The peak value of an alternating current is 5 A and frequency is 60 Hz. How long will the current, starting from zero, take to reach the peak value? ____.

For a sinusoidal alternating current the instantaneous current is described by

$I=I$_max·sin(ωt)

At the start the current is zero (t = 0). The current reaches its maximum when the sinusoid equals 1, i.e., when the argument of the sine function is π⁄2 radians.

$\omega t=\pi /2$

The angular frequency ω is related to the ordinary frequency f by

$\omega =2·\pi ·f$

Given f = 60 Hz, we have

$\omega =2·\pi ·60=120\pi$

Solving the earlier equation for the time t:

$t=(\pi /2)/\left(120\pi \right)=1/240 s$

Thus the current, starting from zero, reaches its peak value after 1/240���seconds.