UBC Theses and Dissertations

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UBC Theses and Dissertations

Dissipation factor measurements of transformer oil Smith, Frank Edward 1951

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DISSIPATION FACTOR MEASUREMENTS OF TRANSFORMER OIL by FRANK EDWARD SMITH A THESIS SUBMITTED I N PARTIAL FULFILMENT OF THE REQUIREMENTS FOR THE DEGREE OF MASTER OF APPLIED SCIENCE i n t h e Department o f E l e c t r i c a l E n g i n e e r i n g We a c c e p t t h i s t h e s i s as c o n f o r m i n g t o t h e s t a n d a r d r e q u i r e d from c a n d i d a t e s f o r the degree o f MASTER OF APPLIED SCIENCE y/?• c THE UNIVERSITY OF BRITISH COLUMBIA A p r i l , 1 9 5 1 ABSTRACT The p r e s e n t methods o f a s c e r t a i n i n g t h e p r o b a b l e s l u d g i n g o f t r a n s f o r m e r o i l s a r e l a b o r i o u s . A s i m p l e t e s t , comparable t o t h a t u s e d I n o b t a i n i n g the d i e l e c t r i c s t r e n g t h , would be o f c o n s i d e r a b l e v a l u e i n r e d u c i n g t e s t manpower, equipment and expense. P r e s e n t I n v e s t i g a t o r s measure such p r o p e r t i e s as oxygen a b s o r p t i o n , c o l o u r change, i n c r e a s e i n a c i d i t y , c arbon d i o x i d e e v o l v e d , w a t e r formed, t h e power f a c t o r , and t h e l n t e r f a c i a l - t e n s i o n v a l u e . Numerous d i e l e c t r i c m a t e r i a l s e x h i b i t anomalous d i s p e r s i o n s . The a t t e n d a n t r i s e i n d i s s i p a t i o n f a c t o r e n c o u n t e r e d a t t h e p o i n t s o f d i s p e r s i o n i s h e l p f u l i n d e t e r -m i n i n g t h e amounts and t y p e s o f p o l a r i z a t i o n p r e s e n t . T r a n s f o r m e r o i l s , a l t h o u g h I n i t i a l l y n o n - p o l a r , a r e s u b j e c t t o o x i d a t i o n . T h i s o x i d a t i o n p r oduces m a t e r i a l s o f p o l a r m o l e c u l a r s t r u c t u r e w h i c h g o v e r n t h e power l o s s i n a l t e r n a t i n g c u r r e n t e l e c t r i c f i e l d s . The problem i s one o f c o r r e l a t i n g such l o s s e s t o t h e s t a t e o f t h e o i l under t e s t . T h i s t h e s i s d e a l s w i t h the I n v e s t i g a t i o n s c a r r i e d o u t on t h e above problem. A b s o r p t i o n bands f o r t r a n s f o r m e r o i l s have been found. The p r e s e n t work d e s c r i b e s t h e presence and l o c a t i o n o f such a b s o r p t i o n bands, and I l l u s t r a t e s how t h e d i p o l a r s t a t e o f t h e o i l a f f e c t s t h e p o s i t i o n o f t h e l o s s peaks. 6S. v ACKNOWLEDGEMENTS The a u t h o r w i s h e s t o e x p r e s s h i s a p p r e c i a t i o n t o a l l t h o s e who have a s s i s t e d him thro u g h o u t t h e c o u r s e o f the r e s e a r c h ; e s p e c i a l l y t o Dr. Prank Noakes f o r h i s g u i d a n c e and encouragement. Acknowledgement i s a l s o made t o the N a t i o n a l R e s e a r c h C o u n c i l o f Canada whose g r a n t made t h e i n v e s t i g a -t i o n p o s s i b l e . TABLE OF .CONTENTS A. INTRODUCTION • » Page 1 B. GENERAL THEORY OF THE PROBLEM 1. T r a n s f o r m e r O i l s 5 2. C a p a c i t o r s 10 3. D i e l e c t r i c s 12 K 0-Meter 12 5. S e r i e s and P a r a l l e l Impedance Components 21 C. DESCRIPTION OF THE EQUIPMENT 1. Low Frequency Equipment 22 2. O i l C e l l 23 3. Low Temperature Equipment 2^ h. Type l 6 0-A Qr-Meter 25 D. PARTICULAR THEORY OF THE PROBLEM 1. T r a n s f o r m e r O i l s 27 2. 0-Meter T e s t s 29 E. TESTS AND RESULTS 1. Low F r e q u e n c i e s 33 2. H i g h F r e q u e n c i e s 35 3 . Low Temperatures 3^ F. CONCLUSIONS AND DISCUSSION 3 6 i DIAGRAMS ^3 l i GLOSSARY 63 i l l LITERATURE CITED 6h i v BIBLIOGRAPHY. 65 v ACKNOWLEDGEMENTS 6g L I S T GF ILLUSTRATIONS TABLE 1 « D i e l e c t r i c C o n s t a n t s and R e f r a c t i v e I n d i c e s Page 4-3 FIG. 1 - C a p a c i t o r C h a r a c t e r i s t i c s 44 FIG. 2 - C a p a c i t o r C h a r a c t e r i s t i c s 44 FIG. 3 - D i e l e c t r i c C h a r a c t e r i s t i c s 44 FIG. 4- - Qr-Meter Measuring C i r c u i t 4-5 FIG. 5 - Qr-Meter M e a s u r i n g C i r c u i t 4-5 FIG. 6 - S e r i e s and P a r a l l e l Components ............ 4-5 FIG. 7 « Low Frequency M e a s u r i n g Equipment 4-5 FIG. g - C a p a c i t o r C o n n e c t i o n s 4 6 FIG. 9 - O i l C e l l 4-7 FIG. 10 - O i l C e l l .. 4-8" FIG. 11 - Low Temperature Equipment 4-6 FIG. 12 - B a s i c Q r - M e t e r C i r c u i t 4-9 FIG. 13 - A n a l y t i c C i r c u i t o f Qr-Meter 4-9 FIG. 14- - Qr-Meter M e a s u r i n g C i r c u i t s 5° FIG. 15 - E q u i v a l e n t Qr-Meter Measuring C i r c u i t ...... 5Q FIG. 16 -.Q-Meter and O i l C e l l 51 FIG. 17 - Low Temperature Equipment ....... ...... 5 2 GRAPH 1 - D i e l e c t r i c C o n s t a n t and D i s s i p a t i o n F a c t o r A g a i n s t Frequency 53 GRAPH 2 - D i s s i p a t i o n F a c t o r A g a i n s t Temperature .... 54-GRAPH 3 - D i s s i p a t i o n F a c t o r A g a i n s t Temperature .... 55 GRAPH 4 - D i s s i p a t i o n F a c t o r A g a i n s t Temperature .... 56 GRAPH 5 - D i s s i p a t i o n F a c t o r A g a i n s t Temperature .... 57 GRAPH 6 - D i s s i p a t i o n F a c t o r A g a i n s t Temperature .... 5& GRAPH 7 * D i s s i p a t i o n F a c t o r A g a i n s t Temperature .... 59 GRAPH 8" «. D i s s i p a t i o n F a c t o r A g a i n s t L o g Frequency .. 60 GRAPH 9 - D i s s i p a t i o n F a c t o r A g a i n s t L o g Frequency .. 6 l GRAPH 10 - D i s s i p a t i o n F a c t o r A g a i n s t L o g Frequency .. 62 A. INTRODUCTION The p r e s e n t methods o f a s c e r t a i n i n g t h e p r o b a b l e s l u d g i n g o f t r a n s f o r m e r o i l s a r e l a b o r i o u s . A s i m p l e t e s t , comparable t o t h a t used i n o b t a i n i n g the d i e l e c t r i c s t r e n g t h w o u l d be o f c o n s i d e r a b l e v a l u e i n r e d u c i n g t e s t manpower, equipment and expense. T r a n s f o r m e r o i l , because o f i t s complex c h e m i c a l s t r u c t u r e , i s s u b j e c t e d t o many d i f f e r e n t t y p e s o f t e s t I n o r d e r t o t e s t i t s r e l i a b i l i t y i n s e r v i c e . I n a d d i t i o n t o t h e d i e l e c t r i c s t r e n g t h t e s t , two c l a s s e s o f t e s t a r e i n use a t th e p r e s e n t t i m e . The f i r s t o f t h e s e i s t h e measurement o f th e power f a c t o r o f t h e o i l . The second i s t h e measurement o f t h e o x i d a t i o n , o r s l u d g i n g c h a r a c t e r i s t i c s o f the o i l . Any c o n t a m i n a t i o n o f a t r a n s f o r m e r o i l w i l l i n c r e a s e i t s power f a c t o r and t h i s i n c r e a s e d power f a c t o r w i l l i n d i c a t e d e t e r i o r a t i o n . The problem i s not t h a t o f f i n d i n g the change i n t h e o i l from i t s o r i g i n a l c o n d i t i o n , b u t t h a t o f f i n d i n g 2. t h o s e changes w h i c h w i l l I n d i c a t e t h a t t h e dangerous o p e r a t -i n g l i m i t o f t h e o i l i s b e i n g approached. F o r example, most t r a n s f o r m e r w i n d i n g s c o n t a i n p r o d u c t s w h i c h , when d i s s o l v e d i n o i l , cause a power f a c t o r i n c r e a s e , a l t h o u g h t h e i r e f f e c t upon d i e l e c t r i c ' s t r e n g t h and s l u d g e f o r m a t i o n i s n e g l i g i b l e . I n a c t u a l o p e r a t i o n , t h e o i l i s b e i n g o x i d i z e d and s u b j e c t e d to w a t e r a b s o r p t i o n . B o t h o f t h e s e e f f e c t s produce an I n c r e a s e i n power f a c t o r ; however, the I n c r e a s e i n power f a c t o r i s depen-dent upon t h e method o f o x i d a t i o n . When t e s t s a re conducted i n the l a b o r a t o r y , t h e method o f o x i d a t i o n v a r i e s w i d e l y . Water, t h e l i g h t e r o i l a c i d s , and o t h e r v o l a t i l e s a r e a l l o w e d t o escape d u r i n g a number o f t h e s e t e s t s . I n a d d i t i o n , a t t h e h i g h t e m p e r a t u r e s o f the u s u a l o x i d a t i o n t e s t the tendency i s toward l e s s a c i d i f i c a t i o n and more s l u d g e s e p a r a t i o n . F o r a g i v e n amount o f o x i d a t i o n , t h e power f a c t o r i n c r e a s e s f o r l a r g e r v a l u e s o f a c i d i f i c a t i o n . Water a b s o r p t i o n causes an I n c r e a s e i n power f a c t o r w h i c h i s not d i r e c t l y r e l a t e d t o t h e d e c r e a s e i n d i e l e c t r i c s t r e n g t h brought about; t h e r e f o r e , t h e power f a c t o r t e s t i s not c o n c l u s i v e i n p r o t e c t i n g a g a i n s t w a t e r e f f e c t s . Sludge t e a t s c o n s i s t o f two d i s t i n c t typess ( l ) t h e s l u d g i n g p r o p e n s i t y t e s t w h i c h e v a l u a t e s the t e n ~ dency o f a new k i n d o f o i l t o form sludge i n terms o f t h e c h a r a c t e r i s t i c s o f an a c c e p t e d o i l , and ( i i ) t he commercial t e s t w h i c h d e t e r m i n e s the u s e f u l l i f e o f the o i l t h a t has been consumed up to t h e t i m e o f t e s t . I n the f i r s t t e s t , new o i l i s b e i n g s t u d i e d , whereas i n the second t e s t , t h e o i l s c o n t a i n c o n t a m i n a t i o n p r o d u c t s . The t y p e o f o x i d a t i o n p r e s e n t i n t h e used o i l i s dependent not o n l y upon the m a t e r i a l s o f w h i c h t h e o i l I s made, but a l s o upon t h e n a t u r e o f t h e o i l , t h e o p e r a t i n g t i m e , and t h e tempera-t u r e o f t h e t r a n s f o r m e r . S l u d g i n g p r o p e n s i t y o f new t r a n s f o r m e r o i l s i s s t u d i e d by o x i d i z i n g the o i l under c o n t r o l l e d l a b o r a t o r y con-d i t i o n s . At p r e s e n t , t h e t e s t p r o c e d u r e s a r e not s t a n d a r d i z e d and t h e o i l s a r e o x i d i z e d a t t e m p e r a t u r e s r a n g i n g from 100 t o 150 d e g r e s s c e n t i g r a d e f o r t i m e s r a n g i n g from t h r e e h o u r s t o s e v e r a l months. P r e s e n t i n v e s t i g a t o r s measure d i f f e r e n t p r o p e r t i e s such as oxygen a b s o r p t i o n , c o l o u r change, I n c r e a s e i n a c i d i t y , c arbon d i o x i d e e v o l v e d , w a t e r formed, t h e power f a c t o r , and t h e i n t e r f a c i a l - t e n s i o n v a l u e . T h i s p r o c e d u r e Imposes t h e d i f f i c u l t y o f r e l a t i n g t h e s e p r o p e r t i e s t o t h e a c t u a l s l u d g i n g p r e s e n t . I n a d d i t i o n , t h e secondary p r o d u c t s o f o x i d a t i o n cannot be o v e r l o o k e d . A s s o c i a t e d w i t h the o x i d a -t i o n o f t r a n s f o r m e r o i l i s t h e f o r m a t i o n o f p e r o x i d e s , m e t a l l i c soaps, a c i d s o f v a r y i n g v o l a t i l i t y and c o r r o s l v i t y , c r a c k e d h y d r o c a r b o n s , and i n s o l u b l e p r o d u c t s o r s l u d g e . The a c i d c o r r o s l v i t y i t s e l f may I n c r e a s e t o such l a r g e p r o p o r t i o n s t h a t t h e t r a n s f o r m e r l i f e i s endangered from t h i s s o u rce. The American S o c i e t y f o r T e s t i n g M a t e r i a l s has d e v e l o p e d two d i f f e r e n t t e s t s . F o r s t u d y i n g new o i l s , t h i s s o c i e t y p r o p o s e s an o x i d a t i o n t e s t i n w h i c h t h e o i l i s sub-j e c t e d to a temperature o f 120 degrees c e n t i g r a d e i n t h e p r e s e n c e o f a copper c a t a l y s t f o r a p e r i o d o f two weeks. I n the second t e s t , the c o n t i n u i t y o f t h e o i l ' s q u a l i t y i s s t u d i e d by o x i d i z i n g the o i l a t 24-0 degrees c e n t i g r a d e f o r a d u r a t i o n o f 24- h o u r s under 250 pounds o f oxygen p r e s s u r e . Power f a c t o r and i n t e r f a c l a l t e s t s a r e a f f e c t e d by a c i d i t y changes i n t h e o i l . A c i d f o r m a t i o n i s dependent upon the o r i g i n o f t h e crude o i l , t h e degree o f r e f i n i n g , and t h e o p e r a t i n g t e m p e r a t u r e o f t h e t r a n s f o r m e r . Moreover, th e a c i d v a l u e i n c r e a s e s r a p i d l y to a maximum v a l u e and t h e n remains f a i r l y s t a b l e . T h i s p r o c e s s o f a c i d s t a b i l i z a t i o n i s not t h o r o u g h l y u n d e r s t o o d , but i s a t t r i b u t e d , a t p r e s e n t , t o t h e e q u i l i b r i u m s e t up between th e f o r m a t i o n o f a c i d and the removal o f a c i d i n s l u d g e d e p o s i t s . The i n t e r f a c i a l - t e n s i o n t e s t measures t h e f o r c e r e q u i r e d t o p u l l a p l a t i n u m r i n g o f s p e c i f i e d d i m e n s i o n s , t h r o u g h t h e I n t e r f a c e w h i c h e x i s t s between a l a y e r o f t h e o i l and a l a y e r o f w a t e r . D u r i n g o x i d a t i o n o f the o i l , o r g a n i c a c i d s w h i c h reduce the t e n s i o n a t t h e i n t e r f a c e a r e b e i n g formed. T h i s r e d u c t i o n o c c u r s a s y m p t o t i c a l l y w i t h t i m e ; hence, i n the e a r l y s t a g e s o f o x i d a t i o n , t h e i n t e r f a c i a l -t e n s i o n v a l u e changes r a p i d l y w i t h s m a l l i n c r e a s e s i n o x i d a -t i o n . As t h e a c i d i t y becomes more pronounced, however, th e i n t e r f a c i a l - t e n s i o n v a l u e changes more s l o w l y and t h e s e n s i -t i v i t y o f t h e t e s t I s d e c r e a s e d . 5 Numerous d i e l e c t r i c m a t e r i a l s e x h i b i t anomalous d i s p e r s i o n s . The a t t e n d a n t r i s e i n d i s s i p a t i o n f a c t o r encoun-t e r e d a t the p o i n t s o f d i s p e r s i o n i s h e l p f u l i n d e t e r m i n i n g t h e amounts and t y p e s o f p o l a r i z a t i o n p r e s e n t . T r a n s f o r m e r o i l s , a l t h o u g h i n i t i a l l y n o n - p o l a r , a r e s u b j e c t t o o x i d a t i o n . T h i s o x i d a t i o n , i n a l l p r o b a b i l i t y , p r o d u c e s m a t e r i a l s o f p o l a r m o l e c u l a r s t r u c t u r e . These s t r u c t u r e s g o v e r n t h e power l o s s i n a l t e r n a t i n g c u r r e n t e l e c t r i c f i e l d s . The problem i s one o f c o r r e l a t i n g such l o s s e s t o t h e s t a t e o f t h e o i l under t e s t . Work on t h i s problem, c a r r i e d out under a g r a n t from t h e N a t i o n a l R e s e a r c h C o u n c i l o f Canada, c o n s i s t e d c h i e f l y o f two p a r t s . I n t h e f i r s t p a r t o f t h e work, t e s t s were r u n on o i l samples m a i n t a i n e d a t c o n s t a n t t e m p e r a t u r e and r e a d i n g s o f d i s s i p a t i o n f a c t o r were t a k e n as a f u n c t i o n o f f r e q u e n c y . The f r e q u e n c y spectrum from 20 c.p.s. t o 10 mc 1^. was u t i l i z e d i n t h e s e t e s t s . I n the second p a r t o f the work, the f r e q u e n c y was m a i n t a i n e d c o n s t a n t and t h e v a r i a t i o n s i n d i s s i p a t i o n f a c t o r w i t h v a r y i n g t e m p e r a t u r e s were o b s e r v e d . B. i GENERAL THEORY OF THE PROBLEM T r a n s f o r m e r O i l s I f t h e i n i t i a l e l e c t r i c a l and p h y s i c a l p r o p e r t i e s o f h i g h l y r e f i n e d o i l s c o u l d be m a i n t a i n e d , t h e n t h e o i l s w o u l d be s a t i s f a c t o r y l i q u i d i n s u l a t i o n f o r t r a n s f o r m e r s . However, d e t e r i o r a t i o n commences e a r l y i n the l i f e o f a t r a n s -f o r m e r o i l , as e v i d e n c e d by changes I n t h e c h e m i c a l c o n s t i t -u e n t s o f the o i l . These changes y i e l d p r o d u c t s w h i c h a r e d e t r i m e n t a l to t h e d i e l e c t r i c p r o p e r t i e s o f the o i l , i t s a b i l i t y t o f u n c t i o n as a c o o l a n t , and i t s i n f l u e n c e upon o t h e r s o l i d I n s u l a t i o n I n t h e t r a n s f o r m e r . M i n e r a l o i l s c o n s i s t o f a complex m i x t u r e o f o r g a n i c compounds c a l l e d h y d r o c a r b o n s . The f o u r main t y p e s o f th e s e h y d r o c a r b o n s a r e t h e p a r a f f i n i c , n a p h t h e n l c , o l e f i n i c , and a r o m a t i c . P a r a f f i n h y d r o c a r b o n s c o n s i s t o f open c h a i n and b r a n c h c h a i n compounds and a r e r e p r e s e n t e d as f o l l o w s ? CH 3 - C H 2 - C H 2 - C H 2 „ C H 2 - CH^ (Hexane, open c h a i n ) C H 3 ~ C H 2 " C H "* C H 3 CH 2 - CH^ ( E t h y l propane, b r a n c h c h a i n ) Naphthenlc h y d r o c a r b o n s have c l o s e d c h a i n s t r u c t u r e s and may be r e p r e s e n t e d by c y c l o - o c t a n e ; 7. Hg Hg H 2 = C C = H 2  H 2 = C X C = H 2 c — c r II II H„ H„ O l e f l n i c compounds, c h e m i c a l l y known as t h e u n s a t u r a -t e d h y d r o c a r b o n s , c o n t a i n d o u b l e bonds between a d j a c e n t c a r b o n atoms. T h e i r s t r u c t u r e may be r e p r e s e n t e d by one o f the Isomers o f amylenej C 3 CH — CH-» OH- / 3 The a r o m a t i c h y d r o c a r b o n s c o n s i s t o f c l o s e d r i n g s t r u c t u r e s such as benzene: H I 0 ^ \ H - C C - H I li. H — C C — H \ / I H The p r e s e n c e o f d o u b l e bonds between c a r b o n atoms I n a r o m a t i c s t r u c t u r e s does not i m p l y t h e same degree o f c h e m i c a l I n s t a b i l i t y w h i c h e x i s t s i n t h e open c h a i n s t r u c t u r e s o f the o l e f l n i c h y d r o c a r b o n s . The o l e f l n i c h y d r o c a r b o n s c o n t a i n i n g d o u b l e bonds a r e c h e m i c a l l y a c t i v e and t h e removal o f t h e s e d o u b l e bonds from t h e crude o i l c o n s t i t u t e s the r e f i n i n g p r o c e s s . The r e f i n e d o i l s c o n s i s t l a r g e l y o f s a t u r a -t e d h y d r o c a r b o n s . The c o n s t i t u t i o n o f i n s u l a t i n g o i l s i s complex and r a r e l y does an o i l b e l o n g e n t i r e l y t o one o f t h e f o u r main groups. T h i s composite c h a r a c t e r o f t h e h y d r o c a r b o n s i s i l l u s -t r a t e d by p r o p y l c y c l o h e x a n e w h i c h c o n t a i n s f o u r p a r a f f i n i c and s i x n a p h t h e n l c carbon atoms: Hg Hg H „ = C C H C — C II II H 2 H 2 Naphthenlc (CHg)^ — CH^ P a r a f f i n i c O i l s o f t h i s composite t y p e e x h i b i t t h e p r o p e r t i e s o f t h e con-s t i t u e n t s . The s i d e c h a i n s a r e more s u s c e p t i b l e t o c h e m i c a l a c t i v i t y t h a n the r i n g p o r t i o n s o f t h e m o l e c u l e s , e s p e c i a l l y I f t h e s e s i d e c h a i n s a r e o l e f l n i c . The crude o i l c o n t a i n s a l a r g e p r o p o r t i o n o f o x i d i -z a b l e c o n s t i t u e n t s and t h e r e f i n i n g p r o c e s s I s d i r e c t e d toward t h e i r r emoval. M i n o r q u a n t i t i e s o f oxygen compounds, n i t r o g e n compounds, and s u l p h u r a r e a l s o removed from the crude d i s t i l l -a t e d u r i n g r e f i n e m e n t . The d e s i r a b i l i t y o f removing a l l o f t h e n i t r o g e n and oxygen compounds i s dependent upon t h e i r p r e c i s e 9 c h a r a c t e r f o r c e r t a i n o f t h e s e compounds, known as n a t u r a l i n h i b i t o r s , a r e i n s t r u m e n t a l i n d e l a y i n g t h e o x i d a t i o n p r o c e s s . T h e r e f o r e , o v e r - r e f i n i n g may remove c e r t a i n c o n s t i t u e n t s w h i c h c o n f e r c h e m i c a l s t a b i l i t y on the o i l . Two fundamental causes a r e r e s p o n s i b l e f o r t h e d e t e r i o r a t i o n o f m i n e r a l I n s u l a t i n g o i l . The f i r s t cause, a p h y s i c a l phenomenon, r e s u l t s f r om e l e c t r i c a l d i s c h a r g e s w h i c h l o w e r t h e d i e l e c t r i c s t r e n g t h o f the o i l . The second cause, a c h e m i c a l phenomenon, r e s u l t s from o x i d a t i o n and i s t h e c h i e f f a c t o r e n c o u n t e r e d i n t h e d e t e r i o r a t i o n o f t r a n s f o r m e r o i l s . O x i d a t i o n i n v o l v e s t h e c h e m i c a l c o m b i n a t i o n o f a t m o s p h e r i c oxygen w i t h c o n s t i t u e n t s o f t h e t r a n s f o r m e r o i l . The r a t e a t w h i c h a c h e m i c a l r e a c t i o n p r o c e e d s i s dependent upon the tem p e r a t u r e . T h e o r e t i c a l l y , f o r s i m p l e s u b s t a n c e s , the r a t e o f r e a c t i o n I s d o u b l e d f o r every 10 degree c e n t i g r a d e r i s e . Hence, a t normal o p e r a t i n g t e m p e r a t u r e s , o x i d a t i o n p r o c e e d s s l o w l y . G e n e r a l l y s p e a k i n g , h i g h l y r e f i n e d o i l s a t h i g h t e m p e r a t u r e s y i e l d a c i d s and o i l s o l u b l e m a t e r i a l s , whereas l e s s h i g h l y r e f i n e d o i l s at the l o w e r t e m p e r a t u r e s y i e l d g r e a t e r p r o p o r t i o n s o f o i l I n s o l u b l e p r o d u c t s , o r s l u d g e . The i n i t i a l p r o d u c t s o f o x i d a t i o n a r e o r g a n i c a c i d s o f h i g h v o l a t i l i t y , w a t e r , and o r g a n i c p e r o x i d e s . D u r i n g t h i s p e r i o d , a l c o h o l s , k e t o n e s and a l d e h y d e s a l s o appear. Then e s t e r s , w h i c h a r e compounds o f a c i d s and a l c o h o l s , may be formed. F i n a l l y , e i t h e r p o l y m e r i z a t i o n ( t h e c o m b i n a t i o n o f two o r more l i k e m o l e c u l e s t o form a compound o f r e l a t i v e l y h i g h m o l e c u l a r 10. w e i g h t ) o r c o n d e n s a t i o n ( t h e c o m b i n a t i o n o f d i s s i m i l a r mole-c u l e s ) between e a r l i e r formed p r o d u c t s o f o x i d a t i o n t a k e s p l a c e . S o l i d p r o d u c t s , whose s o l u b i l i t y d e c r e a s e s w i t h d e c r e a s i n g t e m p e r a t u r e , a r e t h u s formed. When the o i l becomes s a t u r a t e d , t h e s e s o l i d p r o d u c t s a r e d e p o s i t e d i n t h e form o f slu d g e . Sludge, a poor t h e r m a l c o n d u c t o r , p a r t i a l l y b l o c k s the c o o l i n g d u c t s and i m p a i r s t h e c o o l i n g o f t h e t r a n s f o r m e r . I n a d d i t i o n , s l u d g e i s u n s t a b l e and, f o r h i g h o p e r a t i n g t e m p e r a t u r e s , b r e a k s down i n t o a c i d s and o t h e r p r o d u c t s o f low m o l e c u l a r w e i g h t . The p e r o x i d e s a r e s t r o n g o x i d i z i n g a g e n t s and r e a c t w i t h m e t a l s i n the t r a n s f o r m e r t o produce m e t a l l i c soaps. The l o w - m o l e c u l a r - w e i g h t a c i d s a r e h i g h l y c o r r o s i v e i n t h e pr e s e n c e o f w a t e r and i n severe I n s t a n c e s , may w a r r a n t t h e removal o f the o i l , even though t h e e l e c t r i c a l c h a r a c t e r i s t i c s have not been s e r i o u s l y i m p a i r e d . C a p a c i t o r s When t h e c a p a c i t o r shown i n P i g . 1 i s empty, i t has a g e o m e t r i c a l c a p a c i t a n c e o f C and a c h a r g i n g c u r r e n t f l o w s under t h e a p p l i c a t i o n o f t h e s i n u s o i d a l s o u r c e v o l t a g e V. T h i s c u r r e n t w i l l be advanced 9 ° degrees i n phase from the a p p l i e d v o l t a g e , as shown i n F i g . 1. I f t h e c a p a c i t o r i s now f i l l e d w i t h a d i e l e c t r i c , i t s c a p a c i t a n c e i n c r e a s e s t o j C V (1) C (2) 11. where and a r e t h e p e r m i t t i v i t i e s o f t h e m a t e r i a l and o f vacuum, r e s p e c t i v e l y . A l o s s c u r r e n t component i n phase w i t h t h e v o l t a g e appears; hence, the power f a c t o r a n g l e o f the t o t a l c u r r e n t I a g a i n s t the v o l t a g e V, i s reduced' to a v a l u e below 90 degrees. T h i s o b s e r v a t i o n does not i n d i c a t e t h a t t h e d i e l e c -t r i c i s e q u i v a l e n t t o the s i m p l e r e s i s t a n c e - c a p a c i t a n c e c i r c u i t o f P i g . 2. The f r e q u e n c y r e sponse o f t h e d i e l e c t r i c may v a r y c o n s i d e r a b l y and t h u s , t h e conductance G, may be dependent upon some energy-consuming p r o c e s s o t h e r t h a n t h e m i g r a t i o n o f charge c a r r i e r s . Because o f t h i s phenomenon, t h e s i m u l t a -neous e x i s t e n c e o f c h a r g i n g c u r r e n t and l o s s c u r r e n t a r e e x p r e s s e d i n terms o f a complex p e r m i t t i v i t y £ = £m W T h e r e f o r e , t h e t o t a l c u r r e n t becomes I = 73T ^ U j £ m * ^  L ^ (5) where e\ I s d e f i n e d as the l o s s f a c t o r o f t h e d i e l e c t r i c . The c o n d u c t i v i t y o f the m a t e r i a l i s r e p r e s e n t e d by £ Co - cr— ( 6 ) and t h e r a t i o o f l o s s c u r r e n t t o c h a r g i n g c u r r e n t € i s c a l l e d t h e l o s s t a n g e n t o f the d i e l e c t r i c . t a n £ = | i _ . . . . . . . . . . . . . . . (7) cm I n P i g . 2, the power f a c t o r i s e q u a l t o t h e r a t i o o f t h e w a t t s l o s s t o t h e v o l t - a m p e r e s , o r t h e c o s i n e o f t h e 12 phase a n g l e 8* . S i s shown as t h e l o s s a n g l e and t h e t a n g e n t o f S as t h e d i s s i p a t i o n f a c t o r D. Prom t h e s e r e l a t i o n s h i p s , t h e power f a c t o r P * = V I f > (*> t h u s , f o r s m a l l l o s s a n g l e s , t h e power f a c t o r and d i s s i p a t i o n f a c t o r a r e a p p r o x i m a t e l y e q u a l . D i e l e c t r i c s \ When an e l e c t r i c f i e l d I s a p p l i e d t o a d i e l e c t r i c , the n e g a t i v e and p o s i t i v e c h a r g e s o f t h e m a t e r i a l 1 s atoms a r e d i s p l a c e d i n o p p o s i t e d i r e c t i o n s . T h i s movement o f charges c o n s t i t u t e s a c u r r e n t f l o w known as the p o l a r i z a t i o n c u r r e n t and t h e d i e l e c t r i c i s s a i d t o be p o l a r i z e d . F o r s t a t i c a l l y i m p r e s s e d f i e l d s , the c h a r g i n g c u r r e n t f l o w s u n t i l t h e m a t e r i a l i s f u l l y p o l a r i z e d . I f t h e m a t e r i a l i s not an i d e a l d i e l e c t r i c , t h e c u r r e n t w i l l not cease when the p o l a r i z a t i o n c u r r e n t c e a s e s , but w i l l drop t o some low v a l u e d e t e r m i n e d by the f r e e - i o n c o n d u c t i v i t y o f t h e d i e l e c t r i c . P o l a r i z a b i l i t y , the q u a n t i t a t i v e measure o f d i e l e c -t r i c p o l a r i z a t i o n , i s d e f i n e d by the number o f bound charges p e r u n i t cube and t h e i r average d i s p l a c e m e n t i n t h e d i r e c t i o n o f t h e i m p r e s s e d f i e l d . Two d i s t i n c t t y p e s o f c h a r g i n g c u r r e n t s a r e o b s e r v e d when an e l e c t r i c f i e l d i s a p p l i e d t o a d i e l e c t r i c . The f i r s t , an i n s t a n t a n e o u s c h a r g i n g c u r r e n t , i s a t t r i b u t e d t o r a p i d l y -13. f o r m i n g p o l a r i z a t i o n s . The second, a s l o w l y - f o r m i n g c h a r g i n g c u r r e n t , i s a t t r i b u t e d t o a b s o r p t i v e p o l a r i z a t i o n s . The sum o f a l l these d i f f e r e n t t y p e s o f d i s p l a c e m e n t o f charge i n t h e d i e l e c t r i c d e t e r m i n e s t h e p o l a r i z a b i l i t y . Thus, t h e c h a r a c t e r i s t i c f o r c e s e x i s t i n g i n the a t o m i c s t r u c -t u r e o f t h e d i e l e c t r i c g o v e r n the magnitude o f the p o l a r i z a -b i l i t y and i t s r a t e o f f o r m a t i o n . The t i m e r e q u i r e d f o r a p o l a r i z a t i o n t o form i s known as the r e l a x a t i o n t i m e . When a l t e r n a t i n g f i e l d s a r e i m p r e s s e d on a d i e l e c -t r i c , t h e p o l a r i z a t i o n s o f an a b s o r p t i v e t y p e r e q u i r e a time t o f o rm w h i c h I s o f t h e same o r d e r o f magnitude a s , o r g r e a t e r t h a n , t h e p e r i o d o f a l t e r n a t i o n s ; hence, t h e p o l a r i z a t i o n s cannot form c o m p l e t e l y and t h e v a l u e o f d i e l e c t r i c p o l a r i z a t i o n and d i e l e c t r i c c o n s t a n t d e c r e a s e as the f r e q u e n c y i n c r e a s e s . The t y p e s o f p o l a r i z a t i o n w h i c h can be i n d u c e d i n d i e l e c t r i c s a r e c l a s s i f i e d as f o l l o w s : ( i ) e l e c t r o n i c p o l a r i z a t i o n s - produced by t h e d i s p l a c e m e n t o f e l e c t r o n s w i t h r e s p e c t t o p o s i t i v e n u c l e i w i t h i n t h e atom; ( i i ) a t o m i c p o l a r i z a t i o n s - produced by t h e d i s p l a c e m e n t o f atoms w i t h r e s p e c t to each o t h e r i n the m o l e c u l e ; ( i l l ) d i p o l e p o l a r i z a t i o n s - produced by o r i e n t a t i o n s o f mole-c u l e s w i t h permanent d i p o l e moments; Civ) i n t e r f a c l a l o r i o n i c p o l a r i z a t i o n s - produced by the a c c u m u l a t i o n o f f r e e I o n s a t t h e i n t e r f a c e s o f m a t e r i a l s p o s s e s s i n g d i f f e r e n t c o n d u c t i v i t i e s and d i e l e c t r i c con-s t a n t s . IK P i g . 3 i a a g r a p h i c a l r e p r e s e n t a t i o n o f the changes I n d i e l e c t r i c l o s s and d i e l e c t r i c c o n s t a n t w i t h f r e q u e n c y f o r a d i e l e c t r i c assumed t o p o s s e s s a l l the f o r e g o i n g polar!za» t i o n s . T h i s d i a g r a m shows t h a t t h e d i e l e c t r i c c o n s t a n t c u r v e has I t s h i g h e s t v a l u e a t the zero f r e q u e n c y p o i n t where a l l the p o l a r i z a t i o n s have t i m e t o form and c o n t r i b u t e t h e i r f u l l amount t o t h e d i e l e c t r i c c o n s t a n t . F o r c e r t a i n bands o f f r e -q u e n c i e s , t h e g r a p h shows t h a t t h e d i e l e c t r i c c o n s t a n t d e c r e a s e s w i t h I n c r e a s i n g f r e q u e n c y . These bands, where t h e p o l a r i z a t i o n i s u n a b l e to f o rm c o m p l e t e l y d u r i n g t h e t i m e o f one c y c l e , a r e c a l l e d r e g i o n s o f a b s o r p t i o n , o r anomalous d i s p e r s i o n . E l e c t r o n i c p o l a r i z a t i o n s a r e c h a r a c t e r i z e d by l a r g e i n e r t i a f o r c e s and n e g l i g i b l e f r i c t i o n a l f o r c e s , except i n the narrow f r e q u e n c y band o f a b s o r p t i o n . The f r i c t i o n a l f o r -ces become l a r g e r f o r a t o m i c p o l a r i z a t i o n s , as e v i d e n c e d by t h e wide i n t e r v a l o f f r e q u e n c i e s I n c l u d e d i n the a b s o r p t i o n band. F o r d i p o l e and i n t e r f a c l a l p o l a r i z a t i o n s , t h e f r i c t i o n a l f o r c e s I n c r e a s e i n magnitude and t h e r e s u l t i n g p o l a r i z a t i o n s a r e h i g h l y damped. I n p r a c t i c a l d i e l e c t r i c s , t h e r e a r e f r e e i o n s w h i c h produce J o u l e h e a t as they d r i f t toward t h e e l e c t r o d e s under t h e a c t i o n o f an a p p l i e d f i e l d . The t o t a l h e a t d e v e l o p e d I s t h e sum o f t h e d i e l e c t r i c l o s s and t h e J o u l e h e a t . Because the J o u l e h e a t I s p r o p o r t i o n a l t o t h e f r e e - i o n o r d i r e c t c u r r e n t c o n d u c t i v i t y , t h e d i e l e c t r i c l o s s i s equal t o t h e t o t a l a l t e r n a t i n g c u r r e n t c o n d u c t i v i t y minus the d i r e c t c u r r e n t c o n d u c t i v i t y . •15. Assume a d i e l e c t r i c o f d i e l e c t r i c c o n s t a n t £ m and l o s s f a c t o r £, i s c o n t a i n e d i n a p a r a l l e l - p l a t e c a p a c i t o r h a v i n g a p l a t e s e p a r a t i o n o f " d M c e n t i m e t e r s , and h a v i n g t h e a r e a o f one o f i t s p l a t e s e q u a l t o W A M square c e n t i m e t e r s . Upon a p p l i c a t i o n o f a p o t e n t i a l d i f f e r e n c e V a c r o s s t h e p l a t e s , a charge "q" p e r u n i t a r e a w i l l appear on e i t h e r p l a t e and a p o l a r i z a t i o n P w i l l be c r e a t e d i n t h e d i e l e c t r i c . I f f r e e - i o n c o n d u c t i v i t y i s n e g l e c t e d , t h e c u r r e n t i n t h e l e a d s o f t h i s c a p a c i t o r w i l l be A 4 * . • (9) d t The c o n d u c t i v i t y becomes * ~- t ^ , • <10> ^ dt 5 where £ - v , (11) Prom the g e n e r a l t h e o r y o f e l e c t r i c i t y (12) ' D = t 4 IT P (13) D = 4 ^ % (1*0 Hence, (10) becomes where e l e c t r o s t a t i c unlt3 a r e used f o r a l l e l e c t r i c a l q u a n t i -t i e s . F o r a l t e r n a t i n g v o l t a g e s , V becomes t h e r e a l p a r t o f Vo (16) where V 0 I s t h e a m p l i t u d e . Now the c u r r e n t d e n s i t y i s ^ =. (r + j V") E e e i ^ t at 1 6 . where V " = ( 1 9 ) 4- TT V. U ' t j V" ( 2 0 ) i s t he complex c o n d u c t i v i t y . The c a p a c i t a n c e i n f a r a d s o f the c a p a c i t o r w i t h a i r a3 the d i e l e c t r i c i s C = _ ^ ( 2 1 ) 4 fr d ( o X IO12-*) • • The d i e l e c t r i c c o n s t a n t and c o n d u c t i v i t y f o r a l t e r -n a t i n g c u r r e n t s a r e de t e r m i n e d by measurements, u s i n g a l t e r n a t -i n g c u r r e n t b r i d g e s , w h i c h y i e l d the c a p a c i t o r a d m i t t a n c e a t th e f r e q u e n c y o f t h e t e s t measurements. I f t h i s a d m i t t a n c e i s e x p r e s s e d i n terms o f an e q u i v a l e n t p a r a l l e l c a p a c i t a n c e and conductance G_ t h e n P P - ( S viCpu^Yoc*"** ( 2 2 ) a t A 3 where G- i s g i v e n i n mhos and C i n f a r a d s . I t f o l l o w s t h a t P P d ~ ~ P . . . . . . ( 2 3 ) C P ( 2 4 ) C OJ r : M . ( 2 5 ) C o n v e r s i o n t o mhos p e r c e n t i m e t e r y i e l d s ( 2 6 ) 1 7 . where C i s t h e c a p a c i t a n c e I n m l c r o m i e r o f a r a d s . E x p r e s s e d i n p o l a r form, : A V " V ° > ( 2 7 ) where Y 0 r ( V * + V" * V * <2«> and e = t c x n - 1 I ! ( 2 9 ) r i s t h e phase a n g l e . The l o s s a n g l e 6, d e f i n e d p r e v i o u s l y as H - e , I s e q u a l t o t a n • (30) Hence, t a n S - ( 3 1 ) C p t o a n d . , , z „iv Kt C 0 5 e = y' C V v V ) — ( 1 2 ) The i n s t a n t a n e o u s power i s o b t a i n e d by m u l t i p l y i n g t h e c u r r e n t i n e q u a t i o n ( 1 7 ) by t h e v o l t a g e E 0 Co?>u/t, The mean power N / V I s o b t a i n e d by i n t e g r a t i n g t h i s i n s t a n t a n e o u s power o v e r a whole number o f h a l f p e r i o d s V. "ft ) F o r d i e l e c t r i c s p o s s e s s i n g t h e p r o p e r t y o f anomalous d i s p e r s i o n , t h e e x p r e s s i o n f o r I033 f a c t o r as a f u n c t i o n o f f r e q u e n c y I s £ . - - - C t - - ^ ^ T . ( 3 5 ) W , £ 1 f \ ^ • W 18. S u b s t i t u t i o n o f t h i s e x p r e s s i o n i n e q u a t i o n (26) g i v e s V'= • - £ ° Q ^ 2 r (36) When (36) i s d i f f e r e n t i a t e d w i t h r e s p e c t t o f r e q u e n c y , V' I s seen t o p o s s e s s no maximum when p l o t t e d a g a i n s t f r e q u e n c y , so t h a t t h e c o n d u c t i v i t y , i f i t changes a t a l l , o f such d i e l e c ~ t r i e s s h o u l d always I n c r e a s e w i t h f r e q u e n c y . D i f f e r e n t i a t i o n o f e q u a t i o n (35) w i t h r e s p e c t to U J shows t h a t t h e d i e l e c t r i c l o s s f a c t o r has a maximum a t <^r=l. The d i e l e c t r i c c o n s t a n t £ m > g i v e n by < ^ f ~ + £ ° ~ £ ° " . . . . . . . . . . . (37) l a c k s a maximum when p l o t t e d a g a i n s t f r e q u e n c y . Qr-Meter The q u a l i t y f a c t o r , Q., o f a c i r c u i t i s d e f i n e d by 0. 3 2 1T Energy s t o r e d l n c i r c u i t ......... (3S) Energy d i s s i p a t e d i n c i r c u i t p e r second A l t h o u g h Q, s h o u l d be a p p l i e d as a c h a r a c t e r i s t i c o f a r e s o n a n t system, t h e term Q, I s o f t e n a p p l i e d to a s i n g l e c i r c u i t element and under t h e s e c o n d i t i o n s , t h e Qr-value s h o u l d be u n d e r s t o o d to a p p l y t o a r e s o n a n t c i r c u i t c o n s i s t i n g o f t h a t element and a s u i t a b l e l o s s - f r e e r e a c t a n c e * I n F i g . 4, a low impedance s i n u s o i d a l s o u r c e i s co n n e c t e d t o a r e s o n a n t c i r c u i t c o n s i s t i n g o f a c a p a c i t y C, and a c o i l (shown as a p u r e i n d u c t a n c e L i n s e r i e s w i t h i t s i n h e r e n t r e s i s t a n c e R ) . When t h e r e s u l t i n g c u r r e n t ( 1 ' I o s i n < - ^ ) 1 9 . i s a maximum, a l l the energy i s s t o r e d i n t h e magnetic f i e l d o f t h e i n d u c t o r so t h a t t h e energy s t o r e d i n t h e c i r c u i t be-comes E - J - L I * s " ° • ( 3 9 ) The energy d i s s i p a t e d p e r c y c l e i s g i v e n by ^ = l Z * "'. . . . . . . . . . . ( 1 K » o v e r one c y c l e t h e energy d i s s i p a t e d becomes L ' ' " R . . . . . . . . . . ( i n ) The r e s u l t i n g 0, o f the c i r c u i t i s g i v e n by = \ • • < ^ When th e c u r r e n t i n t h e c i r c u i t i s a t a minimum, t h e t o t a l s t o r e d energy r e s i d e s i n t h e e l e c t r i c f i e l d o f t h e c a p a c i t o r , and by s i m i l a r r e a s o n i n g t o t h a t g i v e n above, t h e Q, o f the. c i r c u i t i s g i v e n by XQ/R. F o r t h i s s i m p l e c i r c u i t , t h e v a l u e o f t h e Q, becomes Q : \ = \ • (4-3) I n F i g . 5, the p u r e I n d u c t a n c e L, has been r e p l a c e d by an unknown r e a c t a n c e X. The Q, f o r t h i s c i r c u i t cannot be o b t a i n e d w i t h o u t f u r t h e r I n f o r m a t i o n c o n c e r n i n g t h e r e a c t a n c e X, because i t I s i m p o s s i b l e t o s t a t e t h a t t h e e n t i r e e l e c t r i c a l energy i s s t o r e d i n the c a p a c i t o r G a t minimum c u r r e n t . I f X i s an i n d u c t i v e impedance such t h a t X= ~hjc. > t h e r e s o n a n t c u r r e n t w i l l be i* - L , and the v o l t a g e a p p e a r i n g a c r o s s t h e 20. c a p a c i t o r w i l l be T h e r a t i o o f t h i s v o l t a g e to t h e i n p u t v o l t a g e i s known as the m a g n i f i c a t i o n f a c t o r ( Q x ) o f the c i r c u i t and i s g i v e n by V . X t ( W The m a g n i f i c a t i o n f a c t o r and t h e t r u e Q, a r e seen t o be e q u a l f o r t h e c o n d i t i o n s s p e c i f i e d . I n g e n e r a l , t h e element X I s more complex and t h e m a g n i f i c a t i o n f a c t o r i s no l o n g e r X c/R; hence, t h e m a g n i f i c a -t i o n f a c t o r d i f f e r s from t h e t r u e Q. C o n s i d e r , f o r example, t h a t X i n f i g u r e 5, c o n s i s t s o f a pure i n d u c t a n c e L, i n p a r a l -l e l w i t h a d i s t r i b u t e d c a p a c i t y C Q. I n t h i s c i r c u i t , t h e m a g n i f i c a t i o n f a c t o r I s g i v e n by = A , (I»5) R where ( W E x p a n s i o n by t h e b i n o m i a l theorem y i e l d s X «*>Lt \- »~*LC 0 1 ^ . . . . . . . . . . (U-7) o r - Q [ I - C.-I (kg). The Qr-meter, an i n s t r u m e n t f o r measuring r a d i o f r e -quency impedances, c o n s i s t s b a s i c a l l y , o f a r e s o n a n t c i r c u i t 21. e x c i t e d from an o s c i l l a t o r y source. Because t h e s e i n s t r u m e n t s g i v e i n d i c a t i o n s w h i c h a r e dependent upon v o l t a g e magnitudes o r r a t i o s , t h e i n d i c a t i o n s a r e r e l a t e d t o m a g n i f i c a t i o n f a c -t o r s o f t h e t e s t e d c i r c u i t s . M a g n i f i c a t i o n f a c t o r s can he used t o deduce the c h a r a c t e r o f Impedance as shown i n t h e f o r e -g o i n g a n a l y s i s o f t h e c i r c u i t s i n F i g . h a n d F i g . 5' S e r i e s and P a r a l l e l Impedance Components C o n s i d e r th e s e r i e s and p a r a l l e l c i r c u i t s shown i n F i g . 6. The g e n e r a l r e l a t i o n s h i p s between the elements o f the s e r i e s and p a r a l l e l arrangements can be f o u n d by e q u a t i n g the c u r r e n t drawn i n t h e two c i r c u i t s . Thus, e ( R i ~ = ^ ^ ^ (j^ j R s x + X5* ~ R P Hence, ± and R - R r 1 + X 5 Z ~ \ . (50) A130, X S _ . j _ (51) > and X p = L 1 + ? 1 1 • The q u a n t i t y Xs/Rs has been d e f i n e d as t h e Q., o r s t o r a g e f a c t o r o f an i n d u c t o r o r c a p a c i t o r ; t h u s , e q u a t i o n s (50) and (51) become RP = R» 11 + <all ( 5 2 ). -- X s [ I + D z ] ) ......... (53) 22. r e s p e c t i v e l y . From e q u a t i o n s (52) and ( 5 3 ) , ~ D • W U s i n g t h e f a c t t h a t X_ = RaQ, i n c o n j u n c t i o n w i t h e q u a t i o n ( 5 3 ) , - = (55) I t i s o b s e r v e d t h a t t h e r a t i o Xs/Xp i s dependent upon t h e v a l u e o f Q. I n p a r t i c u l a r , i f Q, s 10 Xa = 100 = 0 . 9 8 9 . , Xp . 101 whereas i f Q = 1, X§ = 1 • Hence, t h e p a r a l l e l r e a c t a n c e Xp 2 , o f an i n d u c t o r w i t h a Q o f one i s t w i c e t h e s e r i e s r e a c t a n c e , so t h a t o n l y h a l f t h e s e r i e s c i r c u i t c a p a c i t a n c e i s r e q u i r e d t o tune i t t o resonance i n a p a r a l l e l c i r c u i t . When the 0, o f an i n d u c t o r i s h i g h , t h e d i f f e r e n c e between i t s s e r i e s and p a r a l l e l r e a c t a n c e i s l e s s t h a n one p e r c e n t . C. DESCRIPTION OF THE EQUIPMENT Low Frequency Equipment I n the f r e q u e n c y band between 20 c.p.s. and 20 k c l s . , the equipment shown i n F i g . 7 was employed. T h i s equipment 23. c o n s i s t s o f a c a p a c i t a n c e b r i d g e type 716-B, a m p l i f i e r and n u l l I n d i c a t o r t y p e 1231-A, and a p r e c i s i o n c a p a c i t o r t y p e 722-D ( p r o d u c t s o f t h e G e n e r a l Radio Company). A H e w l e t t P a c k a r d o s c i l l a t o r , t y pe 9726, was used as t h e s i n u s o i d a l v o l t a g e source f o r t h e b r i d g e . The d e s c r i p t i o n and s p e c i f i c a -t i o n s f o r t h e G e n e r a l Radio a p p a r a t u s can be found i n t h e G e n e r a l Radio C a t a l o g u e L, 1 9 k g 1 . The H e w l e t t Packard, o s c i l l a t o r i s d e s c r i b e d i n s p e c i f i c a t i o n 9 7 2 6 , o b t a i n a b l e from t h e m a n u f a c t u r e r s . The method o f c o n n e c t i n g t h e p r e c i s i o n c a p a c i t o r t o th e b r i d g e i s shown i n F i g . g. The t e s t c e l l i s s i m i l a r l y c o n n e c t e d . The t h e o r e t i c a l c o n s i d e r a t i o n s o f t h i s method 2 have been d i s c u s s e d i n the G e n e r a l Radio E x p e r i m e n t e r . O i l C e l l The o i l t e s t c e l l was r e q u i r e d t o have n e g l i g i b l e l o s s a n g l e o v e r the temperature and f r e q u e n c y ranges employed, low s u r f a c e l e a k a g e , s m a l l o i l volume, and a s u i t a b l e c a p a c i t y f o r s e n s i t i v e b r i d g e measurements. I n a d d i t i o n , t h e c e l l was t o be d i s m a n t l e d e a s i l y so t h a t i t s component p a r t s c o u l d be t h o r o u g h l y c l e a n s e d . These p a r t s were t o be l o c a t e d a c c u r -a t e l y when t h e c e l l was reassembled. The c e l l shown i n F i g . 9 meets t h e b a s i c r e q u i r e m e n t s . The i n n e r e l e c t r o d e A (l„2>95 i n c h e s o u t s i d e d i a m e t e r d u r a l t u b i n g ) was f a s t e n e d t o the p o l y s t y r e n e p l a t e B by the 24. h e x a g o n a l nut C. T h i s p l a t e was s e c u r e d t o the o u t e r e l e c -trode. D ( I . 6 9 6 i n c h e s i n s i d e d i a m e t e r d u r a l t u b i n g ) by e i g h t e q u a l l y - s p a c e d &/j,2 screws. O i l was i n t r o d u c e d t o t h e c e l l v i a t h e removable b r a s s f u n n e l E, and was d r a i n e d from t h e c e l l v i a t h e s p i g o t F. F o r t h e c o n s t a n t t e m p e r a t u r e t e s t s , t h e thermometer G, was used. I n t h e v a r i a b l e t e m p e r a t u r e t e s t s , t h e ttermometer was r e p l a c e d by a c o n s t a n t i n - i r o n thermocouple. The s e c t i o n a l ! z e d d r a w i n g o f F i g . 10 i l l u s t r a t e s t h e l o w e r base p l u g J ( c o n ! c a l l y - s h a p e d t o f a c i l i t a t e d r a i n a g e ) , and t h e i n n e r base p l u g K, w h i c h was machined t o r e t a i n the thermometer. C i r c u l a r g r o o v e s p l a c e d on t h e u n d e r s i d e o f t h i s l a t t e r p l u g ensure r a p i d heat t r a n s f e r from th e o i l t o the thermometer b u l b . E x c e s s i v e o i l added t o t h e c e l l f l o w s t h r o u g h t h e o v e r f l o w p i p e H, t h u s m a i n t a i n i n g a c o n s t a n t o i l l e v e l . An Abbe R e f r a c t o m e t e r was used t o measure the r e f r a c -t i v e i n d e x o f t h e o i l s i n the o p t i c a l range of f r e q u e n c i e s . T h i s I n s t r u m e n t i s d e s c r i b e d by Monk^. Low Temperature Equipment F o r t h e low t e m p e r a t u r e t e s t s , t h e plywood chamber A,, shown i n F i g . 11, was c o n s t r u c t e d . The a d d i t i o n a l compart-ment B, was p r o v i d e d t o house th e t e s t c e l l . A l l i n s i d e s u r f a c e s were l i n e d w i t h r o c k wool i n s u l a t i o n . The t e s t c e l l C was Immersed i n the m e t h y l a l c o h o l c o n t a i n e d i n t h e g l a s s 25. v e s s e l D. T h i s v e s s e l was surrounded by d r y i c e u n t i l compart-ment B was f i l l e d c o m p l e t e l y . Movement o f the a i r i n the chamber was e f f e c t e d by t h e f a n E, w h i c h was d r i v e n by t h e s m a l l a-c motor P. The speed o f t h i s motor was c o n t r o l l e d by the v a r i a c G-. Type l 6 0 - A Q-Meter The Boonton l o w - l m p e d a n c e - i n j e c t i o n Q-meter, t y p e 160-A, was employed f o r measurements i n t h e f r e q u e n c y spectrum from 50 k c ' s . t o 10 mc fs. The p r i n c i p a l p a r t s o f t h e I n s t r u -ment a r e a r a d i o f r e q u e n c y o s c i l l a t o r , a measuring c i r c u i t , and a power s u p p l y . The b a s i c diagram i s shown i n F i g . 12. The o s c i l l a t o r ( c o n t i n u o u s l y v a r i a b l e from 50 k c f s . t o 75 m^s.) s u p p l i e s a c a l i b r a t e d v o l t a g e to t h e measuring c i r c u i t . The o s c i l l a t o r output i s connected, v i a a thermocouple meter, t o a 0 ,0k ohm r e s i s t o r i n t h e measuring c i r c u i t . The c u r r e n t t h r o u g h t h e 0.Ok ohm r e s i s t o r , and hence t h e v o l t a g e drop a c r o s s i t , i s known. The thermocouple meter i s c a l i b r a t e d as a m u l t i p l i e r o f the c i r c u i t Q, as i n d i c a t e d by t h e Q, v o l t m e t e r . The measuring c i r c u i t c o n t a i n s a vacuum tube v o l t m e t e r , h a v i n g n e g l i g i b l e power consumption, and t h e main and v e r n i e r t u n i n g c a p a c i t o r s . When a s u i t a b l e i n d u c t o r i s connected t o t h e e x t e r n a l i n d u c t o r t e r m i n a l s , resonance i s e s t a b l i s h e d and t h e vacuum tube v o l t m e t e r i n d i c a t e s the m a g n i f i c a t i o n f a c t o r o f the r e s o n a n t c i r c u i t . 26 The a n a l y t i c a l c i r c u i t o f t h e l o w - i m p e d a n c e - i n j e c t i o n Q-meter i s i l l u s t r a t e d i n F i g . 13. The s t r a y e f f e c t s , such as l e a d i n d u c t a n c e s and c a p a c i t a n c e s , a r e I n c l u d e d as d e f i n i t e c i r c u i t components. The I n j e c t i o n v o l t a g e i s m o n i t o r e d by measuring t h e c u r r e n t I , w h i c h f l o w s i n t o the 0.C4 ohm r e s i s -t o r R Q. T h i s t y p e o f i n j e c t i o n i s r e s p o n s i b l e f o r two sources o f c o r r e c t i o n t o t h e i n d i c a t i o n . The f i r s t e r r o r i s I n t r o d u c e d because t h e r e s i s t a n c e R Q i s i n s e r i e s w i t h t h e r e s o n a n t c i r -c u i t . T h i s e r r o r i s s m a l l a t low f r e q u e n c i e s , b u t becomes a p p r e c i a b l e a t f r e q u e n c i e s i n exce s s o f 10 mc's. When t h e a d d i t i v e method i s employed, t h i s e r r o r c a n c e l s . I n t h e a d d i t i v e method, a s u i t a b l e i n d u c t o r i s co n n e c t e d a c r o s s t e r m i n a l s XX and the unknown a d m i t t a n c e G , B i s c o n n e c t e d a c r o s s t e r m i n a l s YY. From r e a d i n g s o f t h e t u n i n g c a p a c i t o r and m a g n i f i c a t i o n f a c t o r w i t h and w i t h o u t the a d m i t t a n c e , t h e s u s c e p t i v e and c o n d u c t i v e components o f t h e unknown can be o b t a i n e d . The second e r r o r i s i n t r o d u c e d by the s e l f - I n d u c t a n c e LQ o f t h e i n j e c t i o n r e s i s t o r . The v o l t a g e i n j e c t e d i s p r o p o r -t i o n a l t o •\/R7+(a?'l» . A l t h o u g h the s e l f - i n d u c t a n c e can be made e x t r e m e l y s m a l l , a c o r r e c t i o n must be a p p l i e d a t f r e q u e n -c i e s i n exce s s o f 10 mc rs. T h i s e r r o r i s p r e s e n t f o r a l l r e a d i n g s , i n v o l v i n g t h e m a g n i f i c a t i o n f a c t o r magnitude. The o s c i l l a t o r c u r r e n t may c o n t a i n h a r m o n i c s o f t h e fun d a m e n t a l , whereas t h e v o l t a g e a p p l i e d t o the vacuum tube v o l t m e t e r i s s u b s t a n t i a l l y f r e e from harmonic c o n t e n t owing t o t h e f i l t e r i n g a c t i o n o f t h e r e s o n a n t c i r c u i t . Because t h e c a l i b r a t i o n i s dependent upon the r a t i o o f o u t p u t t o i n p u t v o l t a g e , h a r m o n i c s w i l l I n t r o d u c e e r r o r s . 27-The i n p u t c i r c u i t o f t h e vacuum tube v o l t m e t e r w i l l c o n t a i n some s e r i e s i n d u c t a n c e L v and p a r a l l e l c a p a c i t a n c e C v w h i c h w i l l make the v o l t a g e between g r i d and cathode o f t h e tube d i f f e r e n t t h a n t h e v o l t a g e a c r o s s the t u n i n g c a p a c i t o r , G g . T h i s e r r o r i s p r e s e n t f o r a l l t y p e s o f measurement, b u t becomes Important o n l y a t t h e v e r y h i g h f r e q u e n c i e s . The s e r i e s r e s i s t a n c e Ry i n the i n p u t c i r c u i t i s dependent upon f r e q u e n c y ; however, t h i s e r r o r v a n i s h e s when the a d d i t i v e t e s t i n g p r o c e d u r e i s adopted. The s e r i e s i n d u c t a n c e and s e r i e s r e s i s t a n c e Rp o f t h e t u n i n g c a p a c i t o r C 2 a r e n e g l i g i b l e , i n w e l l d e s i g n e d c a p a c i t o r s , a t t h e l o w e r f r e q u e n c i e s . D. PARTICULAR THEORY OF THE PROBLEM T r a n s f o r m e r O i l s The s a t u r a t e d h y d r o c a r b o n s a r e e s s e n t i a l l y n o n - p o l a r , b u t upon o x i d a t i o n , t h e y decompose i n t o a c i d s , e s t e r s and s o l i d m a t e r i a l s w h i c h a l l c o n t a i n p o l a r m o l e c u l e s . I n p o l a r s u b s t a n c e s , t h e c e n t r e o f g r a v i t y o f t h e p o s i t i v e c harges i n t h e m o l e c u l e s i s not c o i n c i d e n t w i t h t h e c e n t r e o f g r a v i t y o f the n e g a t i v e charges. Upon a p p l i c a t i o n o f an e l e c t r i c a l s t r e s s t o t h e s e m a t e r i a l s , two d i s p l a c e m e n t c u r r e n t s f l o w . The f i r s t c u r r e n t , o f v e r y s h o r t d u r a t i o n , i s t h e normal c h a r g i n g 2&. c u r r e n t w h i c h a r i s e s from t h e d i s p l a c e m e n t o f e l e c t r o n s w i t h i n t h e m o l e c u l e s . The second c u r r e n t , o f t h e a b s o r p t i v e t y p e , r e s u l t s from t h e g r a d u a l o r i e n t a t i o n o f the p o l a r m o l e c u l e s i n t o t h e d i r e c t i o n o f t h e a p p l i e d f i e l d . The r a t e o f the a b s o r p t i o n i s a f u n c t i o n o f t h e the t e m p e r a t u r e , v i s c o s i t y , and s i z e o f t h e permanent p o l a r d i p o l e s i n t h e medium. A c c o r d -i n g t o Debye, the r e l a x a t i o n time o f d i l u t e s o l u t i o n s o f p o l a r m o l e c u l e s i n n o n - p o l a r s o l v e n t s i s g i v e n by T = 4TT ? xx b ( 5 6 ) AT T h i s r e l a t i o n i s based upon t h e assumptions t h a t p o l a r molecu-l a r i n t e r a c t i o n i s n e g l i g i b l e , t h a t t h e i d e a l gas l a w s a p p l y , and t h a t S t o k e 1 s law f o r f a l l i n g s pheres i n a v i s c o u s medium r e l a t e t o t h e f o r c e s between p o l a r and n o n - p o l a r m o l e c u l e s . E x p e r i m e n t a l work has shown t h a t these a s s u m p t i o n s a r e not always v a l i d because the e x p e r i m e n t a l v a l u e o f T i s g r e a t e r t h a n t h e v a l u e o b t a i n e d from f o r m u l a ( 5 6 ) . I t has been sugges-t e d by Lowry and Murphy t h a t t h e a s s o c i a t i o n o f a g g r e g a t e s o f p o s i t i v e and n e g a t i v e n u c l e i to form i o n i c d i p o l e s r e s u l t s i n d i m e n s i o n s o f M a " w h i c h g r e a t l y exceed t h o s e o f i n d i v i d u a l p o l a r m o l e c u l e s . C l a r k has p r e s e n t e d a t h e o r y i n v o l v i n g t h e forma-t i o n o f p o l a r groups o r i e n t i n g w i t h i n , and r e l a t i v e t o , the c e n t r a l p a r t o f the m o l e c u l e . The e l e c t r o n i c p o l a r i z a t i o n s mentioned e a r l i e r a r e u n a f f e c t e d by t e m p e r a t u r e changes. The r e f r a c t i v e Index changes w i t h t e m p e r a t u r e , but t h i s change i s c o m p l e t e l y accoun-t e d f o r by t h e accompanying v a r i a t i o n i n d e n s i t y . Atomic 29. v i b r a t i o n s a r e a f f e c t e d by t e m p e r a t u r e because t h e b i n d i n g f o r c e between atoms i s r e d u c e d as the t e m p e r a t u r e i s i n c r e a s e d . Atomic p o l a r i z a t i o n s would p o s s e s s a p o s i t i v e t e m p e r a t u r e c o e f f i c i e n t i f t h e d e n s i t y d i d not change. The v a r i a t i o n i n d e n s i t y r e s u l t s i n a n e g a t i v e temperature c o e f f i c i e n t and the n e x t net e f f e c t y i e l d s z e r o , o r s l i g h t l y p o s i t i v e v a l u e f o r the t e m p e r a t u r e c o e f f i c i e n t o f atomic p o l a r i z a t i o n s ; A c c o r d -i n g t o Debye, the v a r i a t i o n o f d i p o l e p o l a r i z a t i o n w i t h t e m p e r a t u r e can be e x p r e s s e d by P - A +- B / T , ( 5 7 ) where A I s a measure of t h e i n s t a n t a n e o u s p o l a r i z a t i o n s w h i c h a r e i ndependent o f t e m p e r a t u r e , and B i s a measure o f t h e d i p o l e p o l a r i z a t i o n s . The m o l e c u l e s i n a l i q u i d a r e i n a c o n t i n u o u s s t a t e o f r o t a t i o n a l and t r a n s l a t i o n a l motion. The f o r c e e x e r -t e d on t h e d i p o l e s by an e x t e r n a l f i e l d i s opposed by the t h e r m a l m o t i o n w h i c h tends to p r e s e r v e t h e random o r i e n t a t i o n s o f t h e s e d i p o l e s . When t h e temperature I s d e c r e a s e d , however, the t h e r m a l energy i s r e d u c e d and f o r a g i v e n a p p l i e d f i e l d , t h e d i p o l e p o l a r i z a t i o n i n c r e a s e s , r e s u l t i n g i n a n e g a t i v e t e m p e r a t u r e c o e f f i c i e n t o f d i p o l e p o l a r i z a t i o n . Oy-Meter T e s t s The f o l l o w i n g a n a l y s i s was d e v e l o p e d t o o b t a i n t h e h i g h e s t p o s s i b l e a c c u r a c y from t h e Q-meter r e a d i n g s . The i n h e r e n t l y d i s t r i b u t e d i n d u c t a n c e and c a p a c i t a n c e o f t h e t e s t c e l l and c o n n e c t i n g l e a d s have s m a l l l o s s e s and d a t a must be t a k e n t o account f o r t h e s e e l e c t r o d e c o n s t a n t s . 30. I t l a n e c e s s a r y t o t a k e t h r e e s e t s o f r e a d i n g s t o a ccount f o r t h e d i s t r i b u t e d c o n s t a n t s and t o d e t e r m i n e a c c u r a t e l y t h e d i e l e c t r i c p r o p e r t i e s o f t h e o i l sample. 1. The c a l i b r a t e d c a p a c i t o r s e t t i n g and Q, r e a d i n g a r e o b s e r v e d at r esonance w i t h t h e i n d u c t o r i n p l a c e , but w i t h o u t t h e t e s t c e l l c onnected. 2. The c a l i b r a t e d c a p a c i t o r s e t t i n g i s o b s e r v e d a t resonance w i t h t h e i n d u c t o r and empty t e s t c e l l c onnected. 3. The c a l i b r a t e d c a p a c i t o r s e t t i n g and Q. r e a d i n g a r e o b s e r v e d at resonance w i t h t h e i n d u c t o r and f i l l e d t e s t c e l l connected. The c i r c u i t s o f P i g . iH- show t h e e q u i v a l e n t m e asuring c i r c u i t s f o r each o f the t h r e e c o n d i t i o n s d e s c r i b e d . The q u a n t i t i e s i n d i c a t e d i n t h e s e c i r c u i t s a r e as f o l l o w s : L = c o i l I n d u c t a n c e r =' c o i l r e s i s t a n c e G l 3 G 2, Gj 5 c a p a c i t a n c e o f Q»*meter t u n i n g c a p a c i t o r a t resonance. C d ~ t h e e f f e c t i v e d i s t r i b u t e d c a p a c i t a n c e o f the c e l l and c o n n e c t i n g l e a d s viewed from the Qr-meter t e r m i n a l s . C e = the d i r e c t c a p a c i t a n c e between t h e e l e c t r o d e f a c e s o f t h e t e s t c e l l . C g ~ t h e d i r e c t c a p a c i t a n c e between the e l e c t r o d e f a c e s o f the t e s t c e l l w i t h t h e o i l sample i n p l a c e . P i - & the e f f e c t i v e r e s i s t a n c e o f t h e sample. 5 1 . I t w i l l be noted t h a t i n c i r c u i t (2) t h e r e i s no component t o r e p r e s e n t power l o s s i n t h e t e s t c e l l . The l o s s i n the t e s t c e l l was e x p e r i m e n t a l l y d e t e r m i n e d t o be n e g l i g i b l e up t o a f r e q u e n c y o f 10 mc's. F o r - f r e q u e n c i e s i n e x c e s s o f t h i s v a l u e , l o s s e s were o b s e r v e d t o appear i n t h e c o n n e c t i n g l e a d s . Because the h i g h e s t t e s t f r e q u e n c y used was 10 mc ts., t h i s l o s s component i s not accounted f o r i n t h e p r e s e n t a n a l y s i s . The same I n d u c t o r i s used f o r t h e t h r e e s e t s o f measurements; t h u s , t h e d i s t r i b u t e d c a p a c i t a n c e o f t h e i n d u c -t o r I s t h e same f o r a l l t h r e e c i r c u i t s and need not be c o n s i d e r e d f u r t h e r . From e q u a t i o n ( 4 3 ) , t h e Q, o f c i r c u i t ( l ) i s I n c i r c u i t ( 2 ) , t h e t o t a l e f f e c t i v e s e r i e s c a p a c i -t a n c e must e q u a l C]_; hence , C ,= Ct + CA + C e . (5g) The v a l u e o f C e can be c a l c u l a t e d from t h e g e o m e t r i -c a l c o n f i g u r a t i o n o f t h e t e s t c e l l . These c a l c u l a t i o n s were checked by t e s t i n g t h e c e l l 'on t h e t y p e 71&*B c a p a c i t a n c e b r i d g e w i t h t h e p r e c i s i o n c a p a c i t o r t y p e 722~D. The t o t a l s e r i e s e f f e c t i v e c a p a c i t a n c e o f c i r c u i t ( 3 ) , i s e q u a l t o C^. C i r c u i t ( 3 ) can be s i m p l i f i e d by r e p l a c i n g t h e p a r a l l e l r e s i s -t a n c e and c a p a c i t a n c e by an e q u i v a l e n t s e r i e s c o m b i n a t i o n , T h i s s i m p l i f i e d c i r c u i t i s shown i n F i g . 15 . 32 The s e r i e s c a p a c i t a n c e and r e s i s t a n c e R can be d e t e r m i n e d from c i r c u i t (3) as f o l l o w s : Ci - ^ 3 + + c 5 (60) R -•• ( 6 l ) From the s i m p l i f i e d c i r c u i t o f F i g . 15, t h e 0, i s d e t e r m i n e d as q , r 1 . (62) The d i s s i p a t i o n f a c t o r o f t h e o i l sample i s b e i n g sought i n t h i s a n a l y s i s , and s i n c e t h i s f a c t o r i s d i r e c t l y r e l a t e d t o th e Q, o f t h e o i l sample, i t i s n e c e s s a r y t o de t e r m i n e t h i s l a t t e r q u a n t i t y . The Q. o f the o i l sample i n terms o f i t s e q u i v a l e n t c i r c u i t q u a n t i t i e s i n F i g . 14- (3) i s **cs . a # ( 6 3 ) From e q u a t i o n (4-3), and from e q u a t i o n ( 6 2 ) , R = CO 33. From e q u a t i o n ( 6 l ) , R s _L_ Q * c u C , Q ( - O , ^ * . . . . (66) and f r o m e q u a t i o n s (60) and (52S), C s = C l " C 3 - °d B ° 1 - G 3 - <C1 - C 2 - °e> C s ~ C 2 - C 3 * 0 e. (67/) I f the v a l u e s o f Cfi and R g a r e s u b s t i t u t e d i n e q u a t i o n ( 6 3 ) , the f o l l o w i n g e x p r e s s i o n f o r Q,x i s o b t a i n e d * Q x = ( 0 2 - * OqHQrjQ^) (6g) Cl Cfti «• Q5) \ where 0^ i s tl|e&A\o;f t h e o i l sample. From e q u a t i o n (5*0, D x " - Cx (Oi - Q3) . . . . . . . . . (69) Q x ( C 2 - C 3 * C ^ U ^ ) where Dx i s the r e q u i r e d d i s s i p a t i o n f a c t o r o f t h e o i l sample. E. TE3T3 AND RESULTS Low F r e q u e n c i e s Throughout the p r e s e n t work, t h e f o l l o w i n g f o u r t r a n s f o r m e r o i l s were t e s t e d ; 1 * i a new t r a n s f o r m e r o i l ; 2 a t r a n s f o r m e r o i l w i t h 5 y e a r s s e r v i c e l i f e j 3 - a t r a n s f o r m e r o i l w i t h unknown s e r v i c e l l f e j 4 ~ a t r a n s f o r m e r o i l w i t h c o n t a m i n a t i o n p r o d u c t s . 3*. P r e l i m i n a r y t e s t s were made on t h e o i l c e l l t o d e t e r m i n e i t s c h a r a c t e r i s t i c s . These measurements were t a k e n , by t h e s u b s t i t u t i o n method, w i t h t h e equipment shown l n P i g . 7. A t 1000 c.p.s., the c e l l d i s s i p a t i o n f a c t o r was 0 .0005. The c e l l was p l a c e d i n a t h e r m o s t a t i c a l l y c o n t r o l l e d oven f o r t h r e e h o u r s a t a temperature o f 100 d e g r e s s f a h r e n h e i t . Upon c o o l i n g t o room t e m p e r a t u r e , the c e l l y i e l d e d a d i s s i p a t i o n f a c t o r o f 0 .0001 . Because t h e s e r e a d i n g s were not s a t i s f a c -t o r y , the c e l l was d i s m a n t l e d , t h o r o u g h l y c l e a n s e d w i t h r e p e a t e d washings o f ca r b o n t e t r a c h l o r i d e , and t r e a t e d a t 170 degrees f a h r e n h e i t f o r s i x hours. The d i s s i p a t i o n f a c t o r r e a d i n g s , a f t e r t h i s t r e a t m e n t , were not d e t e c t a b l e . These r e a d i n g s a r e i n d i c a t i v e o f t h e c a r e w h i c h must be e x e r c i s e d i n r emoving adsorbed s u r f a c e m o i s t u r e f r o m t h e c e l l . Tempera-t u r e r u n s on t h e empty c e l l showed t h a t t h e c a p a c i t y remained c o n s t a n t from 64- degrees t o 120 degrees f a h r e n h e i t . T e s t s , u s i n g a s u b s t i t u t i o n method, were made o v e r a range o f 20 c.p.s. t o 20 k c ^ s . w i t h t h e equipment shown i n F i g . 7' S e v e r a l r u n s were made w i t h each o i l a t a c o n s t a n t t e m p e r a t u r e o f 7 ° degrees f a h r e n h e i t . The d i s s i p a t i o n f a c t o r r e a d i n g s f o r a l l t h e o i l s I n c r e a s e d w i t h d e c r e a s i n g f r e q u e n c y u n t i l t h e r e g i o n o f 4-5 t o 5° c.p. s. where maxima o c c u r r e d . A mica c a p a c i t o r , w i t h a known r i s i n g d i s s i p a t i o n f a c t o r c u r v e down t o 10 c.p. s, , e x h i b i t e d t h e same l o s s hump a t 5 ° c.p.s., t h u s showing t h a t t h e f r e q u e n c y response o f t h e b r i d g e and d e t e c t o r was r e s p o n s i b l e f o r t h e s e maxima. A c c u r a t e v a l u e s f o r t h e d i e l e c t r i c c o n s t a n t were o b t a i n e d , but v a l u e s f o r t h e 35. d i s s i p a t i o n f a c t o r were not o b t a i n a b l e f o r f r e q u e n c i e s i n e x c e s s o f 5000 c. p. s. f o r a l l , e xcept t h e h i g h - l o s s o i l 4-. Graph 1 shows th e b e h a v i o u r o f t h i s o i l . The measurement o f l o w - l o s s o i l s , a t , t h e s e f r e q u e n c i e s and t e m p e r a t u r e s , i s not p o s s i b l e w i t h o u t t h e i n c l u s i o n o f a g u a r d c i r c u i t f o r use w i t h t h e c a p a c i t a n c e - b r i d g e t y p e JlG-B. However, th e d i e l e c t r i c c o n s t a n t s o f t h e o i l s remained c o n s t a n t t h r o u g h o u t t h e s e t e s t s ; t h u s , t h e I n d i c a t i o n i s . t h a t no a b s o r p t i v e phenomena ar e p r e s e n t under the s t a t e d t e s t i n g c o n d i t i o n s . F u r t h e r t e s t s were made w i t h t h e Boonton t y p e l 6 0-A Q-meter from 50 k c t s . t o 10 1110*8. The equipment i s shown i n F i g . 16. Experiment showed t h a t the i n h e r e n t c e l l and c o n n e c t -i n g l e a d i n d u c t a n c e became n o t i c e a b l e a t f r e q u e n c i e s i n excess o f 10 mc*s. As i n t h e p r e v i o u s t e s t s , t h e d i s s i p a t i o n f a c t o r o f t h e l o w - l o s s o i l s was not o b t a i n a b l e . The c u r v e f o r o i l 4-i s shown i n graph 2. The d i e l e c t r i c c o n s t a n t r e a d i n g s had a maximum d e v i a t i o n o f f i v e p e r c e n t from t h e mean v a l u e . None o f t h e o i l s e x h i b i t e d d i s p e r s i o n s i n t h i s r e g i o n , however, the d i s p e r s i o n s , i f they do e x i s t , p r o b a b l y produce d e v i a t i o n s l o w e r t h a n f i v e p e r c e n t . H i g h F r e q u e n c i e s An Abbe R e f r a c t o m e t e r y i e l d e d t h e r e f r a c t i v e i n d e x o f t h e o i l s i n the v i s i b l e spectrum a t a t e m p e r a t u r e o f 7° degrees f a h r e n h e i t . The M a x w e l l i a n r e l a t i o n £--nJ was used t o d e t e r m i n e the d i e l e c t r i c c o n s t a n t . These v a l u e s were compared 36. w i t h t h e c o r r e s p o n d i n g v a l u e s taken a t t h e l o w f r e q u e n c i e s on the c a p a c i t a n c e b r i d g e type 716-B. The r e s u l t s a r e shown I n t a b l e 1. Low Temperatures F u r t h e r t e s t s were made w i t h t h e equipment shown i n F i g , I J . F o r t h e s e t e s t s , the f r e q u e n c y was m a i n t a i n e d c o n s t a n t and t h e temperature was v a r i e d from p l u s 60 degrees t o minus 60 degrees f a h r e n h e i t . P r e l i m i n a r y t e s t s c o n ducted on t h e o i l - c e l l showed t h a t t h e Q, and c a p a c i t y o f t h e empty c e l l d i d not v a r y o v e r t h i s t e m p e r a t u r e range. The r e s u l t s are shown i n graphs 3 to 10 i n c l u s i v e . A d d i t i o n a l t e s t s were made a t 2 mc ls. w i t h t h e same equipment. I n t h e s e t e s t s , t h e o i l - - . f I l l e d c e l l was h e a t e d to 160 degrees f a h r e n h e i t , p l a c e d I n the i n s u l a t e d chamber, and a l l o w e d t o c o o l g r a d u a l l y t o 2>0 degrees f a h r e n h e i t . The r e s u l t s f o r a l l t h e o i l s f o l l o w e d t h e same p a t t e r n and graph 2 r e p r e s e n t s t h i s t y p i c a l b e h a v i o u r f o r o i l 4. P. CONCLUSIONS AND DISCUSSION I n t h e f r e q u e n c y band from 20 c.p.s. t o 20 k c r s., at the c o n s t a n t t e m p e r a t u r e o f 7 ° degrees f a h r e n h e i t , t h e d i s s i p a t i o n f a c t o r o f l o w - l o s s t r a n s f o r m e r o i l s i s t o o low t o 37. be r e a d a c c u r a t e l y w i t h t h e equipment shown i n F i g . 7. T h i s equipment would be s a t i s f a c t o r y f o r s u c h measurements i f a g u a rd c i r c u i t were used i n c o n j u n c t i o n w i t h the c a p a c i t a n c e b r i d g e t y p e "JlS-B. T h i s equipment p r o v i d e s a c c u r a t e r e a d i n g s f o r t h e d i e l e c t r i c c o n s t a n t . The steady v a l u e o f d i e l e c t r i c c o n s t a n t p l o t t e d a g a i n s t f r e q u e n c y would i n d i c a t e t h a t no a b s o r p t i v e phenomena ar e p r e s e n t , under th e s t a t e d t e s t i n g c o n d i t i o n s , i n t h i s range. The r i s i n g d i s s i p a t i o n f a c t o r c u r v e s a t t h e low f r e q u e n c y v a l u e s a r e a f u n c t i o n o f the b r i d g e and d e t e c t o r response, as e x p l a i n e d p r e v i o u s l y . T h i s s u g g e s t s t h a t s p e c i a l equipment, s u i t a b l e f o r t e s t i n g t r a n s -f o r m e r o i l s from th e low f r e q u e n c i e s down t o a few c y c l e s p e r second, s h o u l d be b u i l t t o d etermine t h e t r u e d i s s i p a t i o n f a c t o r and d i e l e c t r i c c o n s t a n t as the f r e q u e n c y approaches z e r o . F u r t h e r t e s t s , c a r r i e d out w i t h d i r e c t c u r r e n t s , would be v a l u a b l e i n comparing t h e measured power I0S3 w i t h i n i t i a l a b s o r p t i o n and c o n d u c t i v i t y . The s t a t i c d i e l e c t r i c c o n s t a n t (£ e) c o u l d not be o b t a i n e d w i t h t h e p r e s e n t c e l l . The b a l l i s t i c g a lvanometer and " s h a r i n g " methods were t r i e d , b u t the low c a p a c i t y o f t h e c e l l i n c o n j u n c t i o n w i t h t h e r e l a t i v e l y h i g h s u r f a c e l e a k a g e o f t h e t e ' s t i n g equipment p r e c l u d e d the employment o f t h e s e methods. I t i s suggested t h a t a s p e c i a l l y c o n s t r u c t e d c a p a c i -t o r , h a v i n g an empty c e l l c a p a c i t a n c e o f a p p r o x i m a t e l y 0.01 m i c r o f a r a d s , would y i e l d s a t i s f a c t o r y r e s u l t s f o r t h e c a l c u l a -t i o n o f £ Q . 3 g " When the Q-meter method I s used a t the tem p e r a t u r e o f 7° degrees f a h r e n h e i t , o n l y the h i g h - l o s s o i l s y i e l d s a t i s -f a c t o r y d i s s i p a t i o n f a c t o r v a l u e s . Because the d i e l e c t r i c c o n s t a n t r e a d i n g s a r e a c c u r a t e t o f i v e p e r c e n t , d i s p e r s i o n d e v i a t i o n s l e s s t h a n f i v e p e r c e n t cannot be d e t e c t e d . Graph 1 shows t h e d i s s i p a t i o n f a c t o r c u r v e f o r o i l 4, I t I s t o be n o t e d t h a t t h e d i s s i p a t i o n f a c t o r c u r v e i s r i s i n g s l i g h t l y as the h i g h e r f r e q u e n c i e s a r e b e i n g approached. I t i s c o n c l u d e d t h a t t h e d i s p e r s i o n method f o r t e s t -i n g t h e c o n d i t i o n o f t r a n s f o r m e r o i l s , i n the f r e q u e n c y spectrum from 20 c.p.s. t o 10 mc la. and a t room temperature^ i s not s a t i s f a c t o r y . The a c t u a l d i e l e c t r i c c o n s t a n t o b t a i n e d a t t h e low f r e q u e n c i e s i s g r e a t e r t h a n t h a t l i s t e d i n t a b l e 1. L e t the c a p a c i t a n c e A r e p r e s e n t t h e t e r m i n a l c a p a c i t a n c e w h i c h does not a l t e r when the c e l l i s f i l l e d , c a p a c i t a n c e B r e p r e s e n t t h e e m p t y - c e l l c a p a c i t a n c e between t h e a c t i v e p o r t i o n o f the e l e c t r o d e f a c e s , and c a p a c i t a n c e C r e p r e s e n t the c a p a c i t a n c e between t h e a c t i v e p o r t i o n o f t h e e l e c t r o d e f a c e s when the c e l l i s f i l l e d . L e t the t o t a l e m p t y - c e l l c a p a c i t a n c e be x mmfds. and t h e f i l l e d - c e l l c a p a c i t a n c e y mmfds. Then, A + B - x mmfd. and A + C = ' y mmfd. The d i e l e c t r i c c o n s t a n t as c a l c u l a t e d i n t a b l e 1 i s g i v e n by A -j- C = y TTB x The t r u e d i e l e c t r i c c o n s t a n t o f t h e o i l i s g i v e n by C/B. 39 T h i s r a t i o I s o b t a i n e d as f o l l o w s ; •A f B = x A * C y B = A ( x ~ y) + C x y y B 5 A ( x - 1 ) + x C" G y y = x (C -fr A) - Ay Gy o = cy B x (C * A) - Ay x (70) 1 + A ( 1 „ j[) C x I f c a p a c i t a n c e A were r e d u c e d to z e r o , t h e n e q u a t i o n (70) shows t h a t t h e a c t u a l d i e l e c t r i c c o n s t a n t o f t h e o i l would e q u a l the d i e l e c t r i c c o n s t a n t v a l u e l i s t e d i n t a b l e 1 . Because t h e r a t i o i s g r e a t e r t h a n u n i t y , t h e t r u e d i e l e c t r i c c o n s t a n t o f the t r a n s f o r m e r o i l i s g r e a t e r t h a n t h a t shown i n t a b l e 1. The magnitude o f £ i s a p p r o x i m a t e l y -|- so t h a t t h e c o r r e c t e d d i e l e c t r i c c o n s t a n t v a l u e s a r e 2.20, 2.185, 2.230, and 2.3SI f o r o i l s 1 , 2, 3> and r e s p e c t i v e l y . Comparison o f t h e s e v a l u e s w i t h t h o s e o b t a i n e d i n t h e v i s i b l e spectrum, shows t h a t t h e d i e l e c t r i c c o n s t a n t has dropped c o n s i d e r a b l y and suggests t h e e x i s t e n c e o f an a b s o r p t i o n band l y i n g between 1 0 1110*6. and the v i s i b l e spectrum. Graph 2 shows t h a t the i n c r e a s e d l o s s i n d-c conduc-t i v i t y w h i c h o c c u r s w i t h i n c r e a s e d t e m p e r a t u r e i s i n s i g n i f i c a n t i n comparison w i t h t h e c o r r e s p o n d i n g d e c r e a s e i n d i p o l a r a b s o r p t i o n l o s s . MO. Graphs 3 , ^, 5, and. 6 show t h e r e l a t i o n s h i p between d i s s i p a t i o n f a c t o r , t e m p e r a t u r e , and f r e q u e n c y f o r t r a n s f o r -mer o i l s 3, 1, 4, and 2, r e s p e c t i v e l y . I t i s o b s e r v e d t h a t the c u r v e s f o l l o w an o r d e r l y pa,ttern. T h i s r e s u l t s u g g e s t s t h a t t h e same a b s o r p t i o n mechanism i s I n v o l v e d a t each o f t h e f r e q u e n c i e s t e s t e d . The l o s s peaks o c c u r around t h e same d i s s i p a t i o n f a c t o r v a l u e . T h i s b e h a v i o u r s u g g e s t s t h a t t h e c o n d u c t i v i t y i s p r a c t i c a l l y c o n s t a n t w i t h r e s p e c t t o f r e q u e n c y . I t i s e x p e c t e d , from e q u a t i o n ( 3 6 ) , t h a t the d-c c o n d u c t i v i t y w i l l i n c r e a s e w i t h an i n c r e a s e i n f r e q u e n c y , i f i t changes at a l l . Graph 6 i l l u s t r a t e s t he i m p o r t a n t f a c t t h a t an i n c r e a s e i n m o i s t u r e c o n t e n t i s evidenced,by an i n c r e a s e i n d i s s i p a t i o n f a c t o r , but t h e l o s s peak r e m a i n s , e s s e n t i a l l y , i n t he same p o s i t i o n . The I r r e g u l a r shape o f t h i s c u r v e i s a t t r i b u t e d t o t h e h e t e r o g e n e i t y o f t h e d i e l e c t r i c . These graphs y i e l d t h e predominant f a c t t h a t as the f r e q u e n c y i s i n c r e a s e d , t h e l o s s peaks a r e s h i f t e d t o t h e r i g h t . T h i s means t h a t an i n c r e a s e i n t e m p e r a t u r e t e n d s t o produce a d e c r e a s e i n t h e time c o n s t a n t o f t h e a b s o r p t i o n p r o c e s s . T h i s r e s u l t a g r e e s w i t h Debye ts e q u a t i o n ( 5 6 ) . The r e l a x a t i o n t ime d e c r e a s e s d i r e c t l y w i t h I n c r e a s i n g tempera-t u r e . I n a d d i t i o n , t h e v i s c o s i t y d e c r e a s e s w i t h I n c r e a s i n g t e m p e r a t u r e , c a u s i n g a f u r t h e r d e c r e a s e i n t h e r e l a x a t i o n t i m e . These c u r v e s c o r r o b o r a t e the c o n c l u s i o n s o b t a i n e d from t h e low f r e q u e n c y e x p e r i m e n t s c a r r i e d out a t room tempera-t u r e . At room t e m p e r a t u r e s , t h e r e l a x a t i o n time w o u l d d e c r e a s e to s m a l l v a l u e s and t h e l o s s peak would appear a t v e r y h i g h 41 f r e q u e n c i e s . Time was not a v a i l a b l e f o r p l o t t i n g v i s c o s i t y -c u r v e s . A t any g i v e n t e m p e r a t u r e , such v i s c o s i t y c u r v e s , i n c o n j u n c t i o n w i t h the g raph d a t a , would a l l o w the c a l c u l a t i o n o f t h e f r e q u e n c y at w h i c h the l o s s peak o c c u r s . T h i s c a l c u -l a t i o n , w h i c h assumes t h a t t h e e f f e c t i v e d i p o l e r a d i u s i s i n v a r i a n t w i t h t e m p e r a t u r e , w o u l d be e x p e c t e d t o y i e l d the a p p r o x i m a t e r e g i o n o f a b s o r p t i o n . Graphs 8, 9, and 10 a r e p l o t t e d from t h e d a t a on g raphs 5, 6, and 3, r e s p e c t i v e l y . These graphs show t h e t r e n d l n d i s s i p a t i o n f a c t o r , a t c o n s t a n t t e m p e r a t u r e , w i t h v a r i a t i o n s i n f r e q u e n c y . Graph 7 shows t h e b e h a v i o u r o f t h e d i f f e r e n t t r a n s -f o r m e r o i l s , a t t h e c o n s t a n t f r e q u e n c y o f 2 mc ts., p l o t t e d a g a i n s t t emperature. The r e l a t i v e l y narrow a b s o r p t i o n band o f o i l 4- i s a t t r i b u t e d t o t h e l a r g e r a t e o f change o f v i s c o s -i t y o f t h e o i l l n t h i s t e m p e r a t u r e range. I t i s seen t h a t a l t h o u g h th e r e l a x a t i o n t i m e i s c o n s t a n t , t h e l o s s peaks o c c u r a t h i g h e r t e m p e r a t u r e s as t h e l o s s f a c t o r o f t h e o i l i n c r e a s e s . Because t h e l o s s f a c t o r i s known to d e c r e a s e (graphs 3» 4-, 5 and 6) w i t h i n c r e a s i n g temperature, t h e e f f e c t i v e d i p o l a r radiu3 must i n c r e a s e to m a i n t a i n a c o n s t a n t r e l a x a t i o n t i m e . The p r e s e n t i n v e s t i g a t i o n h a 3 y i e l d e d t h e f o l l o w i n g i n f o r m a t i o n . (1) A b s o r p t i o n bands have been f o u n d i n t r a n s f o r -mer o i l s . (2) The l o c a t i o n o f t h e s e a b s o r p t i o n bands has been found f o r t e m p e r a t u r e s r a n g i n g from - 6 0 ° F. t o 6 0 ° F. 42. ( 3 ) The r e l a x a t i o n t i m e o f t h e a b s o r p t i o n p r o c e s s has been found to v a r y w i t h t e m p e r a t u r e . (4) The p o s i t i o n o f t h e l o s s peak has been f o u n d t o v a r y w i t h t h e d i p o l a r s t a t e o f the o i l . I n a d d i t i o n , t h e I n v e s t i g a t i o n h a s s u g g e s t e d t h a t f u r t h e r work s h o u l d be u n d e r t a k e n to d e t e r m i n e t h e l o c a t i o n o f t h e a b s o r p t i o n bands a t any r e q u i r e d t e m p e r a t u r e , t h e q u a n t i t a t i v e measurement o f t h e e f f e c t i v e d i p o l a r r a d i u s , and t h e v a r i a t i o n o f t h e e f f e c t i v e d i p o l a r r a d i u s w i t h t h e s t a t e o f the o i l . * 3 . OIL AUDIO SPECTRUM VISIBLE SPECTRUM D i e l e c t r i c C o n s t a n t R e f r a c t i v e Index R e f r a c t i v e I n d e x D i e l e c t r i c C o n s t a n t 1 2.190 1. 4S0 I .4765 2. ISO 2 2.17S 1.476 I .4769 2.179 3 2. 220 1.490 1.471 2.165 4 2.376 1.541 1.433 2.199 TABLE 1 D i e l e c t r i c C o n s t a n t s and R e f r a c t i v e I n d i c e s Capacitor Character!atlos 44. V CO Scot Vcosatf © C ±. I FIG. 1 Electronic.. ^ — — - •-3-J Atomic Loss Factor V i s i b l e Frequency D i e l e c t r i c C h a r a c t e r i s t i c s PIG. 3 0,-Meter Measuring C i r c u i t 0 FIG. 4 FIG. 5 * 5 . -v^^ 1 J3L , -msuw—' FIG. 6 Series and P a r a l l e l Components 1 - Amplifier and Null-Indicator Type 1231-A. 2 - Hewlett Packard Audio O s c i l l a t o r 9 7 2 6 . x - Test C e l l . - Capacitance Bridge Type 716-B. 5 - Precisio n Capacitor Type 722-D. FIG. 7 Low Frequency Measuring Equipment 46. FIG. S C a p a c i t o r C o n n e c t i o n s FIG. 11 Low Temperature Equipment 49. 1 2 <!>! 5 -O s c i l l a t o r Thermocouple Ammeter Vacuum Tube Voltmeter Calibrated Tuning Capacitor I n j e c t i o n Resistor FIG. 12 Basic Qr-Meter C i r c u i t Y P l R 2 FIG. 13 Analytic C i r c u i t of Q-Meter 50 7 T o ; ( i) (2) FIG. 14 Qr>Meter Measuring Circui t s (3) FIG. 15 Equivalent Q-Meter Measuring .Circuit 51. • PIG. 16 Qr-Meter and O i l C e l l FIG. 17 Low Temperature Equipment M U o +» o r* Ct. c o at O. -H CO CO 50 15-10. 10 \ 10' 10-0 I H o 10" Dielectric Constant s 2«31 Dielectric Cons Factor ant and Afeainst GRAPH 1 l o l Dissipation Frequency LOG FREQUENCY IN M£*S. VJ1 ( -H-T-! ' r r r t . -1 T.T." - ; ! t i ---H4 w m ±4 41.:.: l-i-K tt . :r.i j. • id:: q:g.|i: 11 GLOSSARY C h a r g i n g c u r r e n t L o s e c u r r e n t Conductance Susceptance D i s s i p a t i o n F a c t o r P o l a r i z a b i l i t y E q u i v a l e n t s e r i e s r e s i s t a n c e E q u i v a l e n t s e r i e s r e a c t a n c e E q u i v a l e n t p a r a l l e l r e s i s t a n c e E q u i v a l e n t p a r a l l e l r e a c t a n c e D i e l e c t r i c C o n s t a n t o f m a t e r i a l D i e l e c t r i c C o n s tant o f vacuum S t a t i c d i e l e c t r i c c o n s t a n t D i e l e c t r i c c o n s t a n t a t v e r y h i g h f r e q u e n c i R e l a x a t i o n time C o e f f i c i e n t o f v i s c o s i t y D i s t r i b u t e d c a p a c i t a n c e R e f r a c t i v e i n d e x D i p o l a r r a d i u s B o l t z m a n n 1 s c o n s t a n t A b s o l u t e t e m p e r a t u r e 64, i i i LITERATURE CITED 1 G e n e r a l Radio C a t a l o g u e , G e n e r a l Radio Company, New Y o r k , 194S. 2 F i e l d , R. F., "C o n n e c t i o n E r r o r s i n C a p a c i t a n c e Measurements", The G e n e r a l R a d i o E x p e r i m e n t e r , V o l . XXI No. 12, G e n e r a l Radio Company, New York, May, 194-7. 3 Monk, G. 3., L i g h t P r i n c i p l e s and E x p e r i m e n t s , New Yor k , M c G r a w - H i l l Book Company, 1937, pp. 96-99. 65. i v BIBLIOGRAPHY Ba l s b a u g h , J . C., "Comprehensive Theory o f a Power F a c t o r B r i d g e " , J o u r n a l o f t h e F r a n k l i n I n s t i t u t e . 1934> V o l . 212, p. 49. B i g g s , A. J . and H o u l d i n , J . E., "The Development o f Qr-meter Methods o f Impedance Measurement", P r o c e e d i n g s o f  the I n s t i t u t i o n o f E l e c t r i c a l E n g i n e e r s . J u l y , 1949, V o l . 96, P a r t I I I , No. 42, p. 295-Bramely, L. N., "An Improved C e l l f o r t h e A.C. and D.C. T e s t i n g o f I n s u l a t i n g O i l s " , The J o u r n a l o f t h e I n s t i t u -t i o n o f E l e c t r i c a l E n g i n e e r s , 1940, V o l . 86, p. 326. C a l v e r t , B., "Transformer I n s u l a t i n g O i l s " , The  I n s t i t u t i o n o f E l e c t r i c a l E n g i n e e r s S t u d e n t s 1 Q u a r t e r l y  J o u r n a l . September 1940, V o l . I I , No. 4 l , p. 19. C l a r k , F. M., "Are New Types o f T r a n s f o r m e r O i l Needed?", G e n e r a l E l e c t r i c Review/ May, 1948, pp. 9~14. C l a r k , F. M., "Are New Types o f T r a n s f o r m e r O i l Needed?", G e n e r a l E l e c t r i c Review, June, 194S, pp. 43-47. Coursey, P. R., E l e c t r i c a l Condensers, London, S i r I s a a c P i t m a n and Sons, L t d . , 1927^ F i e l d , R. F., "A B r i d g e f o r P r e c i s i o n Power F a c t o r Measurements", A. I . E. E. T r a n s a c t i o n s . 1933, V o l « 52> P« 5 2 g * 66. F i e l d , R. F,, "C o n n e c t i o n E r r o r s i n C a p a c i t a n c e Measurements", G e n e r a l R a d i o E x p e r i m e n t e r , May, 194-7, V o l . 21, No. 12, pp. 1-4. F i e l d , R. F., " I n c r e a s e d A c c u r a c y f o r t h e P r e c i s i o n Condenser", G e n e r a l Radio E x p e r i m e n t e r , June, 194-7, V o l . 22, No. 1, pp. 1-6. F i e l d , R. F. and E a s t o n , I . G., "A Wide-Frequency Range C a p a c i t a n c e B r i d g e " , G e n e r a l R a d i o E x p e r i m e n t e r , A p r i l , 194-7, V o l . 21, No. I I , pp. 1-5. F r o h l i c h , H., Theory o f D i e l e c t r i c s , O x f o r d a t the Cl a r e n d o n P r e s s , 194-9. G a r t o n , C. G., " D i e l e c t r i c L o s s i n T h i n F i l m s o f I n s u l a t i n g L i q u i d s " , The J o u r n a l o f the I n s t i t u t i o n o f E l e c -t r i c a l E n g i n e e r s . 194-1, V o l . &&, P a r t 3 , p. 23. 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