The effect of an electric current upon the elasticity of wires

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1 University of Iowa Iowa Research Online Theses and Dissertations 1912 The effect of an electric current upon the elasticity of wires Homer Levi Dodge State University of Iowa This work has been identified with a Creative Commons Public Domain Mark 1.0. Material in the public domain. No restrictions on use. This thesis is available at Iowa Research Online: Recommended Citation Dodge, Homer Levi. "The effect of an electric current upon the elasticity of wires." MS (Master of Science) thesis, State University of Iowa, Follow this and additional works at:

2 THE EFFECT OF AN ELECTRIC CURRENT UPON ELASTICITY By THE OF W IRES H. L. Dodge Thesis to presented the FACULTY OF THE GRADUATE COLLEGE of the STATE UNIVERSITY OF IOWA for the Degree of M aster of Science Juno, 1912

3 1. At least as early as 1644 an attempt as made to discover the effect of the electric current upon Young'3 modulus..vertheir, (Wiedemann s Eloktricitat, II, 218) using wires of gold, iron, 3teel, and silvor, stretched by means of weights found a decrease in Young's modulus due to the presence of current. Ho also found that the passage of current lowered the pitch of the musical tones from stretched wires. It would 3eem as if these effects could "be best accounted for through the heating effect of the current, "but Wertheim is quite emphatic upon thi3 point saying that this could not "be the case since the vires immediately upon the removal of the current assumed their former elasticity, Edlund (Annal. d. Phys. 129, 15, 1866) was not satisfied with V/ertheim s results. He made allov/ance for the temperature effect of the current measuring the temperature by the change in resistance

4 2. of the v;ire itself. His conclusion was that the current, except for the temperature effect does not change Young's modulus. On the other hand he found that there is an additional lengthening due to current, over and above the expansion due to temperature, the increase in length due to the pure current effect "being equal to the effect of an increase in temperature of from one to nine degrees Jentigrade. The following year Edlund (Annal. d. Phys. 131, 337, 1867) reports having found a source of error in the former method. His new observations result however in the very same conclusions. Streintz (Annal. d. Phys. 150, 368, 1873) feeling that the. results of Y/ertheim and Edlund wero somewhat contradictory, made the wires which ho studied part of a torsion pendulum. He found changes in iv\«_ modulus as given "below, the numbers showing by what per cent of the change due to temperature is

5 '3. the effect in the case of current greater than the pure temperature effect. Observations were taken at room temperature and at 55.5 C. (molting point of 3tearinc). P.esulte: Brass (a), -5.9; (b), +12.6; Copper, 0.0 ; 'Jilvor, +3.9; Iron, +3.1; Steel, It is a little surprising to find Streintz talcing the average (0.3) and from it concluding that there is no change in Young s modulus due to current. Another series of experiments showed an increase in length due to current a3 had been found by Hdlund. Mebius (V/iedemann illektricitat, II, 220) employing rods of stool, iron, brass, and silver, and using the method of bending found the change in the elasticity of the respective rods to be loss than , , , 0.0C37 per cent. LIlss IToyos (Phys. Rev. II, 279, 1895) using 3toel piano wires mounted horizontally upon a dividing engine secured rather consistent results

6 4. when the wires were heated externally hut no regularity in the case of current heating. The following year (Phys. -*ov. Ill, 433, 1896) with a 30mewhat improved apparatus and using steel, 3ilver and copper wires she reached the conclusion that except for the heating effect current has no effect upon Young s modulus. An inspection of her results leads one to question whether they justify this conclusion for although according to tho report each measurenent was made with great care the plotted results indicate a very great experimental error. Walker (Proc. Roy. Soc. Edin. 27, 343, 1907) following identically the same plan as Miss Noyes except that he used resistance to measure temperature (a method abandoned by Miss IToyes) found very irregular changes. A small current caused a decrease in the modulus in the caeo of 3teel, soft iron, and copper. This was not observed in the case of platinum.

7 Further increase in current resulted in a rapid increase in Young s modulus to a maximum value, followed by a decrease to about the original value. Upon cooling a maximum value was passed but the values of the modulus for decroasig current were considerably different from those for increasing, A more critical detailed discussion of the work of previous investigators is unnecessary here. It is evident that their results lead to no satisfactory conclusion. The writer upon careful examination of the literature arrived at the opinion that the inability of the investigators to secure consistent results or of any single investigator to secure results of unquestionable value was duo to the use of apparatus and methods which introduced groes errors. It was his conclusion that the working assumption should be that the changes in Yo u n g s modulus have some system and that inconsistent results should be attributed to faulty apparatus as long as

8 6. a possibility of improvement remains. Consequently in the work herein described no attempt has been made to refine the individual measurements but rather to set a certain standard of accuraccy that all measurement must satisfy and to eliminate from the apparatus every possible source of gross error. Form of Apparatus. 'rhe wire to be tested must of course bo enclosed in a box so that it may be raised to a high temperature. However it must not be permitted to come in contact with any portion of this box but rmist be freely suspended. The method employed to secure free suspension i3 3hown in * ig. 1 A light flexible cord passes from the weights (\V) over the pulley (P) and is joined to the wire to bo tested by means of the glass coupling (a) which servos as an insulator, as does also the adjustable support (b) at the other end of the wire.

9 Fig

10 8. Current is load to the wire at (d) and (d) "by mean3 of the mercury cups (c). Three thermoelements (th) wrapped around the wire are for temperature measurement. These are of very fine flexible wire. It will "be observed that except for the thermoelements the wire i3 freely suspended and is subjected to no mechanical forces other than its own weight and that of the weights (V/). In order that the heat generated by the current in the wire may be retained and to furnish a moans of heating the wire from outside a long narrow box a3 3hown in Fig. 2 i3 placed about the wire. I'he base (e), bottom piece (f), and back (1), t he latter two being covered with asbestos are securely fastened together. The asbestos covered front (h) which has two windows of mica (m) for observing the wire and the glass cover (i) are held by clamps, fhe glass tubes (k) are large enough to give a largo clearance to the wire (g) but small enough to prevent convection or other air currents.

11 9.

12 10. The space ( j) between the tubes and th e box is f i l l e d w ith g la ss w o o l. Z ig z a g g in g back and f o r t h across th e bottom p ie c e ( f ) i3 p la ce d a h e a tin g w ire o f german s ilv e r. I t is o f th e g re a te s t im portance th a t th e fo rc e o f th e w e ig h ts (W) be tra n s m itte d to th e w ire w ith no lo s s. A w h eel, th e means u s u a lly employed, was n o t c o n sid e re d a t a l l. In s te a d a p u lle y o f the form 3hovm in * 'ig. 3 was c o n s tru c te d. An aluminum d is c (D) was tu rn e d out and a s m a ll h o le (n) d r i l l e d e x a c tly in i t s c e n te r w h ile i t was s t i l l in th e la th e. By means o f a d ju s ta b le brass p ie ces (p) two sharp p o in te d screws (s) are b ro u g h t in to such a p o s itio n th a t th e lin e between th e two p o in ts as determ ined "by t r y square and s ig h tin g th ro u g h th e h o le passes p e rp e n d ic u la rly th ro u g h th e c e n te r o f th e d is c. P a rt o f th e p u lle y is c u t away b u t a c o u n te r w e ig h t is added as in d ic a te d. I t has been found by t r i a l th a t th e e r r o r due to th e p u lle y is to o sm a ll to bo d e te c te d.

13 Fig

14 12. The s tre tc h in g o f th e w ire is measured by means o f two m ic ro m e te r m icroscopes a tta c h e d to th e engine bod. The a d d itio n a l w e ig h t (\7») is added and removed q u ic lc ly and w ith o u t ohoclc by an a p p a ra tu s o p e ra te d by th e f o o t, Measurement o f Tem perature. A tte n tio n has a lre a d y been c a lle d to th e fa c t th a t some o f th e e a r lie r in v e s tig a to r s found th a t c u rre n t caused le n g th e n in g. The w o rk o f Basso, E x n e r, B lo n d lo t, and R ig h i (Wiedemann's S l e k t r i c it a t ) a lth o u g h n o t c o n c lu s iv e seems to in d ic a te th a t th e o n ly change in le n g th duo to c u rre n t can be accounted f o r by th e te m p e ra tu re. I t w ould seem as i f change o f le n g th should bo an a c c u ra te method o f m easuring te m p e ra tu re, b u t s in c e th e evidence is n o t c o n c lu s iv e and t h is m ethod has n o t re s u lte d in a n y th in g lik e s a tis f a c t o r y r e s u lts in th e case o f H is s Hoyes i t was d e cid e d to employ a means o f m easuring te m p e ra tu re independent o f any te m p e ra tu re e f fe c t in th e w ire i t s e l f.

15 13. *he tem p era ture is determ ined a t th re e p o in ts on th e w ire "by moans o f c o p p e r-c o n s ta n t in thorm o-elem ents o f #36 s i l k covered w ire. These are connected to a Siemens and H alske galvanom eter th ro u g h a th re e way s w itc h. A th e m o s b o t t le has been found a most r e lia b le means o f ke e p in g th e c o ld ju n c tio n s a t z e ro. The tem p era ture c a lib r a t io n is made d ir e c t ly in term s o f galvanom eter d e fle c tio n s as in d ic a te d in P ig. 4. Since h e a t is generated in every p a rt o f a c u rre n t c a rry in g w ire th e re is c o n d u c tio n o f heat from th e in s id e o f th e w ire outw a rds. C onsequently th e re i3 an in crease o f tem p era ture in th e c e n te r r e s u lt in g in a number o f e ffo c ts each o f v/hich has i t s e f fe c t upon th e c u rre n t d is t r ib u t io n and in tu r n upon th e te m p e ra tu re d is t r ib u t io n. Since th e therm o elem ents read s u rfa c e tem perature o n ly, i t is necessary when th e w ire is c a r ry in g c u rre n t to c o rre c t t h is re a d in g in o rd e r to f in d th e average tem p era ture th ro u g h o u t th e cross s e c tio n o f th e w ire.

16 C a l i b r a t i o n o f T h e r m o - e l e m e n t s. Fig

17 15. A m athem atioal a n a ly s is w ould g iv e a fo rm u la f o r average tem p era ture in term s o f s u rfa c e te m p e ra tu re, c u rre n t, and a number o f co n sta n ts v a ry in g w ith th e air^e and m a te ria l o f th e w ir e. The use o f 3uch a fo rm u la is open to th e o b je c tio n th a t th e accuraccy o f th e r e s u lts depends on w hether o r n o t th e th o m o -e le m c n ts road th e tru e s u rfa c e tem p era ture o f th e w ir e. I t was decided to get around t h is d i f f i c u l t y by m aking th e assum ption th a t constancy o f le n g th in d ic a te s constancy o f.a v e ra g e te m p e ra tu re. c o r re c tio n curves can bo made as fo llo w s. Then The w ire is heated e x te r n a lly to a c e r ta in temperature as is in d ic a te d by th e galvanom eter (therm o-elem ent) re a d in g s. The le n g th is observed and m a in ta in e d c o n s ta n t w h ile g re a te r and g re a te r c u rre n t is passed th ro u g h th e w ir e, th e c u rre n t th ro u g h the h e a tin g c o i l b o in g o f course decreased a t th e 3ame tim e. In t h is way, as th e c u rre n t in c re a s e s, th e same average tem p era ture is found to be re p re se n te d

18 16. by d e cre a sin g galvanom eter d e fle c tio n s. The s e rie s o f curves is shown in F ig. 5, in w h ich th e v e r t ic a l lin e s aro o n ly to f a c i l i t a t e th e re a d in g o f th e c o r re c tio n s. O b servations wore taken a t fo u r tem peratures (a v e ra g e ), 41 (X, 72 CL, 101 (i, and 137 C. a p p ro x im a te ly. Each s e rie s o f p lo tto d p o in ts in d ic a te s observed com binations o f c u rre n t and th o m o -e le m e n t re a d in g s th a t accompanied th o same le n g th. For in s ta n c e th o sane le n g th (sane average tem p era ture) was caused by a therm o-elem ent re a d in g o f and zero c u r re n t, by a therm o-elem ent re a d in g o f 128 C. and 8.7 amperes, and by a th o m o -e le m e n t re a d in g o f and 13,8 amperes. I t w i l l bo n o tic e d th a t i f th e th e m o -e le m c n ts do n o t read th e exact su rfa ce te m p e ra tu re, t h is is taken care o f a u to m a tic a lly by t h is m ethod. When no c u rre n t is p a ssin g th o w ire is o f u n ifo rm tem p era ture th ro u g h o u t and th e therm o elem ents g iv e th e tru e average te m p e ra tu re. But as

19 Fig. 5.

20 18. more and more c u rre n t is passed th e d iffe r e n c e "between th o average tem p era ture and th e therm o elem ent re a d in g in c re a s e s. F or any com b in a tio n o f s u rfa c e tem p era ture and c u rre n t th e re e x is ts a d e f in it e average te m p e ra tu re. For in s ta n c e i f we have a therm o-elem ent re a d in g o f and a c u rre n t o f 8 amperes we f in d t h is p o in t to bo on th e 120 C. c u rv o. The c o r ro c tio n w i l l bo 5 G.w hich is to be added to th e observed s u rfa c e te m p e ra tu re to f in d th e average te m p e ra tu re. The use o f therm o-elem ents has one decided advantage and th a t is th a t b?/ s lip p in g th o elem ents to d if f e r e n t p a rts o f th e w ire the d is t r ib u t io n o f te m p e ra tu re can bo found. As i t to o k tho a u th o r a number o f days to secure u n ifo r m ity o f tem p era ture i t is b o lio v o d th a t h e re in lie s a f e r t i l e source o f e r r o r in p re v io u s w ork in w h ich th e te m p e ra tu re wa3 measured by change o f le n g th o r re s is ta n c e. In these in sta n co s th e p re c a u tio n s ta ken to e o cu ro u n ifo r m ity o f te m p e ra tu re were o f a s o r t found by th e p re se n t w r it e r to be in adoquate.

21 1 9. I.fea3uremonts. The measurements th a t e n te r in to th e d e te rm in a tio n o f Young s modulus are mado as fo llo w s : Length o f w ir e * 7,'hile the o b se rvin g m icroscopes are s t i l l in p o s itio n th e w ire and h e a tin g box are removed and a standard m oter s u b s titu te d. The d is ta n c e between th e cross h a irs is the le n g th o f th o w ire. D iam eter o f w ir e. U sing one o f the m icroscopes and ta k in g o b se rva tio n s b o th from the s id e and from th e to p a s e rie s o f readings are taken and the average d iam e ter computed. Llass o f w e ights (\7f and ). U sing th o Iowa S ta te standard k ilo g ra m and o th e r standard w e ig h ts the th e mass o f the s tre tc h in g w e ig h ts i3 found. Value o f The v a lu e o f "g is used as computed f o r th e la t it u d o and e le v a tio n o f Iowa C ity. Value o f d iv is io n s o f m icrom eter head. The number o f re v o lu tio n s p e r mm. i3 determ ined f o r s e ve ra l d iff e r e n t d iv is io n s o f th e standard m eter and th e number o f ram. p e r re v o lu tio n computed.

22 20. Measurement of stretch. A scratch upon the copper wire is always brought by means of the dividing engine screw between the cross hairs of one microscope Tho stretch of the wire is observed by tho other telescope. G a lib ra t io n o f th e m o -e le m o n ts. This is done w ith an a ccu ra te therm om eter.?;easurement o f te m p e ra tu re. A sdescribed above.

23 21. M ethod of Taking Observations. Observations have been taken during the past winter upon two copper v/ires. Each was first heated to a high temperature and straightened by the weight (\7t). Thi3 weight was always kept upon the wire. The range of temperature was about 20 C. to T^e usual plan was to start in the morning with an observation at room temperature and gradually heat the wire by 20 to 30 stops taking observations as often as possible (half hour to hour). It was found that at least twenty minutes was required for the wire and enclosing box to reach a state of temperature equilibrium. The wire would then be cooled by similar steps and again heated if time permitted. This method was of course subject to groat variations, the wire being at times heated at once to high temperatures. At other times only extreme temperature conditions were observed etc. etc.

24 22. For any g ive n tem p era ture th e o b s e rv a tio n s were as fo llo w s. The th re e th o m o -e le m e n t readings are ta k e n. The r ig h t o b s e rv in g p o in t is then b ro u g h t between th e cro ss h a irs o f th o te le s c o p e by moans o f th o engine screw. The cross h a irs o f th e l e f t m icroscope a re b ro u g h t to th e l e f t o b s e rv in g p o in t and th o re a d in g o f th e m icro m e te r head re co rd e d. The a d d itio n a l w e ig h t (W ) is added by means o f th o fo o t lo v e r and tho r ig h t o b s e rv in g p o in t brought in to p la ce a g a in. As q u ie t ly as p o s s ib le th e l e f t cross h a irs are again s o t, th o d iffe re n c e in th e s e ttin g s o f th o l e f t m icrom e ter screw g iv in g th e amount o f s tr e tc h. About te n such re a dings a re taken and th e therm o-elem ents read a g a in. Sources o f K r r o r and Aocuraocy o f.york. When a w ire i3 s tre tc h e d h o r iz o n ta lly i t s w e ig h t causes i t to hang as a c a te n a ry. C onsequently a p a rt o f th e apparent le n g th e n in g caused by th e a d d itio n o f a w e ig h t is due to th e s tra ig h te n in g o f th e w ir e. In o rd e r to

25 2 3. determ ined th e in flu e n c e o f thi3 fa c to r, th e v a lu e o f (c) in th e fo rm u la f o r th e ca te n a ry (y + c = / c* + ) was computed in term s o f le n g th o f w ire. The v e r t ic a l m otion o f th e two o b se rvin g p o in ts and tho c e n te r was computed and found to correspond to th e observed m o tio n. Prom these values was found th e e r r o r due to s tra ig h te n in g o f th e w ire, w hich e r r o r amounted to about 1/100 o f th e s m a lle s t re a d in g o f th e m icrom e ter screw. About 3,000 s in g le o b s e rv a tio n s have boon made b u t tho c h ie f use o f th e g re a te r p a rt o f those has beon to in d ic a te in what d ir e c tio n to seek f o r improvement in th e apparatus and method. A t th e tim e o f w r it in g the apparatus possesses th e fo llo w in g advantages. The w ire is fre e from c o n ta c t w ith any body w hich n ig h t a ffe c t it s p o s itio n o r apparent le n g th. The w ire is mounted in a box arranged to socuro u n ifo r m ity o f tem perature over th e p o r tio n under o b s e rv a tio n. The fo rc e o f th o w e ig h ts is a p p lie d to th e w ire i t s e l f w ith o u t lo s s o r g a in. A lth ough those c o n d itio n s are e s s e n tia l to s a tis fa c to r y work th e r e s u lts o f p re v io u s in v e s tig a to rs would in d ic a te th a t th e y have n o t been secured.

26 Results. On the following shoet3 aro found data and curves for four series of readings for Wire #2. The meaning of the symbols used at the head of tho colimns of data on the following sheets i3: Obs. no... Observation number Time Temp. T (obs) T (cor) I Stretch... Timo of observation... Average temperature of wire... Temp, of surface as indicated by thermo-elements... Correction applied to T (obs) in the case of current heating in order to get "Temp., Temp. = T (obs) + T (cor)... Current in tho wire (cmpcros)... Stretch in terms of revolutions of micrometer screw Y. M Young's modulus, (the numbers giyon are to be multiplied by 10 to give tho modulus in dynes per cm.2

27 25. Data Concern inf; the W ire. Length o f w ire (observed p o rtio n ) cm. Diam eter o f v / i r e mm. Mass o f W, g. Mass o f W» g. Value o f " g " S tre tc h in g fo rc e due to x 10 dynes. "5 tr c tc h in g fo rc e due to W x 10 dynes. Value o f d iv is io n s o f m icrom eter head 1 mm. = re v s. 1 re v. =.047 mm. 1/50 re v. = mm. (s m a lle s t reading) Amount "by w hich w ire s tra ig h te n s when Y.' is added, o r the v e r t ic a l m otion o f the ce n te r r e la tiv e to the obse rvin g p o i n t s mm. Formula used... M = 46.8 x IQ11 Revs, (s tre tc h ) (no account is taken o f change o f le n g th w ith tem perature)

28 26. Wire #2, Series #4. Obs, no. Time Temp. Stretch Y.M. 1 3:15 P.M. 25 C : :40 A.M : : » :00 P.M : External heating. March G t 7, 1912.

29

30 28. W ire #2, Series #5. Obs. no. Time Temp. stretch Y.M. 1 9:00 A*M. 18 C :30 oo : : : : :00 P.M : : : : : : : : : : External heating. Tnarch 9, 1912.

31 W i r e # 2, S e r i e s #

32 3 0. Wire #2, Series $6. 0bs, no Ṭ i m e T (obs) T(cor) Temp. I Stretch Y.M. 1 8:40 A.M amp : : : : :00 N : : : : Internally heated. March 12, 1912.

33 31.

34 32. Wire #2, Series #7. Obs. no. Time T(ob3) T(cor) T mp. I Stretch Y.M. 1 10:30 P.M. 20 C 0 G 20 G 0.0 amp :15 A.M : :05 P.M : : : : : :10 27 e : : : : : : : : Internally heated. March 13, 1912.

35 33.

36 34. W ire #2, Series #9. Observations taken with internal heat inf;, both A.3. and D.C., and with external heating. The length v;as kept as constant as possible. O b s e r v a t i o n number M e t h o d o f R e a d i n g o f s c r e w i n d i c a t i n g heating l e n g t h S t r e t c h ( r e v s. o f s c r e w ) 3 External A.C D.C External (D.C.) external (A.C.) D.C The greatest variation in length is 0.15 rev. of the micrometer head or about.000 mm. This corresponds to a temperature variation of less than one degree Centigrade. The variation in 3tretch is not more than the experimental error.

37 35. Discussion of Results. Fron the curves and data 3hovm on previous pages and other results that aro not shown we can at once reach a number of important concisions regarding the particular wires employed. (1) Young's modulus decreases about 10 when the wire i3 heated either externally or internally, from 20 C. to 140 C. (2) The decrease in Young s modulus is not a linear function of temperature. (3) The indications are that the permanent changes in Young's modulus duo to repeated heating and cooling are relatively small and that the nature of the temporary changes i3 not much altered by any permanent changes there may bo. (4) Passing from D.C. to A.C. internal heating and to external heating and regarding constancy of length as an indication of constancy of mean temperature, no change in Young's modulus can bo detected.

38 36. (5) There are indications however of a difference due to current when the wire has been allowed to codl in the meantime. But it is believed that tho use of a more steady current and slight changes in the apparatus may show this to be caused by experimental error. It will be so regarded until another conclusion is inevitable. Future Work. Only enough curves and observations have been referred to and shown to indicate that already some very consistent and conclusive results have been obtained. The way i3 now open for a large amount of work upon different materials. Preparations are being made for the use of steady direct current from storage cells so that the work can be continued at once.

39 37. Although the use of thermo-elements has been essential to the securing of uniform temperature along the wire, it is expected, that the measurement of temperature in terms of lengthening may prove to possess some advantage. It is expected that tho presence of current will prove to have no measurable effect upon Young's modulus except through the heating effect, but it is still an open question as to whether or not a wire heated by a current will have a different elastic history than dne heated otherwiso. The study of various kinds of wire and the use of much higher temperatures will undoubtedly prove of great value. While this is being done the pure temperature effect will of course be found with considerable accuraccy. These results of theso control experiments alone will be worth the labor. Regarding the temperature effect but little is known. Some Investigators have measured Young's modulus at

40 two or three temperatures. Only a few have taken observations at frequent intervals over considerable temperature ranges, and their work does not agree. Consequently the continuation of this investigation will not only lead to a knowledge of the effect of current upon the elasticity of wires but also the effect of temperature and of history. In conclusion I wish to express my great appreciation of the assistance of Professor Stewart who not only suggested tho problem but has kept in constant touch with the work and aided with suggestion and encouragement. Thesis, *he Effect of an Electric Current upon the Elasticity of 7/ires, State University of Iowa, iowa City, Iowa, May, 1912, H. L. Podge.