# Arbitrary current with mesh analysis

• garr6120
In summary: I think you're trying to tell me something, but I'm not sure what. :confused::confused::confused:Re-reading my own post, I see a typo in the 2nd last line20*ib = 5.8620689656should have been20*ib = -5.8620689656which makes the total -204.8275862069So, I stand by my assertion, that the total is 0. :oldfrown:I am speaking of the two currents 3ib and ib.In summary, the conversation involves a circuit diagram and a series of equations for calculating the mesh currents. The conversation also includes a
garr6120
Members are reminded to use the 3 header template in the homework help forums
Given the circuit in the diagram I was wondering would I be able to make ib equal to the mesh i3.

I have the equation for my Super Mesh at i1 and i3 which is:

-25+30i3+5Va+20(i3-i2)+10(i1-i2)=0 (1).

The mesh i2 is equal to -2A (2).

subbing (2) into (1) gives:
-25+50i3+5Va-30i2+10i1=0 (3).

Va=i1-i2 (4).

subbing (4) into (3) gives: -25+50i3-35i2+15i1=0 (5).

subbing (2) into (5).
45+50i3+15i1=0 (6).

3ib=i1-i3 (7).

Now I almost have one unknown. Is it possible to set ib equal to i3 so i can isolate for i1 in equation 7. If i can't how would i be able to solve it.

Also, are the steps to finding the mesh currents correct for this problem?

ib is the current through the 20Ω (from right to left). I can see that resistor's current is composed of 2 mesh currents, I3 flowing R to L, and I2 flowing L to R.

Your eqn (4) is missing a 10, it's a 10Ω resistor.

The current through the 10Ω can also be equated to the sum of the currents into the node above it.

scottdave
NascentOxygen said:
ib is the current through the 20Ω (from right to left). I can see that resistor's current is composed of 2 mesh currents, I3 flowing R to L, and I2 flowing L to R.

Your eqn (4) is missing a 10, it's a 10Ω resistor.

The current through the 10Ω can also be equated to the sum of the currents into the node above it.
What do you mean the current of the 10Ω resistor? Do you mean mesh current 3?

garr6120 said:
What do you mean the current of the 10Ω resistor? Do you mean mesh current 3?
I am speaking of the two currents 3ib and ib.

What it is still missing is: i1=3*ib-i3 and since ib=i3+2 and ua=10*(i1-i2) you may reduce the first equation so that only i3 stays as unknown.

scottdave
What it is still missing is: i1=3*ib-i3 and since ib=i3+2 and ua=10*(i1-i2) you may reduce the first equation so that only i3 stays as unknown.
After doing all of the calculations is an answer for mesh current 1 -17/27A correct?

garr6120 said:
After doing all of the calculations is an answer for mesh current 1 -17/27A correct?
Nope.

garr6120 said:
After doing all of the calculations is an answer for mesh current 1 -17/27A correct?

The Electrician said:

I have the equation for my Super Mesh at i1 and i3 which is:

-25+30i3+5Va+20(i3-i2)+10(i1-i2)=0 (1).

The mesh i2 is equal to -2A (2).

subbing (2) into (1) gives:
35+50i3+5Va+10i1=0 (3).

Va=10(i1+2) (4).
Va=10i1+20 (4)

subbing (4) into (3) gives: 135+50i3+60i1=0 (5).

3ib=i1-i3 (6).

ib=i3-i2 (7)

subbing (7) into (6)
3i3-3i2=i1-i3
i1=4i3-3i2
i1=4i3+6 (8)

subbing (8) into (5)
135+50i3+240i3+360
290i3=-495
i3=-99/58

I was wondering if i went wrong anywhere in my steps?

Last edited:
garr6120 said:
I have the equation for my Super Mesh at i1 and i3 which is:

-25+30i3+5Va+20(i3-i2)+10(i1-i2)=0 (1).

The mesh i2 is equal to -2A (2).

subbing (2) into (1) gives:
35+50i3+5Va+10i1=0 (3).

Va=10(i1+2) (4).
Va=10i1+20 (4)

subbing (4) into (3) gives: 135+50i3+60i1=0 (5).

3ib=i1-i3 (6).

ib=i3-i2 (7)

subbing (7) into (6)
3i3-3i2=i1-i3
i1=4i3-3i2
i1=4i3+6 (8)

subbing (8) into (5)
135+50i3+240i3+360
290i3=-495
i3=-99/58

I was wondering if i went wrong anywhere in my steps?

You made a sign error with respect to i2 in the red part above. Fix this and recalculate.

The Electrician said:
You made a sign error with respect to i2 in the red part above. Fix this and recalculate.

Well 20(-1)(-2)=40 and 10(-1)(-2)=20

So -25+40+20=35

where is the sign error

garr6120 said:
Well 20(-1)(-2)=40 and 10(-1)(-2)=20

So -25+40+20=35

where is the sign error

Never mind. I had a situation of poor visibility on my laptop, and the 35 looked like 85.

You're all good. i3 does indeed equal -99/58

garr6120 said:
I was wondering if i went wrong anywhere in my steps?
The customary check is to substitute your provisional 3 answers back into the 3 equations. If all equations are satisfied, then conclude you have the correct solution to those equations. That works out faster than waiting for someone to look over your calculations...and running the risk of having them miss something anyway.

NascentOxygen said:
running the risk of having them miss something anyway.

Your above eq.no.6 it is incorrect.
It has to be i1=3ib-i3.
Then i3= -2.9117647 A.

Your above eq.no.6 it is incorrect.
It has to be i1=3ib-i3.
Then i3= -2.9117647 A.
OP's eqn 6 is correct. You were wrong in post #5

It may be but this is the solution. Check this with first equation and see it fits.
i3=-2.9117647 A
i2=-2
ib=i3-i2=-0.9117647
i1=3*ib-i3=3*(-0.9117647)+2.9117647=0.1764706 A
ua=10*(i1-i2)=10*(2.1764706)=21.764706 V
SUM=-25+30*i3+5*ua+20ib+ua=0

I get:
i1 = -.82759
i2 = -2
i3 = -1.7069

Check -25+30*i3+5*ua+20*ib+ua=204.827 with your results, but has to be 0.

Check -25+30*i3+5*ua+20*ib+ua=204.827 with your results, but has to be 0.

OK, let's evaluate all the terms using my values for i1, i2 and i3, using the fact that ua = 10*(i1-i2), ib = i3-i2
Listing the results, I get:
-25 = -25
30*i3 = -51.2068965516
5*ua = 58.620689655
20*ib = 5.8620689656
ua = 11.724137931

Adding all these up, I get zero, not 204.827

Perhaps @garr6120 has been given the solution?

It is very interesting: both results seem to be correct.

It is very interesting: both results seem to be correct.
I ran it through a simulation, and the results agree with @The Electrician's solution.

The Electrician said:
OK, let's evaluate all the terms using my values for i1, i2 and i3, using the fact that ua = 10*(i1-i2), ib = i3-i2
Listing the results, I get:
-25 = -25
30*i3 = -51.2068965516
5*ua = 58.620689655
20*ib = 5.8620689656
ua = 11.724137931

Adding all these up, I get zero, not 204.827

It is very interesting: both results seem to be correct.

Check -25+30*i3+5*ua+20*ib+ua, has to be 0.

OK, let's evaluate all the terms using your values for i1, i2 and i3, using the fact that ua = 10*(i1-i2), ib = i3-i2
Listing the results, I get:

-25 = -25
30*i3 = 87.352941
5*ua = 108.82353
20*ib = 98.235294
ua = 21.764706

These add up to 291.176471, not zero

Something goes wrong in your last calculation The Electrician. See post no.17 for i3 and ib values.

Something goes wrong in your last calculation The Electrician. See post no.17 for i3 and ib values.

I missed the minus sign on i3 in post #17. You had i3=-2.9117647 A.
I think it helps to leave spaces in appropriate places like this: i3 = -2.9117647 A

So I'll redo the calculation:

Check -25+30*i3+5*ua+20*ib+ua, has to be 0.

OK, let's evaluate all the terms using your values for i1, i2 and i3, using the fact that ua = 10*(i1-i2), ib = i3-i2
Listing the results, I get:

-25 = -25
30*i3 = -87.352941
5*ua = 108.82353
20*ib = -18.235294
ua = 21.764706

These add up to .000001, essentially zero.

For any value of i1, a value of i3 = -27/10 - (6*i1)/5 gives a value of zero. However, this is only the solution to one equation, and not a solution to the complete network. It is also necessary to satisfy the equation 3ib = i1-i3, but you assumed i1=3*ib-i3, which is incorrect.

Here are two solutions:

Unfortunately, the second one is incorrect.

It has to be a conventional rule in order to state if i1=3ib-i3 or 3ib=i1-i3
since i1 and i3 are virtual [ghosts] but 3ib it is a concrete one.
Since I am only an engineer –master it does not help here, I think-and not a professor
I get the professors’ opinion.

It has to be a conventional rule in order to state if i1=3ib-i3 or 3ib=i1-i3
since i1 and i3 are virtual [ghosts] but 3ib it is a concrete one.
Since I am only an engineer –master it does not help here, I think-and not a professor
I get the professors’ opinion.

The branch current 3ib is clearly composed of some combination of the loop currents i1 and i3.

The loop current i1 is in the same direction as the 3ib source current, and i3 is in the opposite direction, thus 3ib = i1 - i3.

Post #23 indicates that simulation gives the same result as assuming 3ib = i1 - i3.

## 1. What is arbitrary current in mesh analysis?

Arbitrary current in mesh analysis is a method used to analyze electric circuits by dividing them into smaller loops, or meshes, and applying Kirchhoff's voltage law to each mesh. It allows for the calculation of unknown currents in a circuit based on known voltages and resistances.

## 2. How is arbitrary current different from conventional current in mesh analysis?

Conventional current refers to the flow of positive charge, while arbitrary current refers to the direction of current chosen for convenience in the analysis. In mesh analysis, the direction of arbitrary current is chosen to simplify the calculations and does not necessarily reflect the actual flow of charge in the circuit.

## 3. When is arbitrary current used in mesh analysis?

Arbitrary current is used in mesh analysis when analyzing complex circuits with multiple loops. It allows for a systematic and organized approach to solving for unknown currents and provides a more accurate analysis compared to other methods.

## 4. How is arbitrary current determined in mesh analysis?

The direction of arbitrary current is chosen by the analyst and is represented by an arrow in the mesh diagram. The direction of the arrow is typically chosen to flow in a clockwise direction, but it can be chosen in any direction as long as the same direction is consistently used for all meshes in the circuit.

## 5. What are the limitations of using arbitrary current in mesh analysis?

One limitation of using arbitrary current in mesh analysis is that it may not accurately reflect the actual direction of current flow in the circuit. Additionally, it can become more complex and time-consuming to solve for unknown currents in circuits with a large number of meshes. Furthermore, arbitrary current may not be suitable for circuits with non-linear elements, such as diodes and transistors.

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