1. Math problem

We have alternating current in the United Sates. This electric current alternates with a frequency of 60 cycles per second. Suppose that at time of t = 0.02 seconds, the current is at its maximum of l = 5 amperes. If the current varies sinusoidally over time, write and expression l(t) for the current as as function of time in t in seconds.

Anybody? I need to show work too.

2. Originally Posted by Airjunkie
We have alternating current in the United Sates. This electric current alternates with a frequency of 60 cycles per second. Suppose that at time of t = 0.02 seconds, the current is at its maximum of l = 5 amperes. If the current varies sinusoidally over time, write and expression l(t) for the current as as function of time in t in seconds.

Anybody? I need to show work too.
$\displaystyle I(t) = I_0~sin( \omega t + \phi )$

We know that f = 60 Hz, so
$\displaystyle \omega = 2 \pi f = 120 \pi$

$\displaystyle I(t) = I_0~sin( 120 \pi t + \phi )$

At t = 0.02 s the current is at its maximum, thus we know that
$\displaystyle 120 \pi (0.02) + \phi = \frac{\pi}{2}$

$\displaystyle \phi = 1.9\pi$

So
$\displaystyle I(t) = I_0~sin( 120 \pi t - 1.9 \pi )$

And finally, $\displaystyle I_0 = 5~A$, so
$\displaystyle I(t) = 5~sin( 120 \pi t - 1.9 \pi )$

-Dan