Zc = 1/(-jwc)
Zl = jwc
w = 2(pi)*f
The Attempt at a Solution
I'm teaching myself circuit analysis, and it's been rough. Ultimately, I been able to mostly figure everything out, but I've ran into a wall with AC. The main problem I am having is finding i(t), but I don't exactly know how to. I've looked for resources online, but I haven't been able to find any. I'm assuming that I just have to find the impedance of all the components and then use V = IZ to find the current source i(t), but it doesn't seem right. Honestly, I'm not even sure if you can combine impedances in parallel like I did.
Zc = -j100
Zl = j60
Zr = 200
Zeq = (1/200 + 1/(j60) + 1/(-j100))^-1
= 72 + j96
For V, I use the 6cos(wt). I assumed that the voltage would be the same as the voltage across the capacitor due to KVL (pretty sure that I am 100% wrong though).
V = IZ
I = V/Z
i(t) = 6/(72 + j96)
i(t) = .03 - j.04
Now what makes me unsure about what I did is this:
ic(t) = [6cos(wt)]/ [-j100]
= .06 /_ 90 deg
This solution for ic(t) is not the same as if I did current division:
ic(t) = (.03 - j.04)*(-j100/(200-j40))
So essentially, I have no clue as to what I am doing. Any help would be appreciated, and also any resources that you may know of for help with AC circuit analysis would also be greatly appreciated.