Electro Magnetic Induction And Alternating Currents Question 162

Question: A coil of inductance 8.4 mH and resistance $ 6\Omega $ is connected to a 12 V battery. The current in the coil is 1.0 A at approximately the time

Options:

A) 500s

B) 25s

C) 35ms

D) 1ms

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Answer:

Correct Answer: D

Solution:

  • Using $ I=I_{0}(1-{{e}^{-t/\tau }}) $

    But $ I_{0}=\frac{V}{R} $

    and $ \tau =\frac{L}{R} $
    $ \therefore I=\frac{V}{R}(1-{{e}^{-Rt/L}})=\frac{12}{6}[ 1-{{e}^{-6t/8.4\times {{10}^{-3}}}} ] $ =1 (given)
    $ \therefore t=0.97\times {{10}^{-3}}s\approx 1ms $



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