SOLUTION: The current in an alternating circuit varies in intensity with time. If I represents the intensity of the current and t represents time, then the relationship between I and t is gi

Algebra ->  Trigonometry-basics -> SOLUTION: The current in an alternating circuit varies in intensity with time. If I represents the intensity of the current and t represents time, then the relationship between I and t is gi      Log On


   

Question 733714: The current in an alternating circuit varies in intensity with time. If I represents the intensity of the current and t represents time, then the relationship between I and t is given by
I = 10 sin(100πt)where I is measured in amperes and t is measured in seconds. Find the maximum value of I and the time it takes for I to go through one complete cycle.
I =______ amp
t= ______ sec
Found 2 solutions by josmiceli, Alan3354:
Answer by josmiceli(19441) About Me  (Show Source):
You can put this solution on YOUR website!
The maximum value of the Sin function is +1+
so the maximum value of +I+=+10%2Asin%28+100%2Api%2At+%29+
is +8%2A1+=+8+
At +t+=+0+,
+10%2Asin%28+100%2Api%2A0+%29+=+10%2Asin%280%29+
+10%2Asin%280%29+=+0+
After 1 cycle, at +t+=+2%2F100+,
+10%2Asin%28+100%2Api%2A%282%2F100%29+%29+=+10%2Asin%28+2%2Api+%29+
+10%2Asin%28+2%2Api+%29+=+0+
So, the time to go through 1 cycle is +2%2F100+=+.02+ sec

Answer by Alan3354(69443) About Me  (Show Source):
You can put this solution on YOUR website!
The current in an alternating circuit varies in intensity with time. If I represents the intensity of the current and t represents time, then the relationship between I and t is given by
I = 10 sin(100πt)where I is measured in amperes and t is measured in seconds. Find the maximum value of I
Max of the sine function = 1
Max current = 10 amps.
--------------------
and the time it takes for I to go through one complete cycle.
----------------
Cycle time = 2pi/100pi = 0.02 seconds
-------
0.02 seconds --> 50 Hz, used in some countries.