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 $
