needs solution

omnispace

Joined Jul 25, 2007
27
4i + 8\(\int\) idt - 3 di/dt = 50 cos(2t +75 degrees)
find the current.
I think this is easiest with phasors...

4*I + (8*I)/(j*w) - 3*j*w*I = 50<75
w = omega = 2
4*I - (j*8*I)/2 - j*6*I = 50<75
add the imaginary terms
4*I - j*65*I = 50<75
convert to polar form
65.123<-86.5 * I = 50<75
divide the magnitudes and subtract the angles
I = 0.7678<161.5
i = 0.7678*cos(2t + 161.5 degrees) A

This is very similar to the Laplace transform...basically "s" becomes "jw", like Fourier. But w is constant, so it is in "phase-domain" instead of frequency-domain.

You might want to double-check my algebra/arithmetic, I'm not really that awake.
 
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