I need some help understanding where I messed up on an assessment problem I was doing. I took a pic with my phone but it didn't come out so well.
Is=10cosωτ
Vs=100sinωτ
R(next to current source on the left)=5Ω
C=9μF
L=100μH
R(next to voltage source on the right)=20Ω
ω=50κ

1st) I changed everything to it's proper form...
Is=10 angle(0°)
Vs=100 angle(90°)
R=5Ω
C=j2.2
L=j5
R=20Ω

2nd) I got the equation for node analysis...
V[100 angle(90)] + V + V + V  10 = 0
20 j5 j2.2 5

3rd) Did some math...
V + V + V + V 10[5 angle(90)]= 0
20 j5 j2.2 5
.05s + (j.2)s + (j.45)s => .05s + (j.25)s => [.26 angle(78.7)]s =>
3.84 angle(78.7) = Z
so............
I=V => 15 angle(90) = ______v______
Z 3.84 angle(78.7)
V= 57.6 angle(168.7)

Problem...
the answer is:
31.62 angle(−71.57◦)
v = 31.62 cos(50,000t − 71.57◦)V
Where did I go wrong? Also it has to be nodal analysis.
Is=10cosωτ
Vs=100sinωτ
R(next to current source on the left)=5Ω
C=9μF
L=100μH
R(next to voltage source on the right)=20Ω
ω=50κ

1st) I changed everything to it's proper form...
Is=10 angle(0°)
Vs=100 angle(90°)
R=5Ω
C=j2.2
L=j5
R=20Ω

2nd) I got the equation for node analysis...
V[100 angle(90)] + V + V + V  10 = 0
20 j5 j2.2 5

3rd) Did some math...
V + V + V + V 10[5 angle(90)]= 0
20 j5 j2.2 5
.05s + (j.2)s + (j.45)s => .05s + (j.25)s => [.26 angle(78.7)]s =>
3.84 angle(78.7) = Z
so............
I=V => 15 angle(90) = ______v______
Z 3.84 angle(78.7)
V= 57.6 angle(168.7)

Problem...
the answer is:
31.62 angle(−71.57◦)
v = 31.62 cos(50,000t − 71.57◦)V
Where did I go wrong? Also it has to be nodal analysis.
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