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18_Ch 20 College Physics ProblemCH20 Induced Voltages and Inductance

# 18_Ch 20 College Physics ProblemCH20 Induced Voltages and Inductance

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192 CHAPTER 20 20.47 ( ) ( ) 2 2 3 1 1 70.0 10 H 2.00 A 0.140 J 2 2 L PE LI = = × = 20.48 (a) The inductance of a solenoid is given by 2 0 L N A µ = l , where N is the number of turns on the solenoid, A is its cross-sectional area, and is its length. For the given solenoid, l ( ) ( ) ( ) ( ) 2 2 2 2 7 2 0 3 4 10 T m A 300 5.00 1 m 4.44 10 H 0.200 m N r L µ π π π × = = = × l 0 × (b) When the solenoid described above carries a current of 0.500 A I = , the stored energy is ( ) ( ) 2 2 3 1 1 4.44 10 H 0.500 A 5.55 10 2 2 L PE LI = = × = × 4 J 20.49 The current in the circuit at time t is ( 1 t I e R ) τ ε = , and the energy stored in the inductor is 2 1 2 L LI = PE (a) As t , →∞ max 24 V 3.0 A 8.0 I I R ε = = = , and ( )(
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