18 Alternating Currents Notes

alternating ul Öõ ent_ (f) e) cp©¥ain the use of a sing©¥e diode for the ha©¥ transfoñ»ãÒ会Þä N p \ '* transfi»rm er and reca©¥©¥ and so©¥ve prob©¥em s using . . į fo r an ideal (e» show an understanding of the ¨¤incip©¥e of operation of a sim p©¥e ironm re using the re©¥ationship ©¥©¥©¥©¥= = for the sinusoida©¥ ©¡se. (d) distinguish betw een r. m . s. a n d peak va©¥ues and reca©¥©¥ and so©¥ve prob©¥em s of the form x = x o s inatt . «c represent an a©¥tem atir©¥g m rrent or an aftem ating voltage by an equation for a sinusoidal aR em ating cu©¥T enL Ob) deduce t» t the m ean pow er in a resistive ©¥oad is half the m axim um pow er cu©¥T ent or vo©¥tage - value and rootm an- s quare (r. m . s . ) va©¥ue as app©¥ied to an a©¥tem ating «a) st©¥ow an understanding of and use the term s period , frequency, peak C an©¢dates shou d be ab©¥e to L E A R N IN G O U T C O M E S 0 R e c t ifica t ion wi th a di od e T r an s m i ss i on of electrica©¥ energy * T h e tra n s fo rm e r R o o t M e a n Square va©¥ue C h a r ac t er isbc s o￠ al lem a t ing cu r ren t s C O N T E N T

S inusoida©¥ a. c . R ectangular a. c. S aw - tooth a. c . currents a©¥ternating E xam p©¥es of a. c . w a v eform s C haracteristics of A n alternating current varies periodica©¥ly w ith tim e i n direction. 18 . 1 C haracteristics of alternating currents answ ers as you go through this topic. H ave funl place? ©¥nstead of answ ering these questions, I will leave you to discover the of alternating current then? W hy is e©¥ectricity supplied in the form of a. c. in the first require d . c. to operatel N ow you are probab©¥y starting to w onder - w hy the need does not hold any practica©¥ advantage over d . c. In fact, m o s t e©¥ectric app©¥iances ©¥n app©¥ications w here e©¥ectricity is used to dissipate energy in the form of heat, a . c. (a. c . ) w hich w as largely brought into the scene by G eorge W estinghouse. success. Y et in less than a decade, d. c. w a s quickly replaced by alternating current w hich generated and supplied direct current (d, c . ) and it earned him great candles " , H e went on to set up the E dison E ©¥ectric lïlum inating C om pany in 1 8 8 0 current m ade a bold claim that he " w ill m ake e©¥ectricity so cheap that only the rich w ill burn W hy a©¥ternating W nen T hom as E dison form ed the E dison E lectric L ight C om pany in 1 8 7 8 , hE ©¥ m roduction Y 5 - 6 P H Y S IC S D E P A R T M E N T R A F F L E S IN S T ©¥T U T ©¥O N 2 0 17 «¤

equare or r. m . s values, ra ther than the average values. value of the sinusoidal alternating current cannot be zero . M ore often, ro o t - m ean - T his indicates that som e pow er ls dissipated In the resistor. T hus the e¨¤ective current, it is independent of the direction of current. resistor. A lthough the Increase in tem perature depends on the m agnitude of the an increase in the internal energy and correspondingly, the tem perature of the ions in the resistor and transfer som e of their energies to these ions, re s u ©¥ting in resistor w hen a potential di¨¤erence is applied across it, they co ©¥de against fixed sam e w ay as w hen a direct current is used. A s free electrons m ove through the A resistor heats up w hen an alternating current is passed through it, m u c h the 0 of tim e and at the sam e m agnitudes as it is m aintained in the opposite direction . current is zero as the current is m aintained in one direction for the sam e am ount dissipated in a resistor. F or instance , the average value of a sinusoidal alternating voltage) to use to com pute electrical quantities such as the average pow er

(r. m . s . ) va©¥ue m agnitude m ay also vary . A problem arises as to w hich value of current (or R oot m ean square ©©n a. c. c ircuits, the direction of current changes periodically w ith tim e and its 18 . 2 R oot M ean S q uare value "

- 1 . o t L !_ 3 . ©¥. U ¡¤ W JT ' 2 . ©¥ L ¡ß ĥ I ¡ß 1 . square the current E E xa m p ©¥e 2 c a ©¥c u ©¥a te I . . In th e fo llo w in g c a s e . 4 . 0 - 2 . 0 + 3 _ 1. . ¡Æ s q u a re ro o t o f m e a n - n ¡¤ 2 . o 0 . 10 0 . 2 0 ¡Æ. I Ļ b 2 . 0 - : ©¥ r period 2 . M ean = a re a u n d e r ©© 2 _ t graph over a period 1 . S quare the currentm l©¥in' ľm ¡¤ - L ' E x a m p ©¥e 1 C a lc u la te th e r. m . s . v a lue of the a©¥ternating current show n. P -M athem atically, !. . - S tep 3 : T ake the square loot of that m ean value. (area under 1 2 _ tgraph over one period divided by the period) S tep 2 F ind the D ean (or average) value of 1 2 i. e . S tep 1 : W e ¡×quare the instantaneous current / r m s T o find r. m . s . current, start the procedure from +h. R i. Ht of the letters Y 6 - 6 P H Y S IC S D E P A R T M E N T R A F F L E S IN S T ©¥T U T IO N 20 17

pn p= . d br W IR - h C lm lw 5 - (not in syllabus) M athem atica©¥ly, m - - į a©¥tem ating current / sinusoidal r. m . s . v a ©¥ue of F ind ©©. . In te rm s o f T . in th e fo llo w in g c a se . Y 5 - 6 P H Y S IC S D E P A R T M E N T R A F F L E S ©¥N S T ©¥T U T ©¥O N 2017

equivalent to 国 İ, m s 2 m o r o r 'rm . a d. c. s o u r c e w ith /ū. - İ . " H e n ce , the average power dissipated in the resistor, T his show s that w e can find the average pow er of an a. c . s o u r c e by treating it as d. l equate the average pow er dissipated as S uppose the resistor in both circuits dissipates heat at the sam e rate, w e c a n tnep 剧国ûö ù»ûð ìé ¡´F . .¡µ ー «·¡£¡£ 2 )R fëà ìé ¡´F . } ìé ' dc 2 R ìÒÐæ«Ë«Èä¨ ìÒÐ櫳 ld. c . = ©©￠m ©¥ a. C . resistor connected to a d. c. s o u r c e , connected to an a. c . s o u r c e, w hile the diagram on the right show s the sam e C onsider the tw o circuits below . T he diagram on the left show s a resistor R pow er rather than the variation of pow er in an a . c. circuit. r. m . s . a n d m ean ' M ost of the tim e, It ls m ore m eaningful for us to know the average or m ean pow er Y 5 - 6 P H Y S IC S D E P A R T M E N T R A F F L E S ©¥N S T ©¥T U T IO N 2 0 1 7

(c) 2(P ) = & value, a s s u m e that it is rm s va©¥ue. (a) If question does not specify whether the given value of the source is rm s or peak J 8 91©¥1116 (c) the m ax©¥m um ©¥nstantaneou s p ow er (b) the m ean pow er output (a) its resistance current of 8 . 0 A flow s. A ņ sum e that the heater is p urely resistlve, c a tcu[ate W hen a do m estic electric heater is o perated from a 2 4 0 V a . c . s u pply, a r . m . s .E xam ple 3 frequency of the sinusoidaE a . c. It can be seen from the graph that the frequency of the pow er is tw ice theÍÝÚ¤¡á¡á F or sinusoidal a. c . - () ĺ ) e M ean power, <F . . > = 1 _ . T herefore, inB tantaneous power P - ©¥v - /. s©¥n ' M - P. sin a a©¥ V e V ain al sinusolda©¥ a. c ©¥= ©¥. E ©¥n ai M ean pow er of F or slnusoldal a. c. . Y S - e P H Y S ©¥C S D E P A R T M E N T R A FF LE S IN S T IT U T IO N 2017

pr' " d by » r ©¥R - ©©. C ©¥m na 8 - crt E . m . f. Induced in the secondary coil = N ©¥ _ - - (2) M agnetic llux linkage through the secondary coil- N * ' P $ m e B e ¡ßE , m . f, induced In the prim ary coil - N .. P ― ― (1) M agnetic flux linkage through the prim ary coil. N p o p d .. In M , I« conda©¥ycca. C om do. . 1. m - - M " " 1 , d l- In m . p©¥i. uycoa' " n " " e turn of w ire in both the prim ary and secondary coi©¥s. changing m agnetic fie©¥d induces an alternating e. m . f. A c r o s s e In accordance to F araday ' s law of e©¥ectrom agnetic induction, the w ith the secondary coi©¥. a varying m agnetic field in the iron core w hich links the prim ary coil W hen an alternating current flow s through the prim ary coil, it sets upprincip©¥e shaped lam inations. the sam e soft iron core w hich is typically m ade from ' E ' a n d T It consists of tw o coils, a prim ary and