Help with Circuit problem

Mar 2010
3
0
I didn't learn to do this properly so please help me and explain it clearly.

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.
 
Jun 2008
1,389
513
Illinois
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.