# Help with Circuit problem

• May 12th 2010, 10:58 PM
bnk0430
Help with Circuit problem

The current in amps in an ac circuit containing a resistance is given by i = 1.5 sin ωt where ω = angular velocity, t = time in seconds, and ωt = angle in radians. If the angular velocity ω = 300 rad/s

(a) Find i in milliamps when t = 2.0 ms
(b) Find the angle ωt in radians between 0 and 2π rad when i = mA

How do I go about doing this problem? Please explain clearly, thanks.
• May 13th 2010, 08:43 AM
ebaines
This is a sine wave of magnitude 1.5. The value of i for any value of t is found by straight-forward sunstitution intoteh formula you gave us. Thus at t = 20 milliseconds you have:

$\displaystyle i = 1.5 \sin(300 /s \cdot 0.020 s) = 1.5 \sin(3) = 1.5 \times 0.1411 = 0.212$

However, you didn't tell us whether this formula yields i in amps, or milliamps. Presumbaly you can convert if need be.

The second queston involves finding the inverse of the sine function. Your post is missing an important part of the question - namely precisely what value of i you were given. So I will give an example where i = 0.75. You have:

$\displaystyle i = 0.75 = 1.5 \sin(300t)$

$\displaystyle \frac 1 2 = sin(300t)$

For what value of $\displaystyle \omega t$ does $\displaystyle sin(\omega t) = \frac 1 2$? From basic triginometry you know that $\displaystyle \sin(\pi/6) = \frac 1 2$ and $\displaystyle \sin(\frac {5\pi}{6}) = \frac 1 2$. Hence:

$\displaystyle \omega t = \frac {\pi} 6$ or $\displaystyle \omega t = \frac {5 \pi} 6$

Hope this helps.