Physics - EMI/AC Question with Solution | TestHub

$\text{I}={\text{I}}_0\left(1-{\text{e}}^{-\frac{\text{t}}{\tau }}\right)$

$\frac{9}{10}{\text{I}}_0={\text{I}}_0\left(1-{\text{e}}^{-\frac{{\text{t}}_1}{\tau }}\right)$

$\Rightarrow {\text{e}}^{-\frac{{\text{t}}_1}{\tau }}=\frac{1}{10}$

$\Rightarrow {\text{e}}^{\frac{{\text{t}}_1}{\tau }}=10$

$\Rightarrow {\text{t}}_1=\tau ln10 \; \; \;$    ............(1)

and $\frac{99}{100}{\text{I}}_0={\text{I}}_0\left(1-{\text{e}}^{-\frac{{\text{t}}_2}{\tau }}\right)$

$\Rightarrow {\text{e}}^{-\frac{{\text{t}}_2}{\tau }}=\frac{1}{100}$

$\Rightarrow {\text{t}}_2=\tau ln100=2\tau ln10 \; \; \;$   ..............(2)

From equations (1) and (2), we have
$\Rightarrow \frac{{\text{t}}_1}{{\text{t}}_2}=\frac{1}{2}$