Answer
$t = 3.56\times 10^{-4}~s$
Work Step by Step
We can rewrite the expression for the current:
$i = (1.60)~sin~(2500 t+0.680)$
The current will reach a maximum when $~~sin~(2500 t+0.680) = 1$
We can find $t$:
$sin~(2500 t+0.680) = 1$
$2500 t+0.680 = \frac{\pi}{2}$
$2500 t = \frac{\pi}{2}- 0.680$
$t = \frac{\frac{\pi}{2}- 0.680}{2500}$
$t = 3.56\times 10^{-4}~s$
