P31_059 - 59. (a) If the battery is applied at time t = 0...

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59. (a) If the battery is applied at time t = 0 the current is given by i = E R ³ 1 e t/τ L ´ , where E is the emf of the battery, R is the resistance, and τ L is the inductive time constant ( L/R ). This leads to e t/τ L =1 iR E = ⇒− t τ L =ln µ 1 iR E . Since ln µ 1 iR E =ln · 1 (2 . 00 × 10 3 A)(10 . 0 × 10 3 Ω) 50 . 0V ¸ = 0 . 5108 , the inductive time constant is τ L = t/ 0 . 5108 = (5
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