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933_Physics ProblemsTechnical Physics

933_Physics ProblemsTechnical Physics - 274 P33.32...

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274 Alternating Current Circuits P33.32 Z R X X L C = + 2 2 b g or X X Z R L C = b g 2 2 X X X X R I V Z V I L C L C = = = F H G I K J = F H G I K J = ° = = = = = ° = b g a f a f b g a fa f a f 75 0 45 0 60 0 60 0 53 1 210 2 80 210 2 80 53 1 353 2 2 1 1 . . . tan tan . . . cos . cos . 45.0 V 75.0 A V A W rms rms rms rms φ φ P P33.33 (a) P = = ° = × I V rms rms W b g a f a f cos . cos . . φ 9 00 180 37 0 1 29 10 3 P = I R rms 2 so 1 29 10 9 00 3 2 . . × = a f R and R = 16 0 . . (b) tan φ = X X R L C becomes tan . ° = 37 0 16 a f X X L C : so X X L C = 12 0 . . P33.34 X L L = = = ω π 2 60 0 0 025 0 9 42 . . . s H b gb g Z R X X L C = + = + = 2 2 2 2 20 0 9 42 22 1 b g a f a f . . . (a) I V Z rms rms V 22.1 A = = = 120 5 43 . (b) φ = F H G I K J = ° tan . . . 1 9 42 20 0 25 2 so power factor = = cos . φ 0 905 . (c) We require φ = 0 . Thus, X X L C = : 9 42 1 2 60 0 1 . . s Ω = π e j C and C = 281 F µ . (d) P P b d = or V I V R b b b d rms rms rms b g b g b g cos φ = 2 V R V I d b b b rms rms rms V A V b g b g b g a fa fa fa f = = =
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