How can i solve this circuit using nodal analysis?

Luminaty

Joined Dec 21, 2022
1
I tried to solve it, but the value i get is too high for N1. What did i do wrong? What am i misunderstanding?

WBahn

Joined Mar 31, 2012
30,253
Since you don't show what you got for the voltage at N1 or how you got it, how can we possibly tell you what you are misunderstanding?

Your schematic is using a convention that is unfamiliar to most of us (just because it's not what we are used to seeing).

Is the arrow on Uq pointing from the higher voltage to the lower voltage, or the other way around (I've seen both conventions from different parts of the world).

The same question applies to U4. If U4 turns out to be positive, does that mean that N2 has a positive voltage relative to the bottom node?

I'm assuming that the arrow below the current source is part of the current source symbol and is showing which direct the 2 A is flowing.

I'm also assuming that you are using conventional current (as opposed to electron-flow)? That is usually a pretty safe bet by the time someone is working with these kinds of circuits.

I see that you have chosen the node above the 30 V source to be your common reference node? That's perfectly legitimate, but a rather odd choice. I see, however, from your equations that it appears you are saying that the bottom node is +30 V, from which I infer that the voltage polarity arrow on the source (and presumably U4) points toward the higher voltage.

You really should get in the practice of properly using, and tracking, your units throughout your work. That will help prevent you from making a lot of mistakes and help you quickly catch a significant share of the ones you still do.

Unless they teach order of operations differently where you are from (and they might, but I think it's pretty universal these days), your current equations are wrong. As an example, you have

i2 = 30 - v1/10

This is the same as

i2 = 30 - (v1/10)

since multiplication/division take precedence over addition/subtraction.

You should write this as

i2 = (30 V - v1) / 10 Ω

Notice the proper use of units. The right-hand side has a voltage subtracted from a voltage in the numerator and a resistance in the denominator, which yields a quotient that is a current, which is in agreement with the left-hand side.

If you track your units through every step of your work, on then ask if the units still work out at each step, you will see the quality of your work improve markedly -- and the time spent tracking your units will more than pay for itself in time not spent cranking through work that was guaranteed to be wrong because of an uncaught error a page and a half before.