PR O B L E M S I N A LTERN A TIN G CU RRENT MA CH INERY BY D LY WAL O V . ON I N S TR TO R I N E LECT R I C A L E N G I N E E R I N ETT U C G . M A S S A C H U S S N S T IT TE O F TE I U C H N O LO G Y . FI RST E DITION M c RA W—HILL BOOK COM P N I Q A Y , N C . 239 WEST 39TH T EE S R T , N EW YO RK e BOU VE I S RE E N O N LO E . R E T T . D . c 1 9 1 4 C P G H 1 9 1 4 TH E O YRI T , , BY - M C G AW H B K C PAN I N C . R ILL OO OM Y , T H E o M A P L E o P R E S S - Y O R K P A PREFA CE These prob lem s chiefly concern the theory of the operation o f n to alternating curre t machinery , and are such as we give the fourth year students in electrical engineering in this subj ect . In each chapter the problems of a similar nature are grouped f together , and those o each group are then arranged in the i approx mate order of their difficulty . The groups in each chapter f f ollow each other in as logical an order as possible , both rom point of difficulty and the presentation of the subj ect . In order that this collection of problems may be useful among iff s o f d d erent clas es students a large variety has been include , ranging from the very simple t o those of considerable difficulty . Wherever it is essential the data have been taken from actual of apparatus . This was possible through the courtesy two of f the large manufacturing companies . In some o the problems so few data are given that approximate methods of solution s must be used , but care has been taken to o state them that the errors thus introduced need n ot be large . This lack of data is frequently met in practice. It has been thought best not to give introductory paragraphs for each chapter as was done in the preceding vol ume o f prob lems inasmuch as they would have to be of considerable length to of be much value . The answers to the problems will probably be ready fo r 4 he publication in the fall o f 1 91 . T y will be available to all but undergraduate students at a nominal price . Undergraduate students can obtain them o nly on the recommendation o f their instructors . L WALDO V . Y O N . MA ACH U S I N TxT T F T C H N G SS ETTS S U S O E OLO Y , ecember l 3 . D , 1 9 CONTENTS C H AP TE R I . TRANSF ORMERS (98 PROBLEMS) I o o m n z c um of ns f c r n l ss, ag eti ing urrent , n ber tur , ef e tive resist c an d c c co o l o c c o an e rea tan e, pper l ss, regu ati n, effi ien y, aut sfo m c o e o a a o o . tran r er, indu ti n r gulat r, p r llel perati n 1 1 . SYN CH RONOU S GE N ERATORS (99 PROBLEMS) G ec om o o c o m f c o m on c con cen enerated el tr tive f r e, f r a t r, har i s, trated an d i c a c a m r distributed wind ngs, leakage rea t n e, r atu e ac o c o o ac nc o a e u o —co m r s o re ti n, syn hr n us re ta e v lt g , reg lati n pa i n of m o ff c of o c o f c c r l o o eth ds, e e t p wer fa t r, e fi ien y, pa al el perati n, in hun t g . III . SYN CH RONO U S M OTORS (50 PROBLEMS) E c a o c c o c o m m m c x it ti n . effi ien y , p wer fa t r, axi u urrent , break ’ o efi cct of n c an d c n c mi o n l d wn, added resista e rea ta e, trans ssi ine m s n u o o ac o co o . reg lati n, p wer f t r pen ati I V . I N N P DU CTIO M OTORS (80 ROBLEMS) . o c c rr o o n c Flux distributi n, ex iting u ent, ir n l ss, windi g pit h , t c r o on o o star ing u rent, t rque, speed regulati , breakd wn t rque, f c of s c an d ac c H e lan d m e fe t added re istan e re tan e, y diagra , c c o of ch a c i c co c o c o en al ulati n ra ter sti s, n atenati n, indu ti n g erat or c ch o o c c o of c , ne essary syn r n us apparatus, al ulati n har ristics acte . V . R OTARY CONV ERTERS (6 1 PROBLEMS) o o ff c of " ux o o s V ltage rati , e e t distributi n, relative utputs, tran o m c c m c o n c o f r er apa ities, ar ature rea ti , ex itati n, series field n c c . tur s, effi ien y > VI . PO L Y1 H A S E C P IRCU ITS (75 ROBLEMS) . an d Y co c o c an d n c d o Delta nne ti n, balan ed u balan e l ads, c rr o m a m u c o neutral u ent , p wer e sure ent with nbalan ed l ads, o m co c o s an d c c o- transf r er nne ti n relative apa ities , aut trans o m s m o o an d c c co m f r ers, tran issi n line regulati n effi ien y , bined c c an d o of o i an d o m s effi ien y regulati n generat r, l ne transf r er , c o an d nc o o m o indu ti n sy hr n us tor loads . - VII . N O N S rN Oso m A L WAV 44 P ES ( ROBLEMS) . an d i o t wo- t hr ~ h Phase l ne v ltages , phase o t ee p ase transforma o c o m m ff c o f c c ti n, neutral urrent , p wer easure ent , e e t indu tan e an d c c c c ic o o f o u c n apa ity, y l rder v ltages , nbalan ed loads, tra s f m or er connecti ons . INTRO DUCTION The great importance of problem work in the training of stu dents of engin eering is n ow generally recognized . No other work so f r e ficiently develops analytical power and clea , logical think so t f . ing , necessary o succ ess in the engineering pro ession Yet i f notwithstand ng the importance o problem work in general , the first consistently developed book of electrical engineering prob 1 r. L 08 lems was that prepared by M yon in 9 , its wide use being conclusive evidence of the needs that were felt among both of teachers and students for such a work , and of the appreciation the importance of the trainin g which it exemplifies . It req uires a special gift to origi n ate and develop problems which shall give sound training in the fundamentals of engineering l n and whose solution sha l ot only interest the student , but develop n l his i te lectual power as well . In general the problems must be to n to closely related engineeri g practice , graded as difficulty , M r . and must carefully avoid being mere mathematical puzzles . L yon , as his earlier book also shows , has a most unusual ability in the preparation of problems for the electrical engineering field . The present collection of problems relating to electrical n f machi ery , more particularly in the field o alternating current as engineering , has been prepared with the same point of view w ’ as M r. L yon s earlier work , and should likewise prove most s l to u efu both instructor and student . E . LI F D F O R . H . C HA V A D N V E R R U I RSITY , ber ecem 1 1 . D , 9 3 PROBLE MS IN A LTERNA TIN G CU RRENT MA CH I NE RY CHAPT ER I TRANSFORM ERS 4 8 1 . The iron loss in a reactor is 24 0 watts of which watts is t If of i due o eddy currents .