A) \[\frac{1}{\ln 2}s\]
B) \[\frac{2}{\ln 2}s\]
C) \[\frac{3}{\ln 2}s\]
D) \[\frac{4}{\ln 2}s\]
Correct Answer: B
Solution :
We know that \[i={{i}_{o}}\left[ 1-{{e}^{\frac{-Rt}{L}}} \right]\]or \[\frac{3}{4}{{i}_{o}}={{i}_{o}}\left[ 1-{{e}^{-t/\tau }} \right]\] (where \[\tau =\frac{L}{R}=\] time constant) \[\frac{3}{4}=1-{{e}^{-t/\tau }}\] or \[{{e}^{-t/\tau }}=1-\frac{3}{4}=\frac{1}{4}\] \[{{e}^{t/\tau }}=4\] or \[\frac{t}{\tau }=\] ln 4 \[\Rightarrow \,\,\tau =\frac{t}{\text{ln}\,4}=\frac{4}{2\,\text{ln}\,2}\Rightarrow \,\tau =\frac{2}{\text{ln}\,2}sec.\]
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