"l,torvhichthemeasurementofthequantitiesshould
be pushed. Suppose a physical constant u is to be 1.4 DRAWING OF GRAPHS
deteimined by measuring the three quantities x, g and z The results of experiments often form a series of values
whose true values are related to u by the equation' of interdependent quantities of which one can be directly
u= -rl * .......-..... {rl controlled by experimental conditions and is called an
dts
Let the expected small errors in the measurenlent of the independ.ent oariable, and the other which undergoes a
quantit.ies x, A, z be respectively 6" 61 6, so that the error in consequent change as an effect is called dependent ooriable.
u is 6rr. IL may be shown by simple calculation that the The relations of such quantities can be expressed in graph'
for Degree Students 7
Practical PhYsics
(a) Representation of the variables along the axes. It is
customary that when the variables are to be plotted in a
graph, independent variables are plotted as the abscissae I
horizontally from left to right and the dependent variables as (p-r) bropt
a
(,
ordinate upwards. The variables plotted along an axis should o u.2
be written on the side of the axis. For example, in load E
elongation graph, the elongation always changes with the o
a
change of the load. Hence load is the independent variable E
(,
and the elongation is the dependent variable.
.,
(b) Markin$ of ori$in. First select the minimum value of lD
the two variables. Take the round numbers smaller than the ao
o
minimum values as origins for the two variables. The values a,
&
of the two variables at the origin need not be equal. In ro 20 30 40 50 60 70 80
certain cases one or both of the co-ordinates o[ the origin Temperolure in oC --
may be required to have zero value of the variables, even
though the minimum value of the corresponding variables Fig - 1.1
may be far above zero values. at O"C comes on the formula, the value of the origin for
Example: In determining the pressure co-efficient of a temperature is chosen to be O'C. Therefore' the value of the
gas, temperature is the independent variable and pressure is origin for temperature should be O"C (Fig. 1.U
the dependent variable. (c) Selection of units alon$ the axes. First determine the
A sample data is shown below: round number greater than the maximum value of the two
variables. Then determine the difference between this round
Temperature in "C Pressure in cms. of Hg. ntrnrber in respect of each variable and its value at the origin.
Divide this dilference b1' the number of smallest divisions
30 75.8
available along that axis of the graph paper. The quotient
35 76.8 tlrrrs obtained gives tlre value (in the unit of the variable
39.5 78.2 qrrantllies) ol' tlte srnallest division along the axis.
42.5 79.1 (d) Marking of data along the axes. After marking the
47.5 80.3 origin and cltoosing the unit, put down the values of the
qurantily corresponding to each large division mark on the
5r.5 81.6
sqrrared paper. These values should be integers, tenths or
60.o 83.5
hundredths, but ne\rer bad fractions.
64.5 84.7 (e) Plotting. Then plot the experimental data- Mark each
69.O 85.5 point by a small dot and surround it by a small circle or put a
72.5 86.7 cross. Co-ordinates of the point need nqt be noted unless it
is required for quick reference. Much writing makes the
Here the minimum values of temperature and pressure are graph look clumsy.
SO'C and 75 cms of Hg respectively. As the value of pressure