An alternating current varying sinusoidal with a frequency $50$ Hz has an rms value of $20$ A$.$

$($i$)$ Write down the equation for instantaneous current

$($ii$)$ Find the instantaneous value of current at $0\mathrm{.}0025$ s

$($iii$)$ Find the instantaneous value of current $0\mathrm{.}125$ s after passing through a positive

maximum value

$($iv$)$ At what time, measured from a positive maximum value, will the instantaneous current

be $14\mathrm{.}14$ A$?$