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.

 

[rezeew]

It seems like you are on the right track with your approach to the problem. Nodal analysis and voltage calculations can be tricky, and it's not uncommon to get different results when using different methods. However, it's important to make sure that your assumptions and calculations are accurate.

Firstly, when you mentioned that the capacitors are saturated and acting as open circuits, that may not necessarily be the case. Capacitors can still have some current flowing through them, depending on the frequency of the circuit and the values of the components. It's important to check the values of the capacitors and the frequency of the circuit to ensure that your assumption is correct.

Secondly, when doing nodal analysis, it's important to consider all of the nodes and their respective voltages. It seems like you may have overlooked the voltage at the node between the 5kΩ and 15kΩ resistors, which would affect your calculations for v1 and v2. Make sure to include all of the nodes in your analysis to get an accurate result.

Lastly, when doing loop analysis, it's important to make sure that your chosen loop is independent and that it includes all of the components in the circuit. It's possible that the loop you chose did not include all of the components, which could explain the discrepancy in your results.

Overall, it's important to carefully check your assumptions and calculations when doing nodal analysis and voltage calculations. Double-checking your work and considering all of the components in the circuit will help you arrive at the correct solution. Keep practicing and don't be discouraged – these types of problems can be challenging, but with persistence and attention to detail, you will be able to master them.