Electro Magnetic Induction And Alternating Currents Question 409

Question: A coil of inductance 300 mH and resistance 2 $ \Omega $ . is connected to a source of voltage 2 V. The current reaches half of its steady state value in

Options:

A) 0.3s

B) 0.15s

C) 0.1 s

D) 0.05s

Show Answer

Answer:

Correct Answer: C

Solution:

  • $ L=300\times {{10}^{-3}}H $

    $ R=1\Omega $

    $ I=\frac{I_{0}}{2} $ Using $ I=I_{0}(1-{{e}^{-Rt/L}}), $

    we get $ \frac{I_{0}}{2}=I_{0}(1-{{e}^{-Rt/L}}) $

    $ \Rightarrow \frac{1}{2}=1-{{e}^{-Rt/L}}\Rightarrow {{e}^{-Rt/L}}=\frac{1}{2} $

    $ \Rightarrow {{e}^{Rt/L}}=2\Rightarrow \frac{R}{L}t={\log_{e}}2=0.693 $

    $ \Rightarrow t=\frac{0.693\times 300\times {{10}^{-3}}}{2}s=0.1s $



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