# Confused about choosing current direction in nodal analysis

• mgmt113
In summary, the conversation is discussing a problem that involves determining the voltage labeled "v" in a circuit. The person is having trouble understanding current directions and how they affect the solution. They have shared their equations and asked for clarification on the direction of the current. Another person helps them understand their mistake and provides additional equations to solve the problem. The final answer they get is 1.73 V. They also ask if the number of equations needed to solve the problem is equal to the number of supernodes, to which the answer is yes.
mgmt113

## Homework Statement

The problem states: Determine the voltage labeled v in the following circuit: https://ibb.co/hz0Q37

The variable is the voltage across the 2 ohm resistor. The ground I chose for this example is located in the center of the circuit.

V=IR I guess.

## The Attempt at a Solution

I have a huge confusion regarding current directions. How come the textbook says that you can choose any current direction you want as long as you're consistent, but when I choose them to be a certain way trying to be consistent, I get the wrong answer? When I check solved problems, they assume current directions and I would have not gotten the same answers if I chose my directions. So, can you really choose the directions you want, and am I missing something important?

These are the equations I got. I got all the terms on one side to avoid confusion. If the current is entering the node, then I assign it a negative sign, if it's leaving the node, it stays positive.

For Node 1 (the one in the uppermost part of the circuit)
1 + (V3-V1)/10 + V1/2 = 0

For Supernode 2-4

-1 + (V2-V4)/12 - V3/20 + 5 -V1/2 = 0

For Supernode 3-4

V3/20 + (V1-V3)/10 -5 + (V4-V2)/12 = 0

The answer for V1 that I get is -0.5 V, however the solution manual says it's 1.7 V.

Are the directions I posted on the image right? If not, why? And is there an strategy to avoid getting confused at directions?

Thank you very much for your help. I really appreciate it.

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If you are consistent then it does not matter what direction you choose. If you get a negative answer, that just means you chose the "wrong" direction and the current is really flowing in the opposite direction from what you chose.

mgmt113 said:
1 + (V3-V1)/10 + V1/2 = 0
This is not consistent.
The basic equation is that the sum of flows into (or out of, if you prefer) a node is zero.
With the arrows drawn as you have them, you would write (flow 3 to 1)=(flow 1 to 2) + (flow 1 to 0).
(V3-V1)/10 = 1 + V1/2.

haruspex said:
This is not consistent.
The basic equation is that the sum of flows into (or out of, if you prefer) a node is zero.
With the arrows drawn as you have them, you would write (flow 3 to 1)=(flow 1 to 2) + (flow 1 to 0).
(V3-V1)/10 = 1 + V1/2.
Forgive me if I'm wrong. I thought that if the current was leaving the node, I could write V1-V3, but because it is entering the node, then it's -(V1-V3) and that's why I have V3-V1. Thanks!

mgmt113 said:
Forgive me if I'm wrong. I thought that if the current was leaving the node, I could write V1-V3, but because it is entering the node, then it's -(V1-V3) and that's why I have V3-V1. Thanks!
Yes, but that is not where you went wrong.
mgmt113 said:
1 + (V3-V1)/10 + V1/2 = 0
you have added a mixture of currents entering the node and currents leaving the node. That doesn't work. For the sum to be zero, they must all be entering or all leaving.

mgmt113 said:

## Homework Statement

For Node 1 (the one in the uppermost part of the circuit)
1 + (V3-V1)/10 + V1/2 = 0

For Supernode 2-4

-1 + (V2-V4)/12 - V3/20 + 5 -V1/2 = 0

For Supernode 3-4

V3/20 + (V1-V3)/10 -5 + (V4-V2)/12 = 0
You have another problem here. Your three equations are not linearly independent. You can see (after you get the signs correct) that adding the first two equations results in the third equation. So you have two linearly independent equations and four unknowns. You need to come up with two more equations from your diagram. There are very simple ones you can use. They are not current balance equations.

Last edited:
Thank you so much for your help! I've been understanding it wrong the whole time.

These are the equations that I came up with:

For Node 1:
-0.6 V1 + 0.1 V3 = 1

For Supernode 3-4:
0.1V1 + 0.083 V2 - 0.15 V3 - 0.083 V4 = -5

For the sources inside the supernodes:

V4-V3=10
V2=5

The answer for v is 1.73 V. Yay!

One more question: When dealing with n supernodes, do I have to only take into account n-1 equations for solving it, as they will repeat themselves?

Thank you so much again!

mgmt113 said:
Thank you so much for your help! I've been understanding it wrong the whole time.

These are the equations that I came up with:

For Node 1:
-0.6 V1 + 0.1 V3 = 1

For Supernode 3-4:
0.1V1 + 0.083 V2 - 0.15 V3 - 0.083 V4 = -5

For the sources inside the supernodes:

V4-V3=10
V2=5

The answer for v is 1.73 V. Yay!

One more question: When dealing with n supernodes, do I have to only take into account n-1 equations for solving it, as they will repeat themselves?

Thank you so much again!
If you have k nodes and n current sources, and can get one potential difference equation for each source, then the number of current balance equations you need is going to be k-n-1.

## 1. What is nodal analysis?

Nodal analysis is a method used in circuit analysis to determine the voltage and current at each node (connection point) in a circuit. It is based on Kirchhoff's Current Law, which states that the sum of currents entering a node is equal to the sum of currents leaving that node.

## 2. How do I choose the current direction in nodal analysis?

The current direction in nodal analysis is chosen arbitrarily. It does not affect the final result as long as the direction is consistent throughout the analysis. You can choose the direction based on your convenience or to simplify the calculations.

## 3. What is the difference between nodal analysis and mesh analysis?

Nodal analysis is used to analyze circuits with multiple nodes, while mesh analysis is used for circuits with multiple loops. Nodal analysis uses Kirchhoff's Current Law, while mesh analysis uses Kirchhoff's Voltage Law. Both methods can be used to solve complex circuits, but one may be more convenient depending on the circuit's structure.

## 4. Can nodal analysis be used for circuits with dependent sources?

Yes, nodal analysis can be used for circuits with dependent sources. The dependent sources can be included in the nodal equations by treating them as variables. This method is particularly useful for solving circuits with dependent sources and multiple nodes.

## 5. Is nodal analysis always the best method to solve a circuit?

No, nodal analysis is not always the best method to solve a circuit. It is best suited for circuits with multiple nodes and few branches. For circuits with multiple loops, mesh analysis may be more efficient. In some cases, a combination of nodal and mesh analysis may be needed to solve a circuit.

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