The circuit shown in the figure is initially in the steady state with the switch $K$ in open condition and $\bar{K}$ in closed condition. The switch $ K$ is closed and $\bar{K}$ is opened simultaneously at the instant $t=t_{1},$ where $t_{1}>0.$ The minimum value of $ t_{1}$ in milliseconds, such that there is no transient in the voltage across the $ 100 \mu \mathrm{F}$ capacitor, is_________(Round off to $2$ decimal places).
