A) \[2{{\log }_{e}}\,2\]
B) \[\frac{4}{{{\log }_{e}}2}\]
C) \[\frac{2}{{{\log }_{e}}2}\]
D) \[\frac{{{\log }_{e\,}}2}{2}\]
Correct Answer: C
Solution :
\[I={{I}_{0}}(1-{{e}^{-t/T}})\] where T = time constant \[\therefore \] \[\frac{3}{4}{{I}_{0}}={{I}_{0}}(1-{{e}^{-4/T}})\] \[\Rightarrow \] \[1-{{e}^{-4/T}}=\frac{3}{4}\] \[\Rightarrow \] \[{{e}^{-4/T}}=\frac{1}{4}\] \[\Rightarrow \] \[{{e}^{4/T}}=4\] \[\Rightarrow \] \[\frac{4}{T}={{\log }_{e}}4\] \[\therefore \] \[T=\frac{4}{{{\log }_{e}}4}=\frac{2}{{{\log }_{e}}2}\]
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