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8_Ch 21 College Physics ProblemCH21 Alternating Current Circuits and Electromagnetic Waves

# 8_Ch 21 College Physics ProblemCH21 Alternating Current Circuits and Electromagnetic Waves

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208 CHAPTER 21 21.15 The ratio of inductive reactance at 2 50.0 Hz f = to that at 1 60.0 Hz f = is ( ) ( ) 2 2 2 1 1 1 2 2 L L X f L f X f L π π = = f , so ( ) ( ) ( ) 54.0 45.0 2 2 1 1 50.0 Hz 60.0 Hz L L f X X f = = Ω = 50.0 Hz The maximum current at 2 f = is then ( ) ( ) rms L L V X X = max max 2 2 100 V 3.14 A 45.0 V I = = = 21.16 The maximum current in this inductive circuit will be ( ) ( ) ( ) rms rms max rms 2 2 2 2 L V V I I X f π = = = max 80.0 mA I < L Thus, if , it is necessary that ( ) ( ) ( ) ( ) ( ) rms 2 2 80.0 mA V f π 2 2 50.0 V or 7.03 H 2 20.0 Hz 8.00 10 A L L π > = > × 21.17 From B N I Φ = L , the total flux through the coil is , B total B N L I Φ = Φ = where is the flux through a single turn on the coil. Thus, B Φ
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