Bab 6 kls xii

1. Generator listrik mampu mengubah energi kinetik menjadi energi listrik melalui proses induksi elektromagnetik. Induksi Elektromagnetik 131 Bab 6 Induksi Elektromagnetik Hasil yang harus Anda capai: menerapkan konsep kelistrikan dan kemagnetan dalam berbagai penyelesaian masalah dan produk teknologi. Setelah mempelajari bab ini, Anda harus mampu: memformulasikan konsep induksi Faraday dan arus bolak-balik, keterkaitannya, serta aplikasinya. A. Gejala Induksi Elektromagnetik B. Aplikasi Induksi Elektromagnetik Faraday C. Arus dan Tegangan Listrik Bolak-balik )1411241C518=5=@51:1A9=541=175CG1749C9=2D;1 ?58 ;1F1C 25A1ADB 9BCA9; 5:11 99 C518 491=1C9 ?58 *. $-%./%* -./! @141 -18D;18 41 218F1 @5AD2181 =541 =175C 41@1C =59=2D;1 1ADB 9BCA9; 5:11 99 49=1611C;1 DCD; =5781B9;1 9BCA9; G17 497D1;1 DCD; 25A21719 ;5@5AD1 ,521719 3?C?8 B5@5AC9 C1=@1; @141 71=21A B52D18 755A1C?A A1;B1B1 497D1;1 B521719 BD=25A 9BCA9; 55A1C?A 99 =5=1611C;1 75:11 94D;B9 55;CA?=175C9; @1;18 94D;B9 55;CA?=175C9; 9CD 41;18 @5=1611C1 19 41A9 94D;B9 55;CA?=17 5C9; B519 755A1C?A 5B1A125B1A1 1@1 B1:1 G17 C5A921C 411= 94D;B9 55;CA?=175C9; #1F121 1C1B @5AC1G11@5AC1G11 C5AB52DC 41@1C 41 C5=D;1 411= 212 99 (58 ;1A51 9CD @51:1A918 212 99 4571 219; Sumber: Physics Today, 1989

2. Tes Kompetensi Awal (0))),(-%'+*.,*!0'.%('/-+)#*/%''-'*($.+(.+(-%'0/!()0'0(/%$* )141=1C5A9212B525D=G141C518=5751 (5ABC54 4571 @55=D1G1 C5C17 1ADB 9BCA9; 1719=11;18 81B9 5;B@5A9=5G1 D7;9;18 65?=51 ;5219;1G1 C5A:149 ,91@1;18 G17 =5=2D;C9;1G1

3. 5DADC 41 =571@1 CA1B6?A=1C?A B51D 49 8D2D7;145711ADB2?1;219;@1G171;1 132 Mudah dan Aktif Belajar Fisika untuk Kelas XII C5A:149 :9;1 CA1B6?A=1C?A 498D2D7;1 @141 1ADB B51A18 -18D;18 41 141 25A1@1 :59B CA1B6?A=1C?A 25A 41B1A;16D7B9G1 @1;18@5A25411;1@1B9C?A4194D;C?A25A41B1A ;1:59B1ADBG1741@1C=51D9G1 A. Gejala Induksi Elektromagnetik 1. Pengertian Induksi Elektromagnetik *. $-%./%* -./! C518 25A81B9 =5=2D;C9;1 218F1 1ADB 9BCA9; 41@1C =59=2D;1 =541 =175C9; D1 251B C18D ;5=D491 B5C518 @55=D1 (5ABC54 B5?A17 189 69B9;1 25A1=1 % $( -!2 J@141 =51D9B5A17;1915;B@5A9=5G17491;D;1 G125A81B9=55=D;161;C1;5219;1G1218F1'('!(-#%*- '(#'.%(+.,#,-+#% 5:1199491=1;1 #(.%,#%-+)'!(-#%1C1D #',%-+)'!(-#% 1C1D B5A97 @D1 49B52DC #(.%,#

4. +2 )5A81C9;1 )- )- =5D:D;;1 @5A11C1 B545A811 B5@5AC9 G17 497D1 ;1 ?58 % $( -!2 $5C9;1 21C17 =175C 4975A1;;1 =5D:D ;D=@1A1 41 =5:1D89 ;D=@1A1 :1AD= 71E1?=5C5A 25A75A1; =5 G9=@17 AC9G1 411= ;1F1C @5781C1A =5719A 1ADB 9BCA9; 5A41B1A;1 61;C1 C5AB52DC 41@1C 49B9=@D;1 218F1 $#% ,. %.'*+( '(!'# *+.( $.' !+#,!+#, !2 '!(-#% .%, '!(-#% * .$.(!.$.(! %0- %.'*+( -#'. !2 !+% #,-+#% !! #9;1 D:D7D:D7 ;D=@1A1 99 498D2D7;1 4571 A17;191 C5ACDCD@ @141 A17;191 C5AB52DC 1;1 =5719A 1ADB 9BCA9; ADB G17 =5719A C5AB52DC 491=1;1 1ADB 94D;B9 41@D 77 @141 D:D7D:D7 ;1F1C 49B52DC 77 94D;B9 Gambar 6.1 Induksi elektromagnetik (a) ketika magnet diam, jarum galvanometer juga diam, (b) ketika magnet dimasukkan ke dalam kumparan, jarum galvanometer bergerak ke kanan, dan (c) ketika magnet dikeluarkan dari dalam kumparan, jarum galvanometer bergerak ke kiri. 1 2 3 Aktivitas Fisika 6.1 Induksi Elektromagnetik Tujuan Percobaan Mengamati arus induksi Alat-Alat Percobaan 1. Kumparan 2. Galvanometer 3. Magnet batang Langkah-Langkah Percobaan 1. Susunlah peralatan seperti gambar berikut. magnet kumparan galvanometer

5. Tokoh Michael Faraday (1791–1867) Sumber: www.allbiographies.com Michael Faraday adalah seorang ahli Fisika, ahli Kimia, dan ahli Filsafat berkebangsaan Inggris, tepatnya lahir di Newington Butts, Surey, pada tahun 1971. Ia bersama-sama dengan Joseph Henry menemukan fenomena induksi elektromagnetik. Penemuan ini merupakan kebalikan dari penemuan Oersted, yaitu dari medan listrik dapat menghasilkan arus listrik. Induksi Elektromagnetik 133 2. Siapkan magnet batang, kemudian dekatkan pada kumparan, dan diamkan. Catat hasil pengamatan Anda. 3. Gerakkan magnet mendekati kumparan atau masukkan ke dalam kumparan. Amati jarum galvanometer dan catat hasil pengamatannya. 4. Diamkan magnet batang di dalam kumparan. Amati jarum galvanometer dan catat hasil pengamatannya. 5. Gerakkan magnet batang dengan arah menjauhi kumparan atau keluar kumparan, amati jarum galvanometer, dan catat hasil pengamatannya. 6. Balikkan polaritas magnet batang, lakukan lagi percobaan langkah 2 dan langkah 5. Catat hasil pengamatannya. 7. Tulis kesimpulan Anda tentang kegiatan ini. 2. Hukum Faraday 7 94D;B9 4981B9;1 41A9 @A?B5B 94D;B9 55;CA?=175C9; 7 94D;B9 C9=2D :9;1 141 @5AD2181 6D;B =541 =175C 49 411= ;D=@1A1 7 94D;B9 9918 G17=5G5212;1=5719AG1 1ADB 9BCA9; 94D;B9 @141 BD1CD A17;191 C5ACDCD@ 5B1AG17794D;B925A71CD7;5@14161;C?A61;C?AB52171925A9;DC 1 $. *+.( .%, '( '!(- ' %.'*+( ,5=1;9 25B1A 1:D @5AD2181G1 B5=1;9 25B1A @D1 77 G17 4981B9;1 2 .' ##-( %.'*+( ,5=1;9 21G1; :D=18 99C1 ;D=@1A1 B5=1;9 25B1A @D1 77 G17 4981B9;1 5A41B1A;181B95;B@5A9=5G17491;D;1G1-!2=5GDBD !D;D= 1A141G !D;D= 99 G17 =5G1C1;1 218F1 !2 !+% #,-+#% #(.%,# ,(#(! (!( $. *+.( .%, '( '!(- 2(! -+$# # ' %.'*+( )5AG1C11!D;D= 1A141G 99 41@1C 49G1C1;1 411= 25CD; @5AB1=11 B521719 25A9;DC - J $5C5A171 77 94D;B9 / - B517F1;CD B @5AD2181 6D;B =175C9; 02 :D=18 99C1 (58;1A51 3?B -.)* 341@1C49G1C1;1411= @5AB1=11 25A9;DC 3?B - J

6. $5C5A171 ;D1C =541 =175C9; 02 =

7. D1B 29417 ;D=@1A1 =

8. BD4DC 1C1A1 1A18 94D;B9 =175C9; 41 1A18 ?A=1 29417 ;D=@1A1 5A41B1A;1 -.)* 3 41@1C 49@181=9 218F1 77 94D;B9 1C1D 1ADB 94D;B9 41@1C C5A:149 1;921C 1 @5AD2181 ;D1C =541 =175C9; 2 @5AD2181D1B29417;D=@1A1G1749C5=2DB?58=541=175C9; Gambar 6.2 Garis-garis gaya magnetik yang membentuk sudut terhadap garis normal. B A garis normal I

9. Tantangan untuk Anda Bagaimana pengaruh perubahan lilitan terhadap ggl induksi? Contoh 6.1 ,52D18=175C4975A1;;1=5:1D89;D=@1A1G17C5A49A91C1B 99C111= F1;CD B6D;B=175C9;G17=55=2DB;D=@1A125A;DA1741A9K J02 =5:149

10. K J025A1@177G174994D;B9;1@141D:D7D:D7;D=@1A1 1 9;5C18D9 99C1 - B

11. K J02JK J02 JK J02 02 -

12. / B #14977G174994D;B9;114118

13. / 3. Ggl Induksi karena Perubahan Luas Bidang Kumparan ,5BD19 4571 !D;D= 1A141G B5C91@ ;19 BD1CD 21C17 ;?4D;C?A 25A75A1; 411= =541 =175C9; 89771 =5=?C?7 71A9B71A9B 71G1 =175C9; 1;1 C9=2D 77 94D;B9 7 94D;B9 41@1C C5A:149 1;921C @5AD2181 D1B 29417 ;D=@1A1 G17 49C5=2DB ?58 =541 =175C9; )5A81C9;1)- 541=175C8?=?754571A1@1C71A9B 71G1 41C571;DADB=1BD;29417;5AC1B#9;1@5781C1A)*4975A1; ;1 ;5 ;11 4571 ;535@1C1 / B5:1D8 1 1;1 C5A:149 @5AD2181 71A9B 71G1 G17 4997;D@9 ?58 21C17 ;?4D;C?A )* 4571 A17;191 ;1F1C . )5AD2181 D1B @5A B1CD1 F1;CD 1;921C @5A75B5A1 21C17 ;?4D;C?A )* =5=5D89 @5AB1=11 25A9;DC B v 134 Mudah dan Aktif Belajar Fisika untuk Kelas XII 1 1 / - - - 571 45=9;91 77 94D;B9 =5=5D89 @5AB1=11 25A9;DC / - - - J -141 571C96 =5D:D;;1 1A18 94D;B9 55;CA?=175C9; 25A1F11 4571 1A18 @5G5212 C5A25CD;G1 94D;B9 .CD; @5G545A8111 @5D9B1 B5A97;19 C141 571C96 C941; 49CD9B .CD; ;D=@1A1 G17 C5A49A9 1C1B B1CD 99C1 @5AB1=11G1 =5:149 / J (58 ;1A51 ;1F1C 25A25CD; . 41 21C17 ;?4D;C?A )* =5=25CD; A17;191 C5ACDCD@ @141 ;1F1C C5AB52DC 1;1 =5719A 1ADB 94D;B9 A18 1ADB 94D;B9 G17 49@5A981C;1 @141 )- 41@1C 49C5CD;1 4571 =55A1@;1 !D;D= %5H G17 =5G1C1;1 218F1 :9;1 1A18 94D;B9 =175C =5D:D ;5 411= 29417 ;5AC1B 41 1A18 / Gambar 6.3 Penghantar PQ digerakkan dengan kecepatan v di dalam medan magnet homogen B. R P Q v x I Gambar 6.4 Gerak elektron dalam batang konduktor bergerak di atas medan magnet. F ve

14. Informasi untuk Anda Information for You Induksi Elektromagnetik 135 ;5 ;11 =D1C1 571C96 @141 21C17 ;?4D;C?A )* 1;1 =541@1C 71G1 ;5 21F18 A18 1ADB 9BCA9; B5BD19 4571 1A18 =D1C1 @?B9C96 B589771 1A18 1ADB 94D;B9 411= 21C17 ;?4D;C?A 14118 41A9 * ;5 ) (58 ;1A51 1A18 1ADB 94D;B9 411= 21C17 ;?4D;C?A 41A9 * ;5 ) B5417;1 1A18 94D;B9=175C9; ;5 411= 29417 ;5AC1B 1;1 C9=2D 71G1 =175C9;

15. G17 1A18G1 ;5 ;9A9 41 41@1C =5=2D;C9;1G1 =577D1;1 ;19418 C171 ;11 5B1AG1 71G1 =175C9; C5AB52DC =5=5D89 @5AB1=11

16. J 41 @5A81C9;1 ;5=219 )- 11= ;1F1C . =5719A 1ADB 9BCA9; 1;921C 141G1 2541 @?C5B91 49 1C1A1 C9C9;)41 * 5B1AG1 2541 @?C5B91 C5AB52DC B1=1 4571 25B1AG1 77 94D;B9 @141 21C17 ;?4D;C?A 5A41B1A;1 !D;D= (8= 25B1AG1 ;D1C 1ADB 9BCA9; G17 =5719A @141 ;1F1C . 14118 B521719 25A9;DC / J 5DADC !D;D= $5;5;11 5A79 55A79 G17 497D1;1 DCD; =5=9418;1 =D1C1 49 411= 21C17 ;?4D;C?A )* B1=1 4571 55A79G17497D1;1DCD;=5=9418;1=D1C1@141;1F1C.(58 ;1A51 9CD ;D1C 1ADB G17 =5719A 411= ;1F1C . B1=1 4571 ;D1C 1ADB94D;B9G17=5719A@14121C17;?4D;C?A)*57145=9;91 -.)* 3 41@1C 49BD2BC9CDB9;1 ;5 411= -.)* 3

17. B589771 49@5A?58 @5AB1=11 21AD B521719 25A9;DC

21. / J $5C5A171

22. 71G1 %?A5CH ' / ;535@1C1 = B ;D1C =541 =175C 02 =

23. @1:17 @5781C1A = 81=21C1 Para teknisi ini sedang memasang generator pada instalasi pembangkit listrik di Meksiko. Bagian yang terlihat di sini adalah stator, yang tidak bergerak. Selanjutnya, ke dalam stator itu dimasukkan rotor. Rotor merupakan sebuah elektromagnetik kuat yang dapat berputar dengan kecepatan tinggi. Akibat perputaran rotor, terjadi perubahan medan magnetik dan membangkitkan arus listrik pada kumparan di dalam stator. The pisture have shown the technician placing generator on electrical instalation in Mexico. You can see a part, called stator. The rotor is put inside it. Rotor is a strong electromagnetic device that can spin with cause the velocity. That spin is what cause the change of magnetic field and generate electrical element on coil inside stator. Sumber: The Oxford Children’s Book of Science, 1995 Contoh 6.2 $1F1C@5781C1A)*@1:17G1

24. 3=41=1BB1G1 741@1C25A75A1;E5AC9;1 2521B;521F18@141;1F1CA17;1919B5;9C1AG1C5A41@1C=541=175CB525B1A -45711A18;5D1A29417;5AC1BB5@5AC9C1=@1;@14171=21A Q P B R 0,25 F w = mg v 20 cm

25. Tantangan untuk Anda Sebuah penghantar berbentuk U terletak di dalam daerah berinduksi magnetik homogen B = 4 × 10–3 T berarah menembus bidang kertas. Penghantar PQ sepanjang 40 cm menempel pada penghantar U dan digerakkan ke kanan dengan kecepatan tetap v = 10 m/s. Hitung ggl induksi antara ujung-ujung PQ. -5CD;1 1 1A181ADB411=;1F1C@5781C1A)* 2 ;535@1C1;?BC1;1F1C@5781C1A 1 1 1G125A1C@5781C1A)*B525B1A

26. '!=5G5212;1@5781C1A)*25A75A1; 4571;535@1C1/;521F18 5A1;@5781C1A)*G17=5=?C?7C571; DADB =541 =175C =59=2D;1 71G1 %?A5CH

27. G17 1A18G1 ;5 1C1B $535@1C1;?BC1@5781C1A)*C5A31@19;5C9;125B1A71G1%?A5CHB1=1 457125B1A71G125A1C@5781C1A)*,5BD194571!D;D=%5H218F1 1A181ADB41@1C49C5CD;145711CDA1;19418C171;11B5@5AC9@141 71=21AA1894D;B9=175C9;;5D1A294171A1871G1%?A5CH;51C1B41 1A181ADB#@141@5781C1A;5;9A9G19CD41A9*;5) '! ;7 = B

28. Informasi untuk Anda Sumber: www.linearmagnetics.com Information for You 136 Mudah dan Aktif Belajar Fisika untuk Kelas XII arah telapak tangan F arah ibu jari arah jari lain B I 2 $535@1C1 ;?BC1 C5A31@19 ;5C9;1 71G1 %?A5CH B1=1 4571 71G1 25A1C @5781C1A 9;5C18D971G1%?A5CH@141-.)* 3

31. B5417;171G1

32. '!B589771

33. / '!

35. / /

36. 02 =

38. = B #149;535@1C1;?BC1;1F1C14118

39. = B 4. Induktansi Diri #9;1 B52D18 ;D=@1A1 4919A9 1ADB 9BCA9; G17 25B1AG1 25AD218 D218 C5A8141@ F1;CD 1;1 C9=2D 6D;B =175C9; ' G17 25B1AG1 :D7125AD218C5A8141@F1;CD)5AD21816D;B=175C9;B5214974571 ;D1C 1ADB ,531A1 =1C5=1C9B 49CD9B B521719 25A9;DC ' 1C1D ' J1 4571 =5AD@1;1 BD1CD ;?BC1C1 G17 49B52DC 4571 94D;C1B9 49A9 ;D=@1A1 C5AB52DC 4D;C1B9 49A9 C571; DADB C5A8141@ 25CD; 75?=5CA9; ;D=@1A1G1 ,1CD1 94D;C1B9 9118 85AG ! 5CD; D=D= 949;1C?A 25AD@1 B?5?941 B531A1 17BD7 94D;C1B9 49A9 B?5?941 99 41@1C 4989CD7 B5@5AC9 25A9;DC 99 J2 ' Induktor adalah sebuah elektromagnet, yaitu sebuah kumparan kawat dengan atau tanpa inti magnetik yang menghasilkan magnetisme jika arus mengalir melewatinya. Inductor is an electromagnet, made of wire coil with or without magnetic core which can produce magnetism when electric current through. Sumber: Jendela Iptek, 1997

40. P L I 1 S S L P 2 Induksi Elektromagnetik 137 (58 ;1A51 6D;B =175C9; DCD; 99C1 @141 B?5?941 14118 ' ( (

41. =1;194D;C1B949A9B?5?94114118 B521719 25A9;DC (

42. J -.)* 3 25A1;D :D71 DCD; 94D;C1B9 49A9 @141 @DB1C C?A?941 ;1A51 25B1A 94D;B9 =175C 49 1C1A1 ;54D1G1 B1=1 G19CD B525B1A ( #9;1@51=@17B?5?9411C1DC?A?941499B9?582181G17=5=99;9 @5A=51299C1B A51C96 + 49=11 @5A=51299C1B 2181 14118 + J 4D;C1B9 49A9 B?5?941 41 C?A?941 4571 2181 C5AB52DC 14118

43. + ( J $5C5A171 94D;C1B9 49A9 B?5?941 1C1D C?A?941 4571 9C9 2181 ! 94D;C1B9 49A9 B?5?941 1C1D C?A?941 C1@1 9C9 ! Gambar 6.5 Sebuah rangkaian tertutup (a) saklar s ditutup, lampu menyala dan (b) saklar s dibuka, lampu masih menyala beberapa saat kemudian padam. Contoh 6.3 -?A?9414571D1B@51=@173=

44. 41@1:17G1 3==5=99;9 99C1 -5CD;11894D;C1B949A9C?A?941C5AB52DC 1 9;5C18D9 3=

45. K J=

46. 3= = K J02 = B58977149@5A?58

47. 02 = =

48. = K J!

49. ! #14994D;C1B949A9C?A?94114118 ! ,D1CD A17;191 G17 C5A49A9 1C1B B52D18 ;D=@1A1 94D;C?A B52D18 1=@D ) 41 BD=25A C57171 G17 4957;1@9 4571 B52D18 B1;1A C1=@1; @141 )-

50. $5C9;1 B1;1A 498D2D7;1 1=@D C941; B575A1 =5G11 =1;B9=D= C5C1@9 141 :541 F1;CD B5B11C )141 B11C 1ADB 49@DCDB;1 @141 B1;1A @578D2D7 1=@D C941; B575A1 @141= C5C1@9 141 :541 F1;CD B5B11C )5A81C9;1 )-

51. )5A9BC9F1 99 =5D:D;;1 C9=2DG1 1ADB 94D;B9 G17 49B5212;1 ?58 141G1 @5AD2181 6D;B =175C9; @141 94D;C?A )5AD2181 1ADB @141 B52D18 ;D=@1A1 41@1C =59=2D;1 77 94D;B9G1725B1AG125A21497DADB457135@1CG1@5AD2181;D1C 1ADBG1 ,531A1 =1C5=1C9B @5AG1C11 G17 49;5=D;1;1 @5AC1=1 ;19 ?58 +.,$ *-2 99 49CD9B;1 B521719 25A9;DC - J

52. Pembahasan Soal Kuat arus listrik dalam suatu rangkaian tiba-tiba turun dari 10 A menjadi 2 A dalam waktu 0,1 s. Selama peristiwa ini terjadi, timbul ggl induksi sebesar 32 V dalam rangkaian. Induktansi rangkaian adalah .... a. 0,32 H b. 0,40 H c. 2,5 H d. 32 H e. 40 H UMPTN 1993 Pembahasan: Diketahui: I = 10 A – 2 A = 8 A ind = 32 V ind dI L d 32 V = 3,2 V 8 A s L = 3,2 8 s V A = 0,4 H Jawaban: e

53. I a b Gambar 6.6 Sebuah kawat induktor yang dialiri arus listrik. -141 571C96 =5AD@1;1 @5G5BD191 4571 !D;D= %5H #9;1 1:D @5AD2181 ;D1C 1ADB - - 138 Mudah dan Aktif Belajar Fisika untuk Kelas XII - ;?BC1 =1;1 -.)* 3 41@1C 49CD9B;1 B521719 25A9;DC

55. - - - J $5C5A171 ;D1C 1ADB 9BCA9; @141 ;51411 1F1

56. ;D1C 1ADB 9BCA9; @141 ;51411 1;89A - -

57. J - B517 F1;CD @5AD2181 ;D1C 1ADB 9BCA9; B Contoh 6.4 ,52D18;D=@1A1457194D;C1B949A9 !4919A91ADBB5217196D7B9F1;CD J-

58. 411=1=@5A541-411=B5;?-5CD;17794D;B949A9G17C5A:149 B11C-

59. B 1 9;5C18D9 ! J-

60. 571=577D1;1-.)* 3 49@5A?58

61. J !J- J J

62. / #1497794D;B949A9@141B11C-

63. 14118/ 5. Energi yang Tersimpan dalam Induktor 4D;C?A=1=@D=5G9=@155A795A79C5AB52DCC5AB9=@1411= 25CD; =541 =175C )5A81C9;1 )- #9;1 B52D18 94D;C?A 4919A91ADB9BCA9; G17B51D25AD218C5A8141@F1;CD25B1AG1C57171 1C1A1 C9C9; 41 14118 J - B589771 25B1AG1 41G1 G17 4925A9;1 @141 94D;C?A 14118 - - J 5A79 G17 4925A9;1 @141 94D;C?A 49@5A?58 4571 =57 9C57A1B9;1 41G1 @141 94D;C?A B589771 49@5A?58 @5AB1=11 - - -

64. Induksi Elektromagnetik 139

66. 6. Rapat Energi dalam Bentuk Medan Magnetik -518 49;5C18D9 25B1AG1 94D;B9 =175C9; 49 @DB1C B?5?941 =5=5D89 @5AB1=11 25A9;DC ( 1C1D ( 41@D 94D;C1B9 49A9 @141 B?5?941 14118 (

67. #9;1 919 41 919 94D;C1B9 41 BD2BC9CDB9;1 ;5 411= -.)* 3 1;1 49@5A?58 @5AB1=11

70. ( J (

71. 571 E?D=5 B?5?941 C?A?941 14118 #9;1 A1@1C 55A79 1C1D 55A79 @5A B1CD1 E?D=5 ;9C1 4925A9 ?C1B9 25A1;D 8D2D71

73. Contoh 6.5 ,52D18 B?5?941 =5=99;9 :D=18 99C1 B521G1; 2D18 @1:17 41 D1B @51=@17B?5?941141183=41

74. 3=

75. !9CD718 1 94D;C1B949A9B?5?941 2 55A79G174981B9;1@141B?5?941:9;11ADB9BCA9;G17=5719AB525B1A 3 25B1A7794D;B949A9G17C5A:149:9;1411=F1;CDB;D1C1ADB25AD218=5:149

76. 1 9;5C18D9 99C1

77. 3=

78. K J=

79. 3=K J

80. = 1 4D;C1B949A9B?5?94114118

81. 02 =

83. ! = 2 5A79G174981B9;1@141B11C 14118

84. ! #

86. 3 5B1A %94D;B949A9:9;11ADB25AD218=5:149

87. 14118

89. / B - Tantangan untuk Anda Sebuah kumparan (solenoida) memiliki induktansi 500 mH. Hitunglah besar induksi ggl yang dibangkitkan dalam kumparan itu jika ada perubahan arus listrik dari 100 mA menjadi 40 mA dalam waktu 0,01 s secara beraturan.

90. Gambar 6.8 I Perubahan arus pada kumparan 1 akan memengaruhi arus pada kumparan 2. Kata Kunci • gaya gelak listrik (ggl) • induksi elektromagnetik • Hukum Faraday • fluks medan magnetik • Hukum Lenz • gaya Lorentz • ggl induksi diri • kumparan primer • kumparan sekunder • induktansi silang 8. Induktansi Silang )5A81C9;1 )- -1=@1; 4D1 2D18 ;D=@1A1 G19CD ;D=@1A1@A9=5A)41;D=@1A1B5;D45A,G1725A45;1C1$D=@1A1 @A9=5A)498D2D7;14571BD=25AC57171 4181=21C1E1A9125 $D=@1A1B5;D45A,498D2D7;14571B52D1871E1?=5C5A #9;1 @141 ;D=@1A1 @A9=5A C5A:149 @5AD2181 ;D1C 1ADB 4571 =57D218D21881=21C11;1C5A:149@5AD21816D;B=175C9;@141 ;D=@1A1 @A9=5A 571 45=9;91 6D;B =175C9; G17 4997;D@9 ;D=@1A1 B5;D45A @D 1;1 25AD218 @D1 )5AD2181 6D;B =175C9; C5AB52DC 1;1 =59=2D;1 77 @141 ;D=@1A1 B5;D45A 7G17C9=2D@141;D=@1A1@A9=5A=1D@D;D=@1A1B5;D45A 49B52DC #(.%-(,# ,#(! 1C1D #(.%-(,# -#' #% 5B1AG1 77 94D;B9 G17 C9=2D @141 ;D=@1A1 B5;D45A ;1A51 @571AD8 @5AD2181 6D;B =175C9; 411= F1;CD - =5=5D89 @5AB1=11 140 Mudah dan Aktif Belajar Fisika untuk Kelas XII

91. - - J

93. - - J

94. #9;1 -.)* 3 49C9:1D 5298 1:DC 49@5A?58

96. 1C1D - - 571 =5C?45 9C57A1B9 1;1 49@5A?58

99. 571 =577D1;1 @511A1 G17 B1=1 =1;1 41A9 -.)* 3 1;1 49@5A?58

100. J

102. 5B1A 6D;B =175C9; G17 49C9=2D;1 ?58 1ADB 9BCA9; 4571 :D=1899C114118 #9;1919 49BD2BC9CDB9 ;1 ;5 411= -.)* 3 49@5A?58 @5AB1=11 25A9;DC

103. J

104. $5C5A171 ;D1C 1ADB 9BCA9; ;D=@1A1 @A9=5A 94D;C1B9 B917 !

105. :D=18 99C1 ;D=@1A1 B5;D45A :D=18 99C1 ;D=@1A1 @A9=5A

106. 6D;B =175C9; G17 4997;D@9 ?58 ;D=@1A1 B5;D45A G17 49 C9=2D;1 ?58 ;D=@1A1 @A9=5A 02 Gambar 6.7 Induktor silang antara dua buah kumparan. R P S G

107. R = 0,5 v = 20 m/s B Induksi Elektromagnetik 141 Contoh 6.6 ,52D18B?5?941;D=@1A1=5=99;9@1:17 3=4571D1B@51=@17 K J =

108. 4121G1;99C1

109. 99C19B5;9C1A@DB1CB?5?941 4999C;1;D=@1A1

110. 457121G1;99C1

111. 99C1-5CD;1 1 94D;C1B9B917;54D1;D=@1A1 2 77G17C9=2D@141;D=@1A1

112. :9;1@141;D=@1A1=5719A1ADBB525B1A

113. G1725A219;1A18411=F1;CD B 1 1 571 =577D1;1 -.)* 3 25B1A 94D;C1B9 B917 41@1C 49C5CD;1B52171925A9;DC

115. 02 =

116. = =

117. K J

118. ! 2 )141;D=@1A1DCD;B517F1;CD- B;D1C1ADB

119. 25A219;1A18 B589771 # J

120. J

121. J5B1A7794D;B9@141;D=@1A1

122. 41@1C49@5A?58B52171925A9;DC 2 -

124. !

125. / B Tes Kompetensi Subbab A -'*($!()0'0(/%$* #9;1=175C@5A=154975A1;;1=5=1BD;9;D=@1A1 ;1F1CG17C5A@1B17B52D181=@5A5=5C5A11CD;DA 1ADB :1AD= 1=@5A5=5C5A 1;1 =5G9=@17 41A9 ;54D4D;1 B5C9=217G1 5B1A1 1@1;18 G17 =5G5212;1 C9=2DG1 @5G9=@171 C5AB52DC @1;18G17C5A:149@141:1AD=1=@5A5=5C5A:9;1 1 21C17=175C491=411=;D=@1A1 2 21C17=175C4975A1;;1529835@1C 3 21C17=175C4975A1;;1;5D1A41A9;D=@1A1

126. D;B =175C9; G17 =5=?C?7 BD1CD ;D=@1A1 25A;DA1741A902=5:149 02411=F1;CD B #9;1;D=@1A1C5A49A91C1B99C1C5CD;177G17 4981B9;1 )141B52D1894D;C?A4571 99C1=5719A1ADB 9BCA9;G1725AD218C5A8141@F1;CDG19CD B 11= F1;CD G17 B1=1 =59=2D;1 @5AD2181 6D;B=175CG174997;D@9G1B525B1A 02 -5CD;1 1 94D;B949A9;D=@1A1 2 7794D;B949D:D7D:D7;D=@1A1 ,5@?C?7;1F1C25A75A1;=5=?C?7=541=175C9; 8?=?75G1725B1AG1

127. -41=5=25CD;BD4DC I#9;1D1B6D;BG17C5A@?C?7 =

128. 411=F1;CD BC5CD;17794D;B9G17C9=2D $1F1C )* B5@1:17

129. 3= 4975A1;;1 ;5 ;11 4571;535@1C1

130. = B41=5=?C?7C571;DADB 94D;B9=175C9; K J

131. -B5@5AC9@14171=21A -5CD;125B1A71G1%?A5CH@141;1F1C)*411A18 1ADBG1 P Q 11=B52D18;D=@1A1C5A41@1C@5AD2181;D1C1ADB B525B1A G17 =59=2D;1 @5AD2181 6D;B =175C9;

132. 02@141;D=@1A1;54D1G17C5A5C1; 49D1A;D=@1A1@5AC1=1-5CD;194D;C1B9B917 ;54D1;D=@1A1:9;1;D=@1A1;54D1=5=99;9 99C1

133. B. Aplikasi Induksi Elektromagnetik Faraday @9;1B9 94D;B9 55;CA?=175C9; 1A141G 411= ;5894D@1 B581A9 81A9 1C1A1 19 B521719 25A9;DC 1. Generator )5A18;18 41 25A;D:D7 ;5 C5=@1C )5=217;9C %9BCA9; -5171 9A G17 141 49 #1C9D8DA #1F1 1A1C 9 B11 C5A41@1C 11C 9BCA9; G17 491=1;1 !(+-)+ 55A1C?A 14118 11C G17 25A6D7B9 =57D218 55A79 ;95C9; =5:149 55A79 9BCA9; 55A1C?A 25;5A:1 25A41B1A;1 @A9B9@ 94D;B9 55;CA?=175C9; -5A41@1C 4D1 :59B 755A1C?A G19CD 755A1C?A 1ADB 2?1;219; 41 755A1C?A 1ADB B51A18 a. Generator Arus Bolak-Balik )- =5D:D;;1 B;5=1 755A1C?A 1ADB 2?1;219; 1A1 ;5A:1 755A1C?A C5AB52DC 14118 B521719 25A9;DC $D=@1A1 G17 495C1;;1 411= =541 =175C9; 49@DC1A B589771 =5711=9@5AD2181:D=1871A9B71G1=175C9;;921CG1C5A:149 77 94D;B9 G17 =1=@D =5781B9;1 1ADB 9BCA9; ADB 9BCA9; G17 4981B9;1G1 25AD@1 1ADB 2?1;219; 1C1D -+(-#(! .++(- ;1A51 B5C91@ ;1A2? 1;1 =541@1C;1 @?1A9C1B 77 94D;B9 G17 25AD218D218 ;DCD2 @?B9C96 41 ;DCD2 571C96 B531A1 25A71C91

134. .CD;=5G1DA;11ADB9BCA9;G1749@5A?58;54D1D:D7;D=@1A1 49@1B179 3939 G17 C5A@9B18 41 49C5=@5;1 @141 B9;1C ;1A2? G17 498D2D7;1 4571 ;125 @5G1DA 142 Mudah dan Aktif Belajar Fisika untuk Kelas XII sikat karbon cincin kumparan arah putaran luncur b. Generator Arus Searah )14141B1AG1@A9B9@;5A:1755A1C?A1ADBB51A18B1=14571@A9B9@ ;5A:1 755A1C?A 1ADB 2?1;219; )5A25411G1 @141 755A1C?A 1ADB B51A18 49@1B17 %)'.--)+ 25AD@1 B52D18 3939 2518 D7B9 ;?=DC1C?A 99 =571CDA 171A B5C91@ B9;1C ;1A2? B51D =541@1C;1 @?1A9C1B 77 94D;B9 G17 C5C1@ B9;1C @5AC1=1 @?B9C96 41 B9;1C 19G1 571C96 2. Transformator (Trafo) +(, )+'-)+ 14118 11C G17 25A6D7B9 =57D218 =519;;1 1C1D =5DAD;1 C57171 9BCA9; (58 ;1A51 9CD CA1B6?A=1C?A 492179 =5:1494D1:59BG19CDCA1B6?A=1C?A,-*.*41CA1B6?A=1C?A,-*)0( Gambar 6.9 Skema generator arus bolak-balik Gambar 6.10 Skema generator arus searah kumparan komutator sikat karbon arah putaran

135. primer Np Induksi Elektromagnetik 143 -A1B6?A=1C?A C5A49A9 1C1B ;D=@1A1 @A9=5A ;D=@1A1 B5;D45A 41 9C9 25B9 ?C?8 CA1B6?A=1C?A 49CD:D;;1 @141 )- a. Transformator Step-up -A1B6?A=1C?A,-*.*25A6D7B9=519;;1C571719BCA9;171 B545A811B52D18CA1B6?A=1C?A,-*.*49CD:D;;1@141)- )141CA1B6?A=1C?ABC5@D@:D=1899C1B5;D45A529821G1;41A9@141 :D=18 99C1 @A9=5A , * b. Transformator Step-down -A1B6?A=1C?A ,-*)0( 25A6D7B9 =5DAD;1 C57171 9BCA9; 171 B545A811 B52D18 CA1B6?A=1C?A ,-*)0( 49CD:D;;1 @141 )- )141 CA1B6?A=1C?A ,-*)0( :D=18 99C1 @A9=5A 5298 21G1; 41A9@141 :D=18 99C1 B5;D45A * , )A9B9@ ;5A:1 CA1B6?A=1C?A 14118 B521719 25A9;DC $D=@1A1 @A9=5A 498D2D7;1 4571 C57171 =1BD;1 25AD@1 1ADB 2?1;219; 25B1A 41 1A18G1 B51D 25AD218D218

136. (58 ;1A51 1ADB G17 25AD218D218 @141 9C9 25B9 C5A:149 @5AD2181 :D=18 71A9B 71G1 =175C9; B531A1 C5ADB=55ADB ;921CG1 @141 ;D=@1A1B5;D45AC5A:1497794D;B9411ADB94D;B9B521719;5D1A1 ).-*.- 41A9 CA1B6?A=1C?A )5A214971 1C1A1 C57171 @A9=5A * 41 C57171 B5;D45A , @141 CA1B6?A=1C?A B1=1 4571 @5A214971 1C1A1 :D=18 99C1 @A9=5A * 41 99C1 B5;D45A , ,531A1 =1C5=1C9B 41@1C 49CD9B B521719 25A9;DC * * J

137. , , $5C5A171 * C57171 @A9=5A / * :D=18 99C1 @A9=5A , C57171 B5;D45A / , :D=18 99C1 B5;D45A #9;1 @141 CA1B6?A=1C?A 491771@ C941; 141 55A79 9BCA9; G17 25A D218 =5:149 55A79 25CD; 19 CA16? 9451 25A1;D 8D2D71 B521719 25A9;DC 41G1 @A9=5A 41G1 B5;D45A @B1C1D@ @B B J

138. $5C5A171 * 41G1 @A9=5A 0 , 41G1 B5;D45A 0 * 1ADB @A9=5A , 1ADB B5;D45A Gambar 6.11 Transformator Gambar 6.12 Bagan transformator step-up sekunder Ns Gambar 6.13 Bagan transformator step-down Sumber: PHYWE, 1989 primer Np sekunder Ns

139. * 144 Mudah dan Aktif Belajar Fisika untuk Kelas XII Aktivitas Fisika 6.2 Membuat Transformator Tujuan Percobaan Membuat transformator step-up. Alat-Alat Percobaan kumparan 1. Kawat tembaga kira-kira 1 m 2. Sumber tegangan 12 V (AC) Langkah-Langkah Percobaan 1. Susunlah peralatan seperti gambar berikut. 2. Lilitkan 10 lilitan kawat pada bagian kiri inti besi, sebagai kumparan primer. Kemudian, sebanyak 20 lilitan pada bagian karena inti besi yang lain, sebagai kumparan sekunder. Hubungkan dengan sumber tegangan. 3. Catat besar tegangan yang terbaca pada voltmeter. 4. Teruskan menambah 10 lilitan pada kumparan sekunder hingga menjadi 50 lilitan. Amati dan catat besar tegangan yang terbaca pada voltmeter. 5. Masukkan data hasil pengamatan Anda pada tabel. Kemudian, buatlah grafik tegangan sekunder terhadap jumlah lilitan sekunder. 6. Berikan kesimpulan Anda dari kegiatan ini. inti besi voltmeter No 1. 2. 3. 4. Jumlah Lilitan Sekunder 20 30 40 50 Data Percobaan Besar Tegangan Sekunder .... .... .... .... Contoh 6.7 ,52D18CA16?BC5@4?F1;1497D1;1DCD;=5G11;1A149?

140. /41A9BD=25A )%'

142. /-5CD;1 1 @5A21497199C1@A9=5A41B5;D45ACA16?C5AB52DC 2 :D=1899C1@A9=5A:9;199C1B5;D45AG1 99C1 3 1ADBG17497D1;1A149?:9;149;D=@1A1@A9=5AC5A41@1C1ADBB525B1A 1 9;5C18D9 *

144. /, 99C1,

146. / * 1 )5A214971C57171B5214974571@5A214971:D=1899C1

148. /

150. / * * * , , , #149@5A214971*B 2 5A41B1A;181B9@5A89CD7121791=1;1 * #149:D=1899C1@A9=5A 99C1 3 .CD;=5789CD71ADB9BCA9;41@1C497D1;1@5AB1=11 *,1C1D* *, ,

152. /

154. / * , , , * , #1491ADBG17497D1;1A149?14118 Tantangan untuk Anda Anda memiliki walkman yang menggunakan baterai 3 V. Bagaimana caranya agar walkman tersebut dapat menggunakan listrik dari PLN yang besarnya 220 V?

155. Ingatlah kumparan arus pusar inti besi 1 2 Induksi Elektromagnetik 145 )141;5G1C11G1C941;141CA1B6?A=1C?AG179451,52179155A79 9BCA9; 25AD218 =5:149 25CD; 55A79 19 411= CA1B6?A=1C?A =9B1G1 55A79 @11B #149 DCD; CA1B6?A=1C?A C941; 9451 B51D 25A1;D 41G1 B5;D45A 5298 ;539 41A9@141 41G1 @A9=5A ,* B589771 569B95B9G1 5298 ;539 41A9 69B95B9 B52D18 CA1B6?A=1C?A 4945699B9;1 B521719 81B9 2179 41G1 9BCA9; B5;D45A 4571 41G1 9BCA9; @A9=5A 69B95B9 CA1B6?A=1C?A 49G1C1;1 411= @5AB5 B531A1 =1C5=1C9B 49CD9B , * J

156. $5C5A171 569B95B9 CA1B6?A=1C?A , 41G1 9BCA9; B5;D45A * 41G1 9BCA9; @A9=5A Contoh 6.8 Tidak ada transformator yang efisiensinya 100% karena sebagian energi listrik berubah menjadi bentuk energi lain. ,52D18CA1B6?A=1C?A411=B52D18A149?CA1B9BC?A41@1C=57D218C5717141A9

158. /=5:149/#D=1899C1B5;D45AG1 99C1C5AG1C1;D1C1ADBG17 =5719A@141A149? #9;1569B95B9CA1B6?A=1C?AC5AB52DC C5CD;1 1 ;D1C1ADB9BCA9;@141;D=@1A1@A9=5A 2 41G1@A9=5A4141G1B5;D45A 1 9;5C18D9 *

160. /, 99C1,/ , 1 -A1B6?A=1C?AC941;25AB961C9451=1;125A1;D , , , * * * /

162. / * * #149;D1C1ADB9BCA9;@141;D=@1A1@A9=5A14118

163. 2 .CD;=5789CD741G1@141B5C91@;D=@1A141@1C497D1;1 @5AB1=11 * * *

165. /

166. 0 #14941G1@A9=5AG1141180 , , ,/ 0 #14941G1B5;D45AG114118 0 c. Arus Pusar pada Transformator )5A81C9;121C17;?4D;C?A1C1A14D1=D;1;DCD255;CA?=175C9; B5@5AC9 G17 49CD:D;;1 @141 )- #9;1 =541 =175C9; 1C1A1 =D;1 ;DCD2 9CD 25AD218 C5A8141@ F1;CD 6D;B G17 =51D9 B5=21A17 B9=@1 C5ACDCD@ 411= 21C17 1;1 25AD218 :D71 B589771 C9=2D 1ADB ADB 99 491=1;1 4571 +., 2 1C1D 1ADB @DB1A ADB @DB1A G17 C5A:149 @141 9C9 CA16? =5AD79;1 B5212 CA16? ;589171 55A79 1C1D 41G1G1 =5:149 @11B #9;1 @11B 99 3D;D@ C9779 CA16? 41@1C C5A21;1A B589771 ADB1; .CD; =535718 ;5AD791 41G1 21C17 ;?4D;C?A CA1B6?A=1C?A 492D1C 25A1@9B1@9B B5@5AC9 @141 )- 9 1C1A1 1@9B1 @51C ?71= 4925A9 9B?1B9 %+ B589771 97;1A1 1ADB @DB1A =5:149 Gambar 6.14 (a) Trafo dengan inti besi. (b) Trafo dengan inti besi berupa lempengan yang terpisahkan oleh laker.

167. ;539 571 31A1 B5@5AC9 99 ;5AD791 41G1 1;921C 1ADB @DB1A 41@1C 49;DA179 -941; B5=D1 1ADB @DB1A 25AB961C=5AD79;1 @141 2525A1@1 @5A11C1 G17 =577D1;1 @A9B9@ 94D;B9 55;CA?=175C9; 1ADB @DB1A G17 C9=2D 41@1C =57DCD7;1 B5@5AC9 @141 A5= =175C9; CD7;D 9BCA9; 41 B5CA9;1 9BCA9; 3. Transmisi Daya Listrik Jarak Jauh -A1B=9B9 41G1 9BCA9; :1A1; :1D8 =5AD@1;1 @A?B5B @5G1DA1 41G1 9BCA9;;5C5=@1CCD:D1C5AC5CDG17:1A1;G1:1D841A9@DB1C@5=217;9C 9BCA9; %9BCA9; G17 B1=@19 49 AD=18AD=18 @54D4D; 14118 81B9 CA1B=9B9 41G1 9BCA9; :1A1; :1D8 41 4D1 31A1 =5CA1B=9B9;1 41G1 9BCA9; :1A1; :1D8 G19CD 4571 ;D1C 1ADB 9BCA9; 25B1A G17 4981B9;1 ?58 755A1C?A

168. 4571 C57171 G17 5298 C9779 41A9 C57171 G17 4981B9;1 ?58 755A1C?A )141D=D=G1CA1B=9B941G19BCA9;:1A1;:1D8=577D1;1C5717 1 C9779 $5DCD71 G17 49@5A?58 4571 =577D1;1 CA1B=9B9 C57171 C9779 14118 1ADB 9BCA9; G17 =5719A =51D9 ;1F1C A51C96 ;539 B589771 D;DA1 ;1F1C CA1B=9B9 G17 ;539 :D71 41@1C =5=25A9;1 1771A1291G1:1D852985;??=9B4141G19BCA9;G178917B5@1:17 ;1F1C CA1B=9B9 :1D8 5298 ;539 B589771 49@5A?58 569B95B9 41G1 9BCA9; G17 25B1A )141@A?B5BCA1B=9B941G19BCA9;:1A1;:1D8497D1;1CA1B6?A=1C?A BC5@D@ G17 C5A41@1C 49 @DB1C @5=217;9C G17 =519;;1 C57171 89771=531@19B5;9C1A /$5=D49141G19BCA9;49CA1B=9B9;1 ;5 ;?C1;?C1 CD:D1 9 ;?C1;?C1 CD:D1 497D1;1 CA1B6?A=1C?A BC5@ 4?F G17 49@1B17 49 71A4D71A4D 9BCA9; B589771 C57171 9BCA9; B91@ 497D1;1 @141 C57171 B5;9C1A

170. / Gambar 6.15 Bagan transmisi daya listrik jarak jauh transmisi tegangan tinggi generator transformator transformator gardu listrik

171. 0 146 Mudah dan Aktif Belajar Fisika untuk Kelas XII rumah pabrik tiang listrik pusat pembangkit listrik Contoh 6.9 ,52D18755A1C?AG1741@1C=5781B9;141G19BCA9;

172. 049CA1B=9B9;1=51D9 @5781C1A457181=21C1

173. !9CD718@5AB5C1B541G1G178917 =5:149;1?A:9;1 1 C57171G17497D1;1CA1B=9B9 ;/ 2 C571714919;;1?58CA16?BC5@D@=5:149 ;/ 1 9;5C18D9

174. 0+

175. 1 )5AB5C1B541G19BCA9;G178917:9;1497D1;1C57171CA1B=9B9 ;/ 41@1C4989CD7B52171925A9;DC CA1B=9B9 / Kata Kunci • generator • Alternating Current • komutator • transformator/trafo • transformator step-up • transformator step-down • efisiensi transformator • arus pusar (arus eddy) Sumber: Jendela IPTEK, 1995

176. Induksi Elektromagnetik 147 1G1G178917=5:149;1?A891714118 8917

177. 0 )5AB5C1B5 8917 0

178. 0 2 1G1G178917:9;1C57171CA1B=9B94919;;1=51D9CA16?=5:149 ;/14118

179. 0 CA1B=9B9 / 1G1G178917=5:149;1?A14118 8917

180. 20 0 8917 ;0 #149@5AB5C1B5 8917

181. 0 ,52D18CA1B6?A=1C?ABC5@D@=5=99;9 99C1@141 ;D=@1A1@A9=5AG141 99C1@141;D=@1A1 B5;D45AG1$D=@1A1@A9=5A4925A91ADB2?1;219; 25AC57171

182. / 1 5A1@1C57171;D=@1A1B5;D45A 2 #9;11ADB411=;D=@1A1B5;D45A

183. 25A1@1 1ADBG17=5719A411=;D=@1A1@A9=5A 3 5A1@1 41G1 =1BD;1 41 41G1 ;5D1A1 CA1B6?A=1C?A

184. ,52D18 CA1B6?A=1C?A 498D2D7;1 4571 BD=25A C57171)%'

186. /41;D1C1ADBG1 -5AG1C1 C57171;5D1A1G1B525B1A

188. /41;D1C1ADBG1 !9CD7 1 569B95B9CA1B6?A=1C?A 2 @5A214971:D=1899C1@A9=5A41 B5;D45A ,52D18 CA1B6?A=1C?A G17 49@1B17 @141 A149? =5=99;9 B@5B969;1B9

189. / C5A=91 @A9=5AG1 498D2D7;14571BD=25A)%'

191. /#9;1:D=18 99C1B5;D45ACA1B6?A=1C?AC5AB52DC 99C141 1ADBG17=5719A411=A149? C5CD;1 1 :D=1899C1@A9=5A 2 ;D1C1ADB@141;D=@1A1@A9=5A 3 41G1@A9=5A4141G1B5;D45A:9;1569B95B9 CA1B6?A=1C?A Tes Kompetensi Subbab B -'*($!()0'0(/%$* C. Arus dan Tegangan Listrik Bolak-balik ADB 41 C57171 9BCA9; 2?1;219; =5=99;9 919 G17 B51D 25AD218D218 C5A8141@ F1;CD B531A1 @5A9?49; 219; 25B1A =1D@D 1A18G1 5B1A1 1ADB 41 C57171 2?1;219; 491=217;1 4571 5F1B1 99 81=@9A B5=D1 @5A11C1 AD=18 C1771 49?@5A1B9;1 4571 55A79 9BCA9; 1ADB 2?1;219; ,5@5AC9 41 ;5C18D9 @5A25411 =541B1A 1C1A1 1ADB 2?1;219; 41 1ADB B51A18 14118 @?1A9C1BG1 .CD; =575C18D9 @?1A9C1B 1ADB B51A18 G17 B51D C5C1@ 41 1ADB 2?1;219; G17 B51D 25AD218 41@1C 497D1;1 ?B9?B;?@ -) 2 ,#),)* 51D9 11C 99 41@1C :D71 491=1C9 919 6A5;D5B9 41 @5AD2181C57171@141B5C91@B11C411=25CD;7A169;41@DDCD; =57D;DA 919 C57171 565;C96 41 ;D1C 1ADB 9BCA9; 565;C96 41@1C 497D1;1 E?C=5C5A 41 1=@5A5=5C5A 1. Sumber Tegangan Bolak-Balik (AC) 5CD; C57171 1ADB G17 C5A2131 @141 =?9C?A ?B9?B;?@ 25AD218 B531A1 @5A9?49; =5DADC 6D7B9 B9DB ,118 B1CD BD=25A G19CD 755A1C?A 1ADB 11= 755A1C?A 141 ;D=@1A1 G17 41@1C 25A@DC1A 2521B 411= =541 =175C 8?=?75

192. V Vm V = Vm sint T 2T I Im I = Im sint T 2T Gambar 6.18 1 2 Pengukuran arus listrik dengan menggunakan volmeter. )5A81C9;1 )- (B91B9 71G1 75A1; 9BCA9; 41 1ADB 2?1; 219; 4981B9;1 41A9 B52D18 ;D=@1A1 G17 25A@DC1A 4571 1:D C5C1@ )14171=21A7A169;C5AB52DC@D31;41B9=@D75?=217=5D:D;;1 ;54D4D;1 ;D=@1A1 C5A8141@ 25B1A BD4DC G17 49C5=@D8G1 5B1A 77 G17 4981B9;1 41A9 B52D18 755A1C?A G17 25A@DC1A =5=5D89 @5AB1=11 25A9;DC 1C1DDCD; - J 1 2 J - 148 Mudah dan Aktif Belajar Fisika untuk Kelas XII - ;1A51 3?B =1;1 3?B J - 1C1D 3?B J - - J

193. #9;1 ;9C1 CDAD;1 -.)* 3 4941@1C B9- J

194. C1D 41@1C :D71 49CD9B;1 4571 =1;B B9- J

195. 1 $1A51 77 94D;B9 B1=1 4571 2541 C57171 49 1C1A1 4D1 ;DCD2 77 94D;B9 =1;1 41@1C 49CD9B =1;B B9- J

196. 2 $5C5A171 '%, 71G1 75A1; 9BCA9; =1;B9=D= E?C E?C '%, C57171 =1;B9=D= E?C 6D;B =175C9; 02 :D=18 99C1 ;D=@1A1 D1B 29417 ;D=@1A1 =

197. 25B1AG1 94D;B9 =175C9; - 6A5;D5B9 BD4DC @DC1A1 ;D=@1A1 A14 B - #9;1 755A1C?A C5AB52DC 498D2D7;1 4571 A17;191 C5ACDCD@ 1;1 =5719A 1ADB 2. Alat Ukur Tegangan dan Arus Bolak-Balik .CD; =575C18D9 141G1 C57171 9BCA9; @141 BD1CD A17;191 B118B1CDG1497D1;1B52D1811CG1749B52DC-,-*()- ;1 C5C1@9 C5BC@5 C941; 41@1C =575C18D9 25B1AG1 C57171 G17 =5719A@141A17;191C5AB52DC41@DDCD;=57D;DA919C57171 41 ;D1C 1ADB 497D1;1 E?C=5C5A 41 1=@5A5=5C5A '919 G17C5A2131@14111CD;DA99=5D:D;;181A71565;C9641A9C57171 41 ;D1C 1ADB 51D9 )- 41 41@1C =5=181=9 81B9 @57D;DA1 1ADB 9BCA9; 411= B52D18 A17;191 Gambar 6.16 Grafik tegangan dan arus listrik bolak-balik terhadap waktu. bagian atas yang berlogam bagian tengah yang transparan lampu logam Gambar 6.17 Cara pengukuran dengan testpen

198. resistor voltmeter Gambar 6.19 Pengukuran tegangan pada sebuah rangkaian Induksi Elektromagnetik 149 Contoh 6.10 1A9@571=1C1=51D9?B9?B;?@BD=2DE5AC9;1491CDA@141C57171 / 3= Gambar 6.20 kWh meter yang ada di rumah digunakan untuk mengukur daya listrik yang terpakai. )141 )- C5A=91 ;DCD2 @?B9C96 498D2D7;1 4571 1ADB=1;B9=D= @1411=@5A5=5C5AC5A21319191ADB B5417 ;1)- C5A=91@?B9C96498D2D7;145711ADB=1;B9=1 C5AG1C1C5A21319191ADB

199. )57D;DA199=5D:D;;1218F1 17;1 G17 C5A2131 @141 11C D;DA 14118 919 565;C96G1 5=9;91 @D1 411= =57D;DA C57171 B52D18 A17;191 B5@5AC9 )- $5C9;1 1ADB =5719A :1AD= @5D:D; E?C=5C5A =D19 25AD218 '919 G17C5A2131=5D:D;;181A71565;C96C57171A17;1919BCA9;41 41@1C :D71 =57D;DA ;D1C 1ADB C57171 41 81=21C1 9BCA9; 219; 1ADB =1D@D 1ADB 4571 =577D1;1 =DC9=5C5A =@5A5=5C5A /?C=5C5A 41 (8==5C5A 41 ?B9?B;?@ B5417;1B517F1;CD=5D:D;;1=B 3=,;11C91@;?C1;=5=99;9D;DA1 3=K3=-5CD;1 1 C57171=1;B9=D= 2 6A5;D5B9BD=25A 1 9;5C18D9** / 3= 1 )14171=21AC5A2131C57171@D31;**141183=;1A51B;11E5AC9;1 / 3==1;1 **3=K / 3=E?C#149C57171=1;B9=D=G114118 '%,

200. **

201. // 2 )5A9?45411=7A169;3=,;118?A9H?C1=B 3==1;1 3=K=B 3=

202. =B

203. B #1496A5;D5B9BD=25A

204. 3. Nilai Efektif Tegangan dan Kuat Arus AC 1C D;DA G17 497D1;1 DCD; =575C18D9 :D=18 41G1 G17 C5A@1;19 @141 ;52DCD81 55A79 9BCA9; 49 AD=18 14118 ;08 =5C5A 5A5C1 17;1 =5D:D;;1 25B1A 55A79 9BCA9; G17 C5A@1;19 )5A81C9;1 )- -1=@1; :51B 17;1 G17 =5D:D;;1 25B1A 55A79 9BCA9; G17 C5A@1;19 411= B1CD1 ;08 %#) -- ).+ 5A799949@5A?5841A9919 41 !1A71565;C961ADB1C1DC57171 2?1;219; 14118 ;D1C 1ADB 1C1D C57171 2?1;219; G17 491771@ B5C1A145711ADB1C1DC57171B51A18G17=5781B9;1:D=18;1?A G17 B1=1 ;5C9;1 =51D9 BD1CD @5781C1A 411= F1;CD G17 B1=1 R A B I Im Ief t ,52D18@5781C1AB5@5AC9)- =5=99;981=21C1411= F1;CD

205. -5B1A55A79;1?AG174981B9;1?581ADB565;C96G114118 Gambar 6.21 (a) Sebuah rangkaian dengan hambatan R; 1 2 (b) Grafik hubungan I dengan t. 1 2 t sin m t

206. !H

207. Contoh 6.11 150 Mudah dan Aktif Belajar Fisika untuk Kelas XII

208. - J 5A79;1?AG174981B9;1411=A17;1911ADB=5=99;9919 G17 B51D 25AD218 B531A1 @5A9?49; 411= F1;CD

209. 41 =5=5D89 @5AB1=11

211. - - J -.)* 3 41-.)* 3 =5=99;9919G17B1=1 B589771 41@1C 49@5A?58 25B1A 1ADB 565;C96G1

212. 56

213. -

214. -

215. -

216. 56

217. -

218. =1;B

219. - J

220. 4571 =577D1;1 31A1=1C5=1C9;1 49@5A?58 1ADB 565;C96 B521719 25A9;DC =1;B

221. J 57131A1G17B1=1C57171565;C96 1;149@5A?58@5AB1=11 =1;B

222. J ,52D18A17;191G17498D2D7;14571BD=25A9BCA9;2?1;219;49D;DA 4571E?C=5C5A41=5D:D;;117;1

223. E?C5A1@1;1881A71=1;B9=D= C571712?1;219;BD=25A41CD9B;1@5AB1=11G1:9;16A5;D5B9G1 !H 1 9;5C18D9

224. / !H 1 '919C57171=1;B9=D==1;B4989CD74571=577D1;1-.)* 3 B58977149@5A?58 =1;B

226. / 2 )5AB1=11C5717149@5A?584571=577D1;1-.)* 3 G19CD =1;BB9 -

228. B9

229. - Tantangan untuk Anda Apakah yang menyebabkan sengatan listrik, arus listrik, atau tegangan listrik?

230. I Imaks Ir Gambar 6.22 Grafik hubungan I dan t Imaks = kuat arus maksimum Ir = kuat arus rata-rata. t Induksi Elektromagnetik 151 Contoh 6.12 +74F3:C3@9=3;3@3CFD4A3=43;=?7?;;=;:3C93E793@93@D74393;8F@9D;H3=EF J3;EF

231. D;@ .!;EF@93: 3 E793@93@?3=D;?F? %#*4 E793@93@BF@53==7BF@53= ((5 E793@93@787=E;8 6 8C7=F7@D;3@9F7C 7 B7C;A67 8 8C7=F7@D; 9 E793@93@D7E73:+ D7=A@ #7#$ 7@93@?7@J3?3=3@B7CD3?33@E793@93@J3@96;=7E3:F;E7C:363B'34#/##0

232. 9?3=36;B7CA7: D;@ +

233. D;@ + %63C;B7CD3?33@E7CD74FE6;B7CA7:

234. .63@ C36 D 3

235. . %4

236. .

237. . ((%5

238. % . .

240. 6 C36 D 7

243. D

244. 8

245. !K 9

246. D;@ +

247. D;@ . 1 2 t 4. Harga Kuat Arus dan Tegangan Rata-Rata !3C93 =F3E 3CFD 4A3=43;= C3E3C3E3 3633: =F3E 3CFD 4A3=43;= J3@9 @;3;@J3 D7E3C3 67@93@ =F3E 3CFD D73C3: F@EF= ?7?;@63:=3@ ?F3E3@ ;DEC;= J3@9 D3?3 633? H3=EF J3@9 D3?3 )7C:3E;=3@ 9C38;= D;@FDA;63 63C; 3CFD D73?3

248. D7=A@ #/$#3

249. -@EF= 3CFD D73C3: D7E73:

250. D7E7@93: B7C;A67 ?F3E3@ J3@9 6;3F;@J3 ?7?7@F:; B7CD3?33@ )

251. N 63BF@ F?3: ?F3E3@ J3@9 6;3F; 3CFD 4A3=43;= 633? C3@9=3;3@ 3633:

252. %#* D;@ ++ N

253. Tugas Anda Arus listrik bolak-balik dapat diamati menggunakan osiloskop. Bersama kelompok belajar Anda, gunakan osiloskop yang ada di laboratorium sekolah Anda untuk mempelajari penggunaan osiloskop tersebut. Catatlah hal-hal yang Anda anggap penting. Mintalah bimbingan guru Fisika Anda untuk melakukan tugas ini. 3C; '34#/##0

254. 9 63@ '34#/##0

255. 9

256. 3=3@ 6;B7CA7: B7C D3?33@ 3CFD C3E3C3E3 D74393; 47C;=FE Contoh 6.13

257. %#* Im Vm t R a b 152 Mudah dan Aktif Belajar Fisika untuk Kelas XII )

258. %#* D;@ ++ N 7@93@ ?7@99F@3=3@ 53C3 ?3E7?3E;=3 6;B7CA7: )

259. %#* N 7@93@ B7@343C3@ J3@9 D3?3 3=3@ 6;B7CA7: B7CD3?33@ E793@93@ C3E3C3E3 F@EF= 3CFD D747D3C )

260. %#* N $7E7C3@93@ ) E793@93@ C3E3C3E3 . %#* E793@93@ ?3=D;?F? . )7CD3?33@E793@93@4A3=43;=DF3EFC3@9=3;3@;DEC;=?7?7@F:;B7CD3?33@ D;@ .,7@EF=3@E793@93@C3E3C3E3J3@96;:3D;=3@DF?47CE7CD74FE #7#$ ;=7E3:F; D;@ .%#* . 7@93@?7@99F@3=3@'34#/##0

261. 9 6;B7CA7: )

262. .

263. . 5. Diagram Fasor -@EF= ?7?B7C?F63: ?7@93@3;D;D 3C3: E793@93@ 63@ =F3E 3CFD 6;9F@3=3@?7EA676;39C3?83DAC3DAC(!*-#+')3633:DF3EF47D3C3@ J3@96;F=;D=3@D74393;DF3EFG7=EACJ3@947D3CDF6FEBFE3C@J3E7C:363B DF?4F:AC;KA@E3 D3?367@93@ DF6FE 83D7@J3 + 3DAC DF3EFG7=EAC 47CBFE3C 47C3H3@3@ 3C3: 3CF? 3? 67@93@ =757B3E3@ DF6FE E7E3B 6;93?43C=3@ A7: D74F3: 3@3= B3@3: F@EF= ?7@J3E3=3@ E793@93@ 63@ =F3E 3CFD 63C; DF3EF C3@9=3;3@ ;DEC;= )363 #/$#3

264. 63B3E @63 B7C:3E;=3@ 6;39C3? 83DAC 63C; E793@93@ 63@ 3CFD 4A3=43;= +F?4F :AC;KA@E3 B363 #/$#3

265. 3633: F@EF= ?7@7@EF=3@ 47D3C@J3 DF6FE 83D7 J3@9 6;F=FC 633? D3EF3@ 67C33E 3E3F C36;3@ D763@9=3@ DF?4F G7CE;=3 F@EF= ?7@7@EF=3@ @;3; E793@93@ 63@ =F3E 3CFD J3@9 ?7CFB3=3@ 47D3C3@ D=33C 4F=3@ G7=EAC 73F; ?7EA67 6;39C3? 83DAC ;@; 6;:3C3B=3@ @63 63B3E ?7?3:3?; 3C3: 83D7 G7=EAC 67@93@ ?F63: 6. Resistor pada Rangkaian Arus Bolak-Balik )363#/$#3

266. D74F3:C7D;DEAC?FC@;6;B3D3@9633?C3@9=3;3@ E7CEFEFB3CFD4A3=43;= C38;=E793@93@DF?47CJ3@947CD;83ED;@FDA;63 3=3@ ?7@9:3D;=3@ 3CFD J3@9 F93 47CD;83E D;@FDA;63 Gambar 6.23 Grafik fasor I dan V Gambar 6.24 Rangkaian arus AC dengan hambatan murni R. I V = Vmsin t

267. rotasi Vm im V = Vm sin t i = im sin t 2 2 3 3 2 Gambar 6.25 Grafik kuat arus I dan tegangan V pada rangkaian hambatan murni, arus I, dan tegangan V sefase. L I = Im V sin t m im 2 2 V = Vm sin ( t ) Induksi Elektromagnetik 153 )7CD3?33@ E793@93@ 4A3=43;= 3@E3C3 FF@9FF@9 C7D;DEAC ?FC@; 3633: %D;@ + N 7@93@?7?7C:3E;=3@6-6/*/ J3@9?7@J3E3=3@43:H3=F3E3CFD J3@9?7@93;C ?7?;;=;:F4F@93@67@93@% % ?3=347D3C 3CFD 4A3=43;= J3@9 ?7@93;C ?73F; C3@9=3;3@ ?7?7@F:; B7CD3?33@ %D;@ + N )7C:3E;=3@ #/$#3

268. 7C63D3C=3@ '34#/##0

269. 9 63@ '34#/##0

270. 9 3CFD ?3=D;?F? 63@ E793@93@ ?3=D;?F? ?7?;;=; 83D7J3@9D3?3CE;@J3=7E;=3BAD;D;=F?B3C3@?7@53B3;DF6FE M E793@93@63@3CFDJ3@9?73F;C3@9=3;3@?7@53B3;@;3;?;@;?F?%74;: 73D@J3 @63 B7C:3E;=3@ #/$#3

271. ;39C3? 83DAC 63C; =F3E 3CFD 63@ E793@93@@J3 ?7?;;=; 3C3: J3@9 D3?3 t Imaks Vmaks Gambar 6.26 Diagram fasor arus I dan tegangan V memiliki arah yang sama. Gambar 6.27 Rangkaian arus bolak-balik dipasang seri dengan sebuah induktor murni. 5 2 t Mari Mencari Tahu *7D;DEAC?7CFB3=3@D33:D3EF=A?BA@7@;DEC;=J3@9D7C;@96;9F@3=3@+7E;3B C7D;DEACJ3@96;F36;B3D3C3@?7?;;=;@;3;C7D;DE3@D;E7CE7@EF,F93D@634F3E3: C7DF?7?7@97@3;53C3?7@9;67@E;8;=3D;@;3;D74F3:C7D;DEAC+7E73:?7?4F3E C7DF?7;@;6;:3C3B=3@@6363B3E?7@97@3;C7D;DEAC63@?3?BF?7@7@EF=3@ @;3;C7D;DE3@D;@J363C;5;C;5;C;J3@96;?;;=;C7D;DEACE7CD74FE93C74;:?7@3C;= D7CE3=3@93?43C?353??353?C7D;DEAC633?EF;D3@@63 a b I = Im sin t 7. Induktor Murni pada Rangkaian Arus Bolak-Balik )7C:3E;=3@ #/$#3

272. +74F3: ;@6F=EAC ?FC@; ?7?;;=; ;@6F= E3@D;6;C;)363D33E3CFD;DEC;=?7@93;C633?C3@9=3;3@3=3@E;?4F 93J3 97C3= ;DEC;= ;@6F=D; 99 6; 3@E3C3 FF@9 ;@6F=EAC J3@9 47D3C@J3 3633: + 63BF@ 4763 E793@93@ 3@E3C3 FF@9FF@9 =F?B3C3@ D74393; 8F@9D; H3=EF 3633: %D;@ + N

273. #;=3 @63 B7C:3E;=3@ C3@9=3;3@ 3CFD 4A3=43;= 633? #/$#3

274. C3@9=3;3@ E7CD74FE ?7CFB3=3@ C3@9=3;3@ E7CEFEFB 63@ 47C3=F !F=F? $;C5:A88 !F=F? $;C5:A88 ?7@J3E3=3@ 43:H3 (7: =3C7@3 633? C3@9=3;3@ E7CD74FE C7D;DEAC ?FC@; E;63= 363 J3;EF @;3; ?3=3 6;B7CA7: B7CD3?33@ =F3E 3CFD D74393; 47C;=FE

275. *,%)

276. ,#+') %D;@ +N + + % D;@ + Gambar 6.28 Grafik kuat arus I dan tegangan V pada rangkaian induktif murni. Tegangan V mendahului arus I sekitar 90°. t

277. 7@FCFE!F=F?(:? ?7CFB3=3@@;3;:3?43E;@6F=EAC 154 Mudah dan Aktif Belajar Fisika untuk Kelas XII % D;@ + + % N 5AD + % D;@ +

278. D;@ N

279. % + N 7@93@ ?7?7C:3E;=3@ B7@FCF@3@ '34#/##0

280. 9 6;=7E3:F; 43:H3 % % J3@9 6;D74FE C73=E3@D; ;@6F=E;8 D7:;@993 63B3E 6;EF;D 3E3F

281. N $7E7C3@93@ C73=E3@D; ;@6F=E;8 =757B3E3@ DF6FE C36 D ;@6F=E3@D; 6;C; ! 8C7=F7@D; !K 7@93@ ?7@93?3E; :F4F@93@ '34#/##0

282. 9 63@ '34#/##0

283. 9 6;=7E3:F; B7C47633@ 83D7 3@E3C3 E793@93@ 63@ =F3E 3CFD J3@9 ?73F; C3@9=3;3@ ;@6F=E;8 E7CD74FE D747D3C

284. 7@93@ DF6FE 83D7 3CFD E7CE;@993 3633:

285. C3663C; DF6FE83D7E793@93@ @63 3=3@ 74;: ?7?3:3?; ;=3 ?7?7C:3E;=3@ 9C38;= E793@93@ D;@FDA;63 63@ 9C38;= 3CFD D;@FDA;63 E7C:363B H3=EF ?73F; #/$#3

286. #;=3 E793@93@ B363 FF@9FF@9 C3@9=3;3@ ?3=D;?F? @;3; 3CFD 633?C3@9=3;3@3=3@?;@;?F? +743;=@J3;=3E793@93@47C@;3; ?;@;?F? 3CFD J3@9 ?73F; C3@9=3;3@ 3=3@ ?3=D;?F? %#* Gambar 6.29 Diagram fasor arus I dan tegangan V. Tegangan mendahului 90°. VL 90° I )363D74F3:C3@9=3;3@3CFD4A3=43;=67@93@8C7=F7@D; !K6;B3D3@9;@6F=EAC D747D3C

287. !*3@9=3;3@;@;?7@9:3D;=3@3CFD?3=D;?F?

288. !;EF@9E793@93@ ?3=D;?F?;@6F=EACE7CD74FE #7#$ ;=7E3:F; 8C7=F7@D; Contoh 6.14 3CFD?3=D;?F?%

289. ;@6F=E3@D;;@6F=EAC

290. ! ,793@93@?3=D;?F?63B3E6;:;EF@967@93@B7CD3?33@ % %

291. %

292. !K

293. !

294. .

295. C a b V = Vmsin t Gambar 6.30 Rangkaian kapasitor Vi V = Vm sin t 2 i = im sin t Gambar 6.31 Grafik I dan V pada kapasitor dalam rangkaian AC. 90° V I Induksi Elektromagnetik 155 8. Kapasitor pada Rangkaian Arus Bolak-Balik )C;@D;B =79F@33@@J3 D3?3 67@93@ ;@6F=EAC $3B3D;EAC 633? C3@9=3;3@3CFD4A3=43;=6;B3D3@9F@EF=?7?B7CA7:7@7C9;;DEC;=J3@9 74;: 47D3C CFD ;DEC;= J3@9 ?73F; =3B3D;EAC J3@9 =3B3D;E3D@J3 D747D3C D73?3 + 3=3@ ?7@J7434=3@ =3B3D;EAC 47C;D; ?F3E3@ D747D3C + N 63BF@ ?F3E3@ J3@9 E7CD;?B3@ 633? =3B3D;EAC #/$#3

296. 3633: N 6; ?3@3 .%D;@ + N 3C;=76F3'34#/##0

297. 9 63@'34#/##0

298. 9 63B3E6;B7CA7: + + D;@ + % + D;@ +% 5AD + % 5AD + %5AD + %D;@

299. + N 7@93@ ?7?7C:3E;=3@ B7@FCF@3@ '34#/##0

300. 9 6;=7E3:F; 43:H3 % % 7@FCFE !F=F? (:? ?7CFB3=3@ @;3; :3?43E3@ =3B3D;EAC J3@9 6;D74FE C73=E3@D; =3B3D;E;8 D7:;@993 63B3E 6;EF;D

301. N 3E3F $7E7C3@93@ C73=E3@D; =3B3D;E;8 =3B3D;E3D =3B3D;EAC 8C7=F7@D; DF6FE C36 D 7@93@ ?7@93?3E; :F4F@93@ '34#/##0

302. 9 63@ '34#/##0

303. 9 6;=7E3:F; B7C47633@ 83D7 3@E3C3 E793@93@ 63@ =F3E 3CFD J3@9 ?73F; C3@9=3;3@ =3B3D;E;8 E7CD74FE D747D3C

304. 7@93@ DF6FE 83D7 3CFD ?7@63:FF; 3633:

305. C36 63C; DF6FE 83D7 E793@93@ @63 3=3@ 74;: ?7?3:3?; ;=3 ?7?7C:3E;=3@ 9C38;= E793@93@ D;@FD;A63 63@ 9C38;= 3CFD D;@FD;A63 E7C:363B H3=EF ?73F; #/$#3

306. #;=3 E793@93@ B363 FF@9FF@9 C3@9=3;3@ ?3=D;?F? @;3; 3CFD 633? C3@9=3;3@ 3=3@ ?3=D;?F? % +743;=@J3 ;=3 E793@93@ 47C@;3; ?3=D;?F? 3CFD J3@9 ?73F; C3@9=3;3@ 3=3@ ?;@;?F? Gambar 6.32 Diagram fasor I dan V pada kapasitor.

307. Tantangan untuk Anda Sebuah kapasitor 100 F dihubungkan dengan sumber tegangan bolak-balik. Arus yang mengalir melalui rangkaian memenuhi persamaan I = 4 sin 200t A. Tuliskan persamaan tegangan kapasitor itu. !#$'.

308. *3@9=3;3@63@B363*3@9=3;3@CFDA3=3;= 1 #0)-#+#0 '#-5#04+ +(#5 +74F3:=3B3D;EAC67@93@

309. 6;B3D3@9B363DF?47CE793@93@4A3=43;= 67@93@8C7=F7@D; 156 Mudah dan Aktif Belajar Fisika untuk Kelas XII !K,793@93@?3=D;?F?% .D7B7CE;B36393?43C 47C;=FE c 200F !;EF@93CFD?3=D;?F?B363=3B3D;EACE7CD74FE #7#$ ;=7E3:F;

310. O N !K% .

311. C36 D C36 D

312. (7:=3C7@3;EF3CFD?3=D;?F?@J33633:% %

313. Contoh 6.15 V = Vmsin t '056- '34#/##0 6056- 4+0 *7D;DEAC D783D7 %D;@ +

314. @6F=EAC $ E7CE;@993 %D;@

315. + D747D3C

316. C36 $3B3D;EAC ?7@63:FF; %D;@

317. + D747D3C

318. C36 !#$'.

319. ?7@993?43C=3@ B7CD3?33@ 3CFD J3@9 ?7@93;C 633? E;3B C3@9=3;3@ #;=3 DF?47C E793@93@ 4A3=43;= 6;3@993B D3?3 J3;EF %D;@ + +747EF@J3@6363B3E?7@7@EF=3@E7C74;:63:FFB7CD3?33@3CFD 43CF =7?F6;3@ B7CD3?33@ E793@93@@J3 ;D3@J3 3CFD J3@9 ?7@93;C 633? E;3B C3@9=3;3@ D3?3 % D;@ + ?3=3 3=3@ 6;63B3E B7CD3?33@ E793@93@ B363 3 C7D;DEAC%D;@ + 4 ;@6F=EAC%D;@

320. + 5 =3B3D;EAC%D;@

321. +

322. R L C v I = Im sin t Gambar 6.34 Diagram fasor V, VR, VL, dan VC. Z – X X L X L C R X C Induksi Elektromagnetik 157 9. R, L, dan C Dipasang Seri dalam Rangkaian Arus Bolak-Balik *3@9=3;3@ 3CFD ;DEC;= 4A3=43;= J3@9 ?7?;;=; :3?43E3@ ?FC@; 6;B3D3@9 D7C; 67@93@ ;@6F=EAC D7CE3 =3B3D;EAC 3=3@ ?7@9:3D;=3@ E3?43:3@ 7@7C9; ;DEC;= J3@9 74;: 47D3C E7E3B; C3@9=3;3@ // D7C; ;@; :3@J3 63B3E 6;9F@3=3@ F@EF= ?7?B7C47D3C 63J3 ;DEC;= J3@9 E7C43E3D CFD?3=D;?F?633?C3@9=3;3@?7?;;=;@;3;63@83D7J3@9D3?3B363 D7E;3B =A?BA@7@ %74;: 73D 63B3E @63 B7C:3E;=3@ #/$#3

323. #;=3 @63 E7E3B=3@ B7CD3?33@ 3CFD 633? C3@9=3;3@ D747D3C %D;@ + B7CD3?33@D7E;3BE793@93@67@93@?7?7C:3E;=3@6;39C3? 83DAC B363 #/$#3

324. J3;EF ? D;@ + ?7?;;=; 83D7 J3@9 D3?3 67@93@ 3CFD ? D;@

325. + ?7@63:FF; 83D7 D747D3C

326. C36 ? D;@

327. + E7CE;@993 83D7 D747D3C

328. C36 )7C:3E;=3@ C3@9=3;3@ // D7C; B363 #/$#3

329. +7E;3B =A?BA@7@ ?7?;;=; E793@93@ 63@ +753C3 83DAC E793@93@E793@93@ ;@; 63B3E 6;F?3:=3@ D74393; 47C;=FE N (7: =3C7@3 63@ D3;@9 E793= FCFD :3C93 63B3E 6; E7@EF=3@ 67@93@ ?7@99F@3=3@ :;EF@9 G7=EAC J3;EF

331. N 67@93@ ?7?7C:3E;=3@ =7?43; #/$#3

332. :3?43E3@ EAE3 C3@9=3;3@ D7C; NN J3@9 6;D74FE 67@93@ ;?B763@D; C3@9=3;3@ . 63B3E 6;:;EF@9 63C; '34#/##0

333. 9

336. N

337. 3 3E3F

339. N

340. 4 (7:=3C7@33CFD?3=D;?F?J3@9?7@93;C6;D7E;3B=A?BA@7@D3?3 47D3C@J3 :F4F@93@ 3@E3C3 E793@93@ ?3=D;?F? 63@ 3CFD ?3=D;?F? ;@; ?7?7@F:;B7CD3?33@ 2J3;EF

342. N $7E7C3@93@ % E793@93@ ?3=D;?F? ;?B763@D; C3@9=3;3@ NC73=E3@D;EAE3 Gambar 6.33 Resonansi rangkaian R–L–C seri Gambar 6.35 Diagram fasor Z, R, XL, dan XC. i L V – C V L V V R V C V

343. 763 83D7 3@E3C3 E793@93@ 63@ =F3E 3CFD 63B3E 6;E7@EF=3@ D74393; V VL Vab VR I ) XL Z R ) Contoh 6.16 158 Mudah dan Aktif Belajar Fisika untuk Kelas XII N N N I = 40 R = 30 X L V L V R V = Vmsin t 47C;=FE E3@ N D7:;@993 B7CD3?33@ E793@93@@J3 3633: D;@ % + B34;3 DF6FE 83D7 47C@;3; BAD;E;8 CE;@J3 E793@93@ ?7@63:FF;3CFD63@C3@9=3;3@47CD;83E;@6F=E;8#;=3 DF6FE83D7 47C@;3; @793E;8 CE;@J3 E793@93@ E7CE;@993 A7: 3CFD 63@ C3@9=3;3@ 47CD;83E =3B3D;E;8 #;=3 6;B7CA7: 63@ CE;@J3 E793@93@?7?;;=;83D7D3?3D763@9=3@C3@9=3;3@47CD;83EC7D;DE;833? :3 ;@; 6;=3E3=3@ E73: E7C36; C7DA@3@D; 10. R dan L Dipasang Seri dalam Rangkaian Arus Bolak-Balik )7C:3E;=3@ #/$#3

344. +7E;3B =A?BA@7@ ?7?;;=; E793@93@ 63@ +753C3 83DAC E793@93@E793@93@ ;@; 63B3E 6;F?3:=3@ D74393; 7@93@?7@99F@3=3@:;EF@93@G7=EAC47D3C@J3E793@93@ EAE3 J3;EF

346. 7D3C@J3 ;?B763@D; C3@9=3;3@ *N% 6;B7CA7: D7B7CE; 47C;=FE

349. 3E3F

350. N 763 83D7 3@E3C3 E793@93@ 63@ =F3E 3CFD 63B3E 6;E7@EF=3@ D74393; 47C;=FE E3@ )7C:3E;=3@ #/$#3

351. E3?B3= 43:H3 E793@93@ ?7@63:FF; 3CFD D747D3C C36D7:;@993;=3%D;@ + ?3=3%D;@ + a R L b I = Imsin t Gambar 6.36 Rangkaian R dan L dipasang seri Gambar 6.37 Diagram fasor VL dan VR Gambar 6.38 Diagram fasor VL dan VR Gambar 6.39 Grafik tegangan mendahului arus dengan beda fase 0 90°. Vab t Iab +74F3:C7D;DEAC 6;B3D3@9D7C;67@93@;@6F=EAC B363E793@93@ 4A3=43;= . 3 !;EF@9;?B763@D;C3@9=3;3@83D7C3@9=3;3@=F3E3CFD63@ 4 ,7@EF=3@83D763@E7C:363B=F3E3CFD #7#$ ;=7E3:F; C7D;DEAC?FC@; C73=E3@D;;@6F=EAC E793@93@DF?47C . V/i

352. R C a b V I = Imsin t Induksi Elektromagnetik 159 3 ?B763@D;6;:;EF@9?73F;'34#/##0

353. 9

354. 2

355. 83D7E793@93@ 6;:;EF@967@93@'34#/##0

356. 9 E3@ M $F3E3CFD .

357. ,793@93@

358. . ,793@93@;@6F=EAC.

359. . 4 D783D767@93@=F3E3CFD ?7@63:FF;D747D3C

360. C36 M ?7@63:FF; M 33?C3@9=3;3@D7C;6;B3D3@9C7D;DEAC?FC@; 63@D74F3:;@6F=EAC ! B363E793@93@4A3=43;=67@93@B7CD3?33@

361. D;@ +.,F;D=3@B7CD3?33@ =F3E3CFD633?C3@9=3;3@E7CD74FE #7#$ ;=7E3:F; A:?

362. D;@ +.?3=3%

363. . !

364. E3@ M C36 #36;B7CD3?33@=F3E3CFD@J33633:%D;@ +

365. D;@ +N Contoh 6.17 11. R dan C Dipasang Seri dalam Rangkaian Arus Bolak-Balik )7C:3E;=3@ #/$#3

366. *7D;DEAC 63@ =3B3D;EAC 6;B3D3@9 D7C; 633? C3@9=3;3@ 3CFD 4A3=43;= ; 3@E3C3 E;E;= 63@ E7C63B3E E793@93@EAE3J3@947D3C@J3D3?367@93@F?3:E793@93@C7D;DEAC 63@E793@93@=3B3D;EAC+753C3G7=EAC47D3CE793@93@EAE3E7CD74FE 3633:

367. N 7D3C@J3 ;?B763@D; C3@9=3;3@ N 63B3E 6;:;EF@9 D7B7CE; 47C;=FE

369. N 3E3F

371. N Gambar 6.40 Rangkaian seri R-C dalam rangkaian arus AC.

372. V R I ab V ab V R Z Gambar 6.42 Diagram fasor vektor hambatan R terhadap Xc. C X C t Gambar 6.43 V ab Grafik tegangan Vab terhadap arus i 763 83D7 E793@93@ 63@ =F3E 3CFD 63B3E 6;E7@EF=3@ D74393; 47C;=FE Contoh 6.18 33? D74F3: C3@9=3;3@ 6;B3D3@9 D7C; 67@93@

373. 63@ 6; :F4F@9=3@=7DF?47CE793@93@4A3=43;=J3@98C7=F7@D;@J3 V = Vmsin t

374. !K C36 D 160 Mudah dan Aktif Belajar Fisika untuk Kelas XII !K!;EF@93: ;?B763@D;C3@9=3;3@E7CD74FE #7#$ ;=7E3:F;

375. O N !K

376. C36 D

377. ?B763@D;C3@9=3;3@63B3E6;:;EF@967@93@?7@99F@3=3@'34#/##0

378. 9

379. J3;EF

380. I C 250F R 30 E3@ N

381. Gambar 6.41 Diagram fasor tegangan Vab terhadap Vc. *3@9=3;3@ D7C; N 67@93@ C7D;DEAC 63@ C73=E3@D; =3B3D;E;8 6;:F4F@9=3@=7DF?47CE793@93@

382. .67@93@8C7=F7@D; !K!;EF@93: 3 ;?B763@D;C3@9=3;3@ 4 3CFDJ3@9?7@93;C 5 =3B3D;E3D=3B3D;EAC 6 4763E793@93@3@E3C3FF@9FF@9 :3?43E3@63@=3B3D;EAC 7 DF6FE83D7C3@9=3;3@ 8 B7CD3?33@3CFD;=3B7CD3?33@ E793@93@%D;@ + #7#$ ;=7E3:F;

383. . !K R = 80 V = Vmsin t I Contoh 6.19 C 60F V/i )363#/$#3

384. E3?B3=43:H3E793@93@E7C3?43ED747D3C C36 63C;3CFD+753C3?3E7?3E;D63B3E6;D;?BF=3@;=3%D;@ +% D;@ + N

385. a L C V L V V C I Induksi Elektromagnetik 161 3 ?B763@D;C3@9=3;3@6;:;EF@967@93@?7@99F@3=3@'34#/##0

386. 9

387. 4 CFDE7CF=FCJ3@9?73F;C3@9=3;3@ 3633:

388. .

389. 5 $3B3D;E3D=3B3D;EAC

390. 6 ,793@93@:3?43E3@63@E793@93@=3B3D;EAC

391. .

392. . 7 +F6FE83D7C3@9=3;3@ E3@ N M 8 -@EF=B7CD3?33@E793@93@%D;@ +?3=3 %D;@ +

393. D;@ +

395. D;@ +N M 12. L dan C Dipasang Seri dalam Rangkaian Arus Bolak-Balik ;=7E3:F; D74F3: C3@9=3;3@ 3CFD 4A3=43;= 6;B3D3@9 D74F3: ;@6F=EAC 63@ D74F3: =3B3D;EAC J3@9 47C=3B3D;E3D $7?F6;3@ =76F3@J3 6;:F4F@9=3@ D753C3 D7C; D7B7CE; #/$#3

396. ?3=3 3=3@ E;?4FB7C47633@83D73@E3C3E793@93@;@6F=EAC63@E793@93@=3B3D;EAC D747D3C C36 3E3F M -@EF= ?7?B7C?F63: B7?3:3?3@ 4763 83D7 633? B7CD3?33@ E793@93@ 6;E7E3B=3@ B7CD3?33@ =F3E 3CFD J3@9 ?7@93;C 633? C3@9=3;3@ 3633:%D;@ +73F;#/$#3

397. E7C435343:H3?7@63:FF; 3CFDD747D3C

398. C3663@E7CE;@993E7C:363BD747D3C

399. C36D7:;@993 D7E;3B E793@93@ 3=3@ ?7?;;=; B7CD3?33@ D74393; 47C;=FE %D;@

400. + D763@9=3@%D;@

401. + )7C:3E;=3@=7?43;6;39C3?83DACB363 #/$#3

402. +753C3 G7=EAC 63B3E 6;F?3:=3@ D74393; 47C;=FE N N #36;E793@93@EAE3C3@9=3;3@47C93@EF@9B363D7;D;:3@E3C3 63@ Gambar 6.44 Rangkaian seri L dan C b I = Imsin t Gambar 6.45 Diagram fasor I, VL, dan VC

403. R Z Gambar 6.46 f r Grafik kurva impedansi Z dan grafik linear R. R/Z Gambar 6.47 Ketika frekuensi resonansi terjadi, harga arus mencapai maksimum. I I m -@EF= :3C93 E793@93@ ?3=D;?F? 47D3C@J3 3633: % % N % D7:;@993 3=3@ 6;B7CA7: :3C93 :3?43E3@ EAE3 D747D3C %%N% %%N% D7:;@993 162 Mudah dan Aktif Belajar Fisika untuk Kelas XII N N C3:83DAC?7CFB3=3@4763DF6FE83D73@E3C3=F3E3CFD63@E793@93@ D747D3C #;=3 ?3=3 M 63@ C3@9=3;3@ 47CD;83E ;@6F=E;8 #;=3 ?3=3 N M 63@ C3@9=3;3@ 47CD;83E =3B3D;E;8 #;=3 ?3=3 B363 =3DFD ;@; E7C36; B7C;DE;H3 C7DA@3@D; 13. Resonansi pada Rangkaian R–L–C *7DA@3@D;633?C3@9=3;3@D7C; 63@ E7C36;=7E;=3 $73633@ ;@; ?7@J7434=3@ ;?B763@D; C3@9=3;3@ ?7?;;=; :3C93 ?;@; ?F?J3@947C@;3;D3?367@93@:3?43E3@?FC@;63BF@3CFD633? C3@9=3;3@ ?7@36; ?3=D;?F? 3C;D D;@99F@9 3@E3C3 =FCG3 63@ 93C;D ;@73C ?7CFB3=3@ E;E;= E7C36;@J3 8C7=F7@D; C7DA@3@D; ; E;E;= E7CD74FE 47D3C3@ 47C@;3; ?;@;?F? )7C:3E;=3@ #/$#3

404. D33E E7C36;@J3 C7DA@3@D;

405. ) ) ) ) ?3=3 N ) (7: =3C7@3

406. ) ) 6;B7CA7: 8C7=F7@D; C7DA@3@D;

407. ) N *3@9=3;3@ C7DA@3@D; 63B3E 6;F?B3; B363 C3@9=3;3@ B7@33 53C3@J3 67@93@ ?7@9F43:F43: 8C7=F7@D; ?73F; =A@67@D3EAC G3C;347 #;=3 8C7=F7@D;@J3 D7DF3; 8C7=F7@D; 97A?43@9 C36;A 3=3@ 6;E3@9=3B 14. Daya pada Arus Listrik Bolak-Balik @6F=EAC 63@ =3B3D;EAC J3@9 E7CB3D3@9 B363 C3@9=3;3@ 3CFD 4A3= 43;= ?7?4FEF:=3@ E3?43:3@ 7@7C9; ;DEC;= 3J3 J3@9 6;D7C3B 633? C3@9=3;3@ C7D;DE;8 47D3C@J3 3633:

408. N 63@ 633? C3@9=3;3@ // D7C; 3633:

411. N f

412. Induksi Elektromagnetik 163 '34#/##0

413. 9

414. 6;D74FE F93 D74393; 63J3 D7?F 63BF@ 63J3 J3@9 D7DF@99F:@J3 3E3F 63J3 C3E3C3E3 3633: 5AD N $7E7C3@93@ 4763 83D7 3@E3C3 3CFD 63@ E793@93@ 5AD 83=EAC 63J3 Contoh 6.20 +74F3: C3@9=3;3@ D7C; 67@93@ ! 63@ 6;:F4F@9=3@67@93@DF?47CE793@93@4A3=43;=J3@9?7?;;=; D;@ +. ,7@EF=3@ 3 ;?B763@D;C3@9=3;3@ 4 B7CD3?33@3CFD 5 63J3C3E3C3E3J3@96;D7C3BC3@9=3;3@ #7#$ 3 ?B763@D;C3@9=3;3@6;:;EF@9D74393;47C;=FE % !

415. D7:;@993 R = 30

419. 4 )7CD3?33@C3@9=3;3@3CFD4A3=43;=3633: . % % C 500F L = 0,6 H (7:=3C7@3 C3@9=3;3@74;:47CD;83E;@6F=E;83E3FE793@93@3=3@ ?7@63:FF;3CFD67@93@4763DF6FE83D7 E3@

420. C36 %D;@ +/ D;@ +N 5 3J3C3E3C3E3J3@96;D7C3BC3@9=3;3@3633: E3@ ?3=35AD % % 5AD 5AD

423. / V = 300sin100t Kata Kunci • arus bolak-balik • tegangan bolak-balik • arus listrik efektif • tegangan efektif • osiloskop • diagram fasor • voltmeter • impedansi • resonansi • daya Tes Kompetensi Subbab C '3,#-#0.#*#.#/$6-6.#5+*#0 #73D=3@3B3J3@96;?3=DF667@93@ 3 :3C93787=E;8=F3E3CFD63@E793@93@4A3=43;= 4 :3C93?3=D;?F?=F3E3CFD63@E793@93@4A3= 43;= 5 :3C93=F3E3CFD63@E793@93@4A3=43;=C3E3 C3E3

424. +F?47C E793@93@ 3CFD 4A3=43;= 47D3C@J3 . +74F3: D7EC;=3 ;DEC;= 67@93@ :3?43E3@

425. 6; :F4F@9=3@=7DF?47CE793@93@E7CD74FE!;EF@93: @;3;787=E;8@;3;?3=D;?F?63@@;3;C3E3C3E3F@EF= 3 E793@93@DF?47C 4 3CFDJ3@9?7@93;C

426. *3@9=3;3@/D7C;6;:F4F@9=3@=7DF?47CE793@93@ 4A3=43;=% .67@93@:3?43E3@?FC@; #;=3 3CFD ?3=D;?F? J3@9 ?7@93;C ?73F; C3@9=3;3@3633:

427. E7@EF=3@3: 3 ;?B763@D;C3@9=3;3@ 4 C73=E3@D;;@6F=EAC 5 E793@93@3@E3C3FF@9FF@9;@6F=EAC +74F3: =F?B3C3@ 67@93@ ;@6F=E3@D; ! 63@ :3?43E3@ ?FC@; 6;:F4F@9=3@ =7 DF?47C E793@93@

429. . !K!;EF@93: 3 3CFDJ3@9?73F;C3@9=3;3@ 4 DF6FE83D7=F3E3CFDE7C:363BE793@93@ 5 B7CD3?33@ =F3E 3CFD ;=3 E793@93@ DF?47C %D;@ + 6 3CFDJ3@9?73F;C3@9=3;3@D33E+O N D +74F3:C7D;DEAC 63@=3B3D;EAC

430. 6;B3D3@9D7C;B363D74F3:C3@9=3;3@E793@93@4A3= 43;=3CFDJ3@9?7@93;C67@93@B7CD3?33@D;@ +,7@EF=3@B7CD3?33@E793@93@B363C3@9=3;3@ E7CD74FE +74F3: C3@9=3;3@ 3CFD ?7?;;=; C7D;DEAC 6;B3D3@9B363E793@93@.787=E;8

431. !K63@ 6;C3@9=3;D7C;67@93@=3B3D;EACD747D3C

432. 164 Mudah dan Aktif Belajar Fisika untuk Kelas XII !;EF@93: 3 ;?B763@D;C3@9=3;3@ 4 E793@93@?3=D;?F?3@E3C3FF@9FF@9C7D;DEAC +74F3:DF?47CE793@93@

433. .6;:F4F@9=3@B363 ;@6F=EAC?FC@;J3@9;@6F=E3@D;@J3 !,7@EF=3@ 3CFD J3@9 ?7@93;C B363 ;@6F=EAC ;=3 8C7=F7@D; DF?47C 3 !K 4 =!K 33? DF3EF C3@9=3;3@ D7C; / ?7@93;C 3CFD 67@93@ 63@C73=E3@D;=3B3D;E;8

434. !;EF@93:63@63@ *3@9=3;3@D7C;E7C6;C;3E3D:3?43E3@ ?7?;;=; ;@6F=E3@D; !67@93@:3?43E3@;@6F=E3@D;63B3E 6;343;=3@ 63@ =3B3D;EAC

435. *3@9=3;3@ 6;:F4F@9=3@ B363 DF?47C E793@93@

436. . !K !;EF@93: 3 63@ 4 63J3J3@9:;3@9 5 DF6FE83D73@E3C3E793@93@63@=F3E3CFD 6 B7@F@F=3@GAE?7E7CB36363@ ,7@EF=3@8C7=F7@D;C7DA@3@D;C3@9=3;3@;@6F=E3@D; ?!63@=3B3D;E3@D; 67@93@C7D;DE3@D;J3@9 63B3E6;343;=3@

437. C36 C36 Induksi Elektromagnetik 165 Rangkuman @6F=D;77=ECA?39@7E;=3633:9733E;?4F@J33CFD ;DEC;= 63C; ?763@ ?39@7E 7D3C@J3 ;@6F=D; 77=ECA?39@7E;= 47C93@EF@9 B363 83=EAC83=EAC D74393;47C;=FE 3 %3F B7CF43:3@ 8F=D ?763@ ?39@7E 633? =F?B3C3@ 4 #F?3:;;E3@=F?B3C3@

438. 9;@6F=D;3E3F3CFD;@6F=D;63B3EE7C36;3=;43E 3 B7CF43:3@=F3E?763@?39@7E;= 4 B7CF43:3@F3D4;63@9=F?B3C3@J3@96;E7?4FD A7:?763@?39@7E;= +753C3?3E7?3E;D47D3C@J399;@6F=D;3633: - D;@ 67@93@ DF6FE3@E3C3 63@4;63@9=F?B3C3@ )363;@6F=EACB7CF43:3@3CFD633?=F?B3C3@63B3E ?7@;?4F=3@99;@6F=D;+753C3?3E7?3E;D47D3C@J3 99;@6F=D;3633:

440. + + +

441. @7C9;J3@9E7CD;?B3@633?;@6F=EAC3633:

443. *3B3E7@7C9;3E3F7@7C9;B7CD3EF3@GAF?73633:

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