The current flowing through an ac circuit is given by I = 5 (120 )A...

If initial value of current is zero, then it will take $\dfrac{T}{4}$ time to reach the peak value, where $T =$ time period.

As we know, $\omega = 120\pi$

Therefore,

$t = \dfrac{T}{4} = \dfrac{\dfrac{2\pi}{\omega}}{4}$ $= \dfrac{\pi}{2\omega} = \dfrac{\pi}{2 \times 120\pi} = \dfrac{1}{240}s$