Electro Magnetic Induction And Alternating Currents Question 603
Question: In an LR-circuit, time constant is that time in which current grows from zero to the value (where $ I_{0} $ is the steady state current) [MP PMT/PET 1998; MP PET 2002]
Options:
A) $ 0.63,I_{0} $
B) $ 0.50,I_{0} $
C) $ 0.37,I_{0} $
D) $ I_{0} $
Show Answer
Answer:
Correct Answer: A
Solution:
Current at any instant of time t after closing an L-R circuit is given by $ I=I_{0}[ 1-{{e}^{\frac{-R}{L}t}} ] $ Time constant $ t=\frac{L}{R} $
$ \therefore I=I_{0}[ 1-{{e}^{\frac{-R}{L}\times \frac{L}{R}}} ]=I_{0},(1-{{e}^{-1}})=I_{0},( 1-\frac{1}{e} ) $ $ =I_{0},( 1-\frac{1}{2.718} )=0.63I_{0}=63% $ of $ I_{0} $
