If current I1=3Asinwt and I2=4Acoswt then I3 is
Question
If current I1=3Asinwt and I2=4Acoswt then I3 is
Solution
The given currents are I1 = 3Asinwt and I2 = 4Acoswt.
These are two orthogonal (90 degrees phase difference) sinusoidal currents.
The resultant current I3 can be found using the Pythagorean theorem, as these two currents can be considered as two sides of a right triangle.
So, I3 = sqrt(I1^2 + I2^2)
Substitute the given values into the equation:
I3 = sqrt((3Asinwt)^2 + (4Acoswt)^2)
I3 = sqrt(9A^2sin^2wt + 16A^2cos^2wt)
As we know that sin^2wt + cos^2wt = 1,
I3 = sqrt(9A^2 + 16A^2)
I3 = sqrt(25A^2)
I3 = 5A
So, the resultant current I3 is 5A.
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