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17_Chapter 20 HomeworkCH20 Induced Voltages and Inductance

# 17_Chapter 20 HomeworkCH20 Induced Voltages and Inductance...

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Induced Voltages and Inductance 191 20.44 The current in the RL circuit at time t is ( 1 t I e R ) τ ε = . The potential difference across the resistor is ( ) 1 t R V RI e τ ε = = , and from Kirchhoff’s loop rule, the potential difference across the inductor is ( ) 1 1 t t L R V V e e τ τ ε ε ε = − ∆ = = (a) At 0 t = , ( ) ( ) 0 1 1 1 R V e 0 ε ε = = = (b) At t τ = , ( ) ( )( ) 1 1 6.0 V 1 0.368 3.8 V R V e ε = = = (c) At 0 t = , 0 6.0 V L V e ε ε = = = (d) At t τ = , ( )( ) 1 6.0 V 0.368 2.2 V L V e ε = = = 20.45 From ( ) max 1 t e I I τ = , max 1 t I e I τ = If max 0.900 I I = at , then 3.00 s t = 3.00 s e τ 0.100 = or ( ) 3.00 s 1.30 s ln 0.100 τ = = Since the time constant of an RL
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