A) \[\frac{{{e}^{2}}}{{{e}^{2}}-1}\]
B) \[\frac{{{e}^{1/2}}}{{{e}^{1/2}}-1}\]
C) \[1-e\]
D) \[{{e}^{-1}}\]
Correct Answer: A
Solution :
The growth of current i is \[i={{i}_{0}}(1-{{e}^{-t/\tau }})\] Also time constant of LR circuit is given by \[\tau =\frac{L}{R}=\frac{5}{10}=\frac{1}{2}s\] ?(i) Current at \[t=\infty ,\,{{i}_{\infty }}={{i}_{0}}\] Similarly, at \[t=1\,s,{{i}_{1}}={{i}_{0}}(1-{{e}^{-2}})\] ...(ii) Ratio is,\[\frac{{{i}_{\infty }}}{{{i}_{1}}}=\frac{{{i}_{0}}}{{{i}_{0}}(1-{{e}^{-2}})}=\frac{1}{(1-{{e}^{-2}})}=\frac{{{e}^{2}}}{{{e}^{2}}-1}\]
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