 #1
HAgdn
 23
 0
 Homework Statement:

I am trying mathematically characterize the current running a wire connected to the AC mains. This wire has a socket and can take n number of loads linear/nonlinear load.
I assumed this:
Considering that the loads have different current draws and the possibility of nonlinear load. And the current running through the wire is the sum of the draw current of the loads (is this valid to say?). Since the overall current running through the wire is the sum of all the draw current of the loads (which is periodic), then, Fourier's theorem can be applied by which the theorem states that a wave is composed of sinusoidal components having a proper amplitude and frequency. And such wave is the "REAL" current running through the wire when loads are connected.
 Relevant Equations:

Through my assumption, what I got is:
I = A_0 * sin(n_0wt + p) + A_1 * sin(n_1wt+p) + ... +A_n * sin(n_nwt+p)
Where:
I = current running through the wire connected to the AC mains whose socket whose socket has loads connected.
A_n = the draw current of an nth load
n_n = the nth load
w = angular frequency
p = phase shift
I = A_0 * sin(n_0wt + p) + A_1 * sin(n_1wt + p) + ... +A_n * sin(n_nwt + p)
Looking at the equation, it only contains sinusoidal waves. Further, there is the possibility of waves having the same shift or no shift at all and even, having the same frequency. Is it really valid or correct to use the concept of Fourier in this scenario? I am trying to use the equation in a study of mine.