(Note, my answer below is also wrong. I've attempted this problem for about 1 hour now and I can't figure it out.)
KCL (Kirchoffs Current Law)
Z for the capacitor, Z = 1/(jwC)[/B]
The Attempt at a Solution
I'm using KCL at V1 with the following convention: +ve for current flowing out of the node, -ve for current flowing in
If the bottom of our circuit is the reference:
V2 = Vs
KCL at Node 1
-i1(t) + i2(t) + V1/23 - (Vs-V1/(-40j) = 0
Now I convert all the current and voltage functions to phasors.
i1(t) = 0.2(60d)
i2(t) = 0.1(-90d)
Vs(t) = 10(-180d)
Subbing into above...
-0.2(60d) + 0.1(-90d) + V1/23 - (10(-180d))/(-40j) + V1/(-40j) = 0
V1( 1/23 + 1/(-40j) ) = 0.2(60d) - 0.1(-90d) + 10(-180d) / (-40j)
V1 = (0.1 + 0.1732j + 0.1j - 10/(40j)) / (1/23 + 1/(-40j))
V1 = 6.93 + 8.05j
Converting this to phasor form,
But this is also wrong. I can't figure out what I'm doing wrong.