Analyze this circuit with 2 sources and 4 resistors

[mkamalzayed]

Homework Statement

Find v1,v2,v3 using nodal analysis

Relevant Equations

"I in" ="I out" (KCL)

How does the current flow in this circuit and what is its actual true path, regardless of any directions in the figure?
What does the “5i” above the dependent source mean, and does the current flow according to the dependent source or the independent source?
Are the two resistors 2 ohms and 6 ohms connected in series or parallel?
I want to know more and more from the Veterans in electricity

 

[BvU]

Hi,

How does the current flow in this circuit and what is its actual true path, regardless of any directions in the figure?

That is asking for the final answer. You'll have to carry out the analysis to find it . I.e. set up a system of N equations with N unknowns and solve.

The diamond

represents a dependent voltage source of $5i$ Volts, where $i$ is the current through the $2\Omega$ resistor (

in the diagram). Be sure to use the correct sign.

$\$

 

[berkeman]

Thread closed for Moderation...

 

[berkeman]

Thread is reopened provisionally.

@mkamalzayed -- You are required to show more effort before we can offer tutorial help. Please show us your attempt at setting up the KCL equations, and begin to solve them. I will send you a Personal Message (PM) with some tips for how to use LaTeX to post math equations at PF.

 

[DaveE]

https://www.khanacademy.org/science/electrical-engineering/ee-circuit-analysis-topic

 

[mkamalzayed]

Hi,


That is asking for the final answer. You'll have to carry out the analysis to find it . I.e. set up a system of N equations with N unknowns and solve.

The diamond View attachment 353099 represents a dependent voltage source of $5i$ Volts, where $i$ is the current through the $2\Omega$ resistor (View attachment 353100 in the diagram). Be sure to use the correct sign.

$\$

Explain more and more

 

[berkeman]

Sigh. Thread is closed again for a bit...

 

[berkeman]

I'm in a PM conversation with the OP at the moment; I'll try to get them to show some effort so we can reopen the thread.

 

[berkeman]

Okay, whew. OP has shown me their work on the problem, so I'll reopen the thread (still provisionally) so they can upload it. I am working with them to help them learn LaTeX, but for the moment they will upload a picture of their hand-written work. (the quality is not too bad, just a little dark)

 

[mkamalzayed]

Explain more and more

I don't the final answer
I want to understand the figure and how the current flows and from any source ???? and I want to understand everything about this figure

Explain more and more

Homework Statement: Find v1,v2,v3 using nodal analysis
Relevant Equations: "I in" ="I out" (KCL)

How does the current flow in this circuit and what is its actual true path, regardless of any directions in the figure?
What does the “5i” above the dependent source mean, and does the current flow according to the dependent source or the independent source?
Are the two resistors 2 ohms and 6 ohms connected in series or parallel?
I want to know more and more from the Veterans in electricity View attachment 353084

 

[berkeman]

Please upload the picture of your work so others can see what you have done. Thanks.

 

[mkamalzayed]

Go ahead

 

[mkamalzayed]

Homework Statement: Find v1,v2,v3 using nodal analysis
Relevant Equations: "I in" ="I out" (KCL)

How does the current flow in this circuit and what is its actual true path, regardless of any directions in the figure?
What does the “5i” above the dependent source mean, and does the current flow according to the dependent source or the independent source?
Are the two resistors 2 ohms and 6 ohms connected in series or parallel?
I want to know more and more from the Veterans in electricity View attachment 353084

 

[BvU]

Can you check your statements

Perhaps it is useful to explicitly declare the three (!) currents at each node.
And 'node 2 has a dependent voltage source' makes no sense!

$\$

 

[BvU]

Explain more and more

It's all pretty basic: you have defined three nodes. At each node KCL says $\sum i=0$.
If you followed my advice

Perhaps it is useful to explicitly declare the three (!) currents at each node.

you have something like the following diagram in front of you:

[edit] the current entering node 3 is named i5, not i4. Updated the image.
No worries about the directions of the currents: the correct sign will come out in the analysis.

The KCL for the three nodes give you three equations, Ohm's law four and the two sources two. Nine equations in nine unknowns. Straightforward math to find e.g. $v_2$ first, then $v_1$ and $v_3$.

If you still need 'more and more', you'll first have to clearly summarize what you know already and what it is that inhibits you from dealing with this exercise.

$\$

 

[The Electrician]

In order to get a unique solution, the equations must be independent. The nine you propose are not independent.

Besides which the TS seems to be gone away.

 

[DaveE]

The nine you propose are not independent.

Maybe you meant sufficient instead of independent?

and the two sources two

Which implies some KVL equations. Let's say a solution is defined by finding the 6 currents, then you only need 6 independent equations. These could be 3 KCL nodes and 3 KVL loops, with Ohm's law to connect them. I bet I could solve this with @BvU 's prescription. Except for the problem of being too busy, too lazy, and not really excited by the solution, whatever it is.

 

[BvU]

The two equations for the sources are $v_1=v_2+25$ V and $v_3=v_2+5i$ V.

 

[The Electrician]

In other words, i5 is not indpendent of i. Likewise, v2 is not independent of v1. These are constraint equations.
Since a network with 3 nodes like this would need at most 3 equations to solve it, given more than 3 equations they are not all independent.
This network needs only one KCL equation and two constraint equations. The 3 nodes can be treated as one supernode.

 

[The Electrician]

Note that the 6 ohm resistor does nothing. It can have any value, or it can be missing.
Also note that the problem statement requires a nodal solution.

 

[BvU]

Checking...
[edit]Aren't we having fun ? Disagreements appear to come from communication issues. Where I think in terms of degrees of freedom and consider something like $\ v_1-v_2=25\$ an equation, someone else calls it a constraint.

I agree the answers to 'Find v1,v2,v3 using nodal analysis' is independent of the value of the resistance in the top branch. But I would select a different wire gauge for the top loop if the resistance would be 0.1 Ohm instead of 6. I didn't dig into the supernode issue but instead wanted to help the OP to set up reasonable KCL equations instead of what came up in #12.

$\$

 

[DaveE]

Note that the 6 ohm resistor does nothing. It can have any value, or it can be missing.
Also note that the problem statement requires a nodal solution.

Yes, it's a good observation. The zero impedance branches can effectively cut the network in two. Of course i₆ does effect i₄ and i₅, but nothing else. So superposition let's you solve the lower loops separately, with 2 nodes and two loops.

KVL #1) $4i_2 - 2i + 25 = 0$
KVL #2) $3i_3 - 4i_2 +5i = 0$
KCL #1) $i + i_2 + i_3 = 0$

 

[BvU]

I do feel a bit from taking over the OP choice of nodes at $v_1, v_2, v_3$ instead of using the one at the bottom

$\$

 

[mkamalzayed]

The two equations for the sources are $v_1=v_2+25$ V and $v_3=v_2+5i$ V.

How ?? "5i" is a current not a voltage

 

[mkamalzayed]

It's all pretty basic: you have defined three nodes. At each node KCL says $\sum i=0$.
If you followed my advice

you have something like the following diagram in front of you:

View attachment 353247​

[edit] the current entering node 3 is named i5, not i4. Updated the image.
No worries about the directions of the currents: the correct sign will come out in the analysis.

The KCL for the three nodes give you three equations, Ohm's law four and the two sources two. Nine equations in nine unknowns. Straightforward math to find e.g. $v_2$ first, then $v_1$ and $v_3$.

If you still need 'more and more', you'll first have to clearly summarize what you know already and what it is that inhibits you from dealing with this exercise.

$\$

I find that the directions of these currents are strange and illogical
On what basis did you do it?
Explain that to me in detail
What is the actual, real, original path that the current is taking?

 

[mkamalzayed]

It's all pretty basic: you have defined three nodes. At each node KCL says $\sum i=0$.
If you followed my advice

you have something like the following diagram in front of you:

View attachment 353247​

[edit] the current entering node 3 is named i5, not i4. Updated the image.
No worries about the directions of the currents: the correct sign will come out in the analysis.

The KCL for the three nodes give you three equations, Ohm's law four and the two sources two. Nine equations in nine unknowns. Straightforward math to find e.g. $v_2$ first, then $v_1$ and $v_3$.

If you still need 'more and more', you'll first have to clearly summarize what you know already and what it is that inhibits you from dealing with this exercise.

$\$

Depending on your assumptions
Node v2 does not receive any current
How do I apply the KCL law?

 

[mkamalzayed]

Yes, it's a good observation. The zero impedance branches can effectively cut the network in two. Of course i₆ does effect i₄ and i₅, but nothing else. So superposition let's you solve the lower loops separately, with 2 nodes and two loops.

KVL #1) $4i_2 - 2i + 25 = 0$
KVL #2) $3i_3 - 4i_2 +5i = 0$
KCL #1) $i + i_2 + i_3 = 0$

What path directions did you take to apply KVL?

Tell me more

 

[The Electrician]

What path directions did you take to apply KVL?

Tell me more

Have learned about the concept of a "supernode"?
As I said in post #19: This network needs only one KCL equation and two constraint equations. The 3 nodes can be treated as one supernode.

 

[mkamalzayed]

Have learned about the concept of a "supernode"?
As I said in post #19: This network needs only one KCL equation and two constraint equations. The 3 nodes can be treated as one supernode.

Explain that to me visually

 

[The Electrician]

Explain that to me visually

Fist you tell me if you have even heard the term "supernode", much less studied it.

https://en.wikipedia.org/wiki/Supernode_(circuit)

 

[The Electrician]

Depending on your assumptions
Node v2 does not receive any current
How do I apply the KCL law?

v2 receives i2, i4, i5.

 

[mkamalzayed]

v2 receives i2, i4, i5.

Where????
These currents flows out of v2
View attachment 1731000456561.png.webp

 

[The Electrician]

Where????
These currents flows out of v2
View attachment 353471

Look at the diagram in post #15. i2, i4 and i5 are shown.

 

[mkamalzayed]

i2,i4,i5 flows from v2
There are not currents entering the node v2

 

[The Electrician]

i2,i4,i5 flows from v2
There are not currents entering the node v2

You are forgetting what BvU said in post #15: "No worries about the directions of the currents: the correct sign will come out in the analysis."

The arrows on the diagram may not be showing the direction of physical current flow. What if i2 has a negative value?