8_Chapter 21 HomeworkCH21 Alternating Current Circuits and Electromagnetic Waves

8_Chapter 21 HomeworkCH21 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 ( ) () 22 2 11 1 2 2 L L X fL f Xf L π == f , so 54.0 45.0 2 21 1 50.0 Hz 60.0 Hz LL f XX f = =Ω = 50.0 Hz The maximum current at 2 f = is then rms V = max max 2 0 0 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 L VV II ∆∆ = max 80.0 mA I < L Thus, if , it is necessary that rms 2 2 80.0 mA V f 2 25 0 . 0 V or 7.03 H 2 20.0 Hz 8.00 10 A >= > × 21.17 From B N I Φ = L , the total flux through the coil is , Bt o t a l B NL I Φ =Φ=⋅ where is the flux through a single turn on the coil. Thus, B Φ max ,m a x max rms 2 2 0 V 2 2 60.0 Hz o t a l L V LI L X V L ππ  Φ=
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