Struggling with Nodal Analysis and Voltage Calculations

[gfd43tg]

I am having a little issue with this problem, because when I do nodal analysis, I get the voltage of the node above the 5 kΩ resistor to be nearly 15 V. I am assuming all of the capacitors are saturated, and therefore act as open circuits. That means no current goes through the 20k or 30k resistors, and therefore the voltage v2 and v1 should be the same as the voltage V, almost 15 V.

However, then I try a different approach and do a loop around the 5k, 15k, and 10k resistors, knowing all other wires lead to an open circuit. I get a current of 0.5 mA. Then to find v3, knowings its in parallel with the 15k resistor, I do the current times 15k to get the voltage, and similarly with the 10k and v4.

for v1 and v2, I do 15V - 5000(0.5x10^-3) = 12.5 V, which does not agree with my nodal analysis. What is going on here??

 

[NascentOxygen]

V2 and V1 would equal V iff there were zero current through the 5k resistor.

Your calculations for V1, V3 and V4 are correct, the loop current is 0.5mA

 

[gfd43tg]

Why is my nodal analysis revealing something different? Also, is my V2 correct?

 

[NascentOxygen]

Why is my nodal analysis revealing something different? Also, is my V2 correct?

You have made an arithmetic blunder in calculating V.