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 \[\frac{3}{4}{{I}_{0}}={{I}_{0}}(1-{{e}^{-4/T}})\] \[1-{{e}^{-4/T}}=\frac{3}{4}\] \[{{e}^{-4/T}}=\frac{1}{4}\] \[{{e}^{4/T}}=4\] \[\frac{4}{T}={{\log }_{e}}4\] \[T=\frac{4}{{{\log }_{e}}4}=\frac{2}{{{\log }_{e}}2}\]
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