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# chap31 - 31.1 a Vrms 31.8 V 2 2 b Since the voltage is...

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31.1: a) V. 8 . 31 2 V 0 . 45 2 rms V V b) Since the voltage is sinusoidal, the average is zero. 31.2: a) A. 97 . 2 ) A 10 . 2 ( 2 2 rms I I b) A. 89 . 1 ) A 97 . 2 ( 2 2 rav I I c) The root-mean-square voltage is always greater than the rectified average, because squaring the current before averaging, then square-rooting to get the root-mean-square value will always give a larger value than just averaging. 31.3: a) A. 120 . 0 ) H 00 . 5 ( ) s rad 100 ( V 0 . 60 ωL V I L IX V L b) A. 0120 . 0 ) H 00 . 5 ( ) s rad 1000 ( V 0 . 60 ωL V I c) A. 00120 . 0 ) H 00 . 5 ( ) s rad 000 , 10 ( V 0 . 60 ωL V I 31.4: a) A. 0132 . 0 ) F 10 20 . 2 ( ) s rad 100 ( ) V 0 . 60 ( 6 C I ωC I IX V C b) A. 132 . 0 ) F 10 20 . 2 ( ) s rad 10000 ( ) V 0 . 60 ( 6 C I c) A. 32 . 1 ) F 10 20 . 2 ( ) s rad 000 , 10 ( ) V 0 . 60 ( 6 C I d)

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31.5: a) . 1508 ) H 00 . 3 ( ) Hz 80 ( 2 2 π πfL ωL X L b) H. 239 . 0 ) Hz 80 ( 2 120 2 2 π πf X L πfL ωL X L L c) . 497 ) F 10 0 . 4 ( ) Hz 80 ( 2 1 2 1 1 6 fC C X C d) F. 10 66 . 1 ) 120 ( ) Hz 80 ( 2 1 2 1 2 1 5 C C fX C fC X 31.6: a) . 1700 Hz, 600 If . 170 H) Hz)(0.450 60 ( 2 2 L L X f π πfL ωL X b) C C X f πfC ωC X , Hz 600 If . 1061 ) F 10 50 . 2 ( ) Hz 60 ( 2 1 2 1 1 6 . 1 . 106 c) rad/s, 943 ) Hz 10 50 . 2 ( ) H 450 . 0 ( 1 1 1 6 LC ω ωL ωC X X L C Hz. 150 so f 31.7: F. 10 32 . 1 ) V 170 ( ) Hz 60 ( 2 A) 850 . 0 ( 5 π ωV I C ωC I V C C 31.8: Hz. 10 63 . 1 ) H 10 50 . 4 ( ) A 10 60 . 2 ( 2 ) V 0 . 12 ( 2 6 4 3 π πIL V f L V L L 31.9: a) ). ) s rad 720 (( cos ) A 0253 . 0 ( 150 ) ) s rad 720 (( cos V) 80 . 3 ( t t R v i b) . 180 ) H 250 . 0 ( ) s rad 720 ( ωL X L c) ). ) s rad 720 ( sin( ) V 55 . 4 ( ) ) s rad 720 (( sin A) 0253 . 0 ( ) ( t t ωL dt di L v L
31.10: a) . 1736 ) F 10 80 . 4 ( ) s rad 120 ( 1 1 6 ωC X C b) To find the voltage across the resistor we need to know the current, which can be found from the capacitor (remembering that it is out of phase by o 90 from the capacitor’s voltage). ). ) s rad 0 12 ( cos( V) 10 . 1 ( ) ) s rad 120 ( cos( ) 250 ( ) A 10 38 . 4 ( ) ) s rad cos((120 A) 10 38 . 4 ( 1736 ) ) s rad 120 cos(( ) V 60 . 7 ( ) ( cos 3 3 t t iR v t t X ωt v X v i R C C C 31.11: a) If . 0 1 1 1 0 LC C LC L X ωC ωL X LC ω ω b) When . 0 0 X ω ω c) When . 0 0 X ω ω d) The graph of X against ω is on the following page.

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31.12: a) . 224 H)) 400 . 0 ( rad/s) 250 (( ) 200 ( ) ( 2 2 2 2 ωL R Z b) A 134 . 0 224 V 0 . 30 Z V I c) V; 8 . 26 ) 200 ( ) A 134 . 0 ( IR V R H) 400 . 0 ( rad/s) 250 ( A) 134 . 0 ( L L V V. 4 . 13 L V d) , 6 . 26 V 8 . 26 V 4 . 13 arctan arctan R L v v and the voltage leads the current. e) 31.13: a) 2 6 2 2 2 )) F 10 00 . 6 ( rad/s) 250 /(( 1 ) 200 ( ) / 1 ( ωC R Z . 696 b) A. 0431 . 0
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