The current in a circuit using nodal analysis

• Engineering
• Gliese123
In summary: Can you please elaborate on how you would go about simplifying the circuit?eq2: V=Io*ReqSo using ohms law the current through R iseq3: I1=V/R1so combining eq2 and eq3 we getI1=Io*Req/R1so generally we get an equation for current division. In any system comprised of parallel resistors and a current source, you can find the resistance through any of the paths by using the following equationIx=Io*Req/Rxdoes that make sense?
Gliese123

Homework Statement

Hi!

"Write an equation for I1."

Here is the circuit:

That is the question. I suppose one could do this many ways but I've decided to do it with nodal analysis. The problem here is that we only got an ideal current source. I have actually no clue.

So, I'd try to apply Kirchoff's Current Law to do this.

KCL:
∑ Ii = 0

The Attempt at a Solution

I know that one is to pick a ground node somewhere. Let's pick the lower one for example.
Then one is to identify all nodes, in this case there are just another one.
Then what? Sorry but my teacher isn't very good at explaining this, at least not so I'd understand.

Am I correct if I'm to assume that an ideal current source and a parallell resistance R could be simplified to just an ideal current source?

If one is to apply KCL then it would maybe be something like:

Am I on the right track? Some general advice to do this smooth is worth it's weight in gold!
Thank you! :D

The right answer for this question is: I1 = -R2I0/R1+R2

Last edited:
You seem to be on the right lines. Perhaps remember the voltage will be the same across all three devices as they are in parallel. Should give you some more equations.

Sorry I might not be around to follow up.

CWatters said:
You seem to be on the right lines. Perhaps remember the voltage will be the same across all three devices as they are in parallel. Should give you some more equations.

Sorry I might not be around to follow up.
Ahh, thanks for replying anyway :) The current is so strange. My teacher said that it's good to imagine it like water and water tubes but I don't know how that would help me with the mathematical part. Lol.

Gliese123 said:
Ahh, thanks for replying anyway :) The current is so strange. My teacher said that it's good to imagine it like water and water tubes but I don't know how that would help me with the mathematical part. Lol.

water through tubes is a good analogy. If 1 gallon of water passes through a pump (your current source) in 1 second and splits and goes through 2 pipes (R and R2), you know that the sum of the water that passes through the 2 pipes in that 1 second will be 1 gallon.

donpacino said:
water through tubes is a good analogy. If 1 gallon of water passes through a pump (your current source) in 1 second and splits and goes through 2 pipes (R and R2), you know that the sum of the water that passes through the 2 pipes in that 1 second will be 1 gallon.
Hi donpacino! :)
I've got the idea of it clear however how do the calculus...

Gliese123 said:
Hi donpacino! :)
I've got the idea of it clear however how do the calculus...

haha. okay!

so first I can tell you your answer is not correct :(
------------------------
The solution:

first look at ohms law
V=IRwe know the voltage across all three components are the same. we can find that voltage by taking the current through the current source (Io) and multiplying it by the equivalent resistance of the two resistors.

eq1: Req=____

i'll let you solve that. hint: they are two resistors in parallel

eq2: V=Io*Req

so using ohms law the current through R is

eq3: I1=V/R1

so combining eq2 and eq3 we get

I1=Io*Req/R1

so generally we get an equation for current division. In any system comprised of parallel resistors and a current source, you can find the resistance through any of the paths by using the following equation

Ix=Io*Req/Rx

does that make sense?

edit: in your case due to the direction of current your I1 will be inverted
also if you really wanted to do it through nodal analysis, you would need 2 equations

nodal analysis

Io=V0/R+Vo/R2
Vo/R=I1

donpacino said:
haha. okay!

so first I can tell you your answer is not correct :(
------------------------
The solution:

first look at ohms law
V=IRwe know the voltage across all three components are the same. we can find that voltage by taking the current through the current source (Io) and multiplying it by the equivalent resistance of the two resistors.

eq1: Req=____

i'll let you solve that. hint: they are two resistors in parallel

eq2: V=Io*Req

so using ohms law the current through R is

eq3: I1=V/R1

so combining eq2 and eq3 we get

I1=Io*Req/R1

so generally we get an equation for current division. In any system comprised of parallel resistors and a current source, you can find the resistance through any of the paths by using the following equation

Ix=Io*Req/Rx

does that make sense?

edit: in your case due to the direction of current your I1 will be inverted
also if you really wanted to do it through nodal analysis, you would need 2 equations

nodal analysis

Io=V0/R+Vo/R2
Vo/R=I1
eq1: Req=____

i'll let you solve that. hint: they are two resistors in parallel

Hmm. Let's see. We have a ideal current source and the current is splitted up like the water tubes we mentioned earlier. If I ain't misstaken one should use current division rules, obtain that very current through that resistance - in this case R (which is where I is) and then use ohm's law on that very place?

So if I0 is the total current and I1 is the sought current, then:

I0 = RI/R2+R which is that very current. Now if I ain't completely lost we could take that whole formula and *bang* - use ohm's law? Or do I even want that? I'm so lost. hahha xD
:D

Seems like nodal analysis in this particular assignment is as wasteful as putting a V8 into a Smart car?
hahah. It's basicall just one thing to do correct?

HOWEVER since the current that is asked for is pointed at the opposite direction, it should therefore be negative correct? I just want be certain of what I do ;)

I think you have a fundamental misunderstanding of how this works.

First you would write the Kcl
I1=current through R
I2=current through R2
Io=source current

Io+I1+I2=0

then find an expression for Vo
I1=-Vo/R
I2=-Vo/R2
Io=-Vo/R-Vo/R2

then solve for Vo
Vo=-Io/(1/R+1/R2)
Vo=-Io*R1*R2/(R1+R2)

then solve for I1
I1=Vo/R
I1=-Io*R2/(R1+R2)

if you were to solve it using the equation i gave you
1/Req=1/R+1/R2
1/Req=(R+R2)/(R*R2)

then plug it into the equation
I1=-Io*R2/(R1+R2)

donpacino said:
I think you have a fundamental misunderstanding of how this works.

First you would write the Kcl
I1=current through R
I2=current through R2
Io=source current

Io+I1+I2=0

then find an expression for Vo
I1=-Vo/R
I2=-Vo/R2
Io=-Vo/R-Vo/R2

then solve for Vo
Vo=-Io/(1/R+1/R2)
Vo=-Io*R1*R2/(R1+R2)

then solve for I1
I1=Vo/R
I1=-Io*R2/(R1+R2)

if you were to solve it using the equation i gave you
1/Req=1/R+1/R2
1/Req=(R+R2)/(R*R2)

then plug it into the equation
I1=-Io*R2/(R1+R2)
Thank you! Yes it seems I have misunderstood. I have just started with this so it's a quite complex for me. However I think I know what I need to do to make it work.

1. What is nodal analysis and how is it used in circuit analysis?

Nodal analysis is a method used to analyze electrical circuits by applying Kirchhoff's Current Law (KCL) at each node or connection point in the circuit. It is a systematic approach that allows us to calculate the currents and voltages at each node in order to determine the behavior of the circuit.

2. What are the advantages of using nodal analysis over other methods of circuit analysis?

Nodal analysis allows for a more organized and systematic approach to circuit analysis, making it easier to solve complex circuits. It also takes into account the direction of currents, making it more accurate. Additionally, nodal analysis can be used for both DC and AC circuits.

3. How do you determine the number of equations needed for nodal analysis?

The number of equations needed for nodal analysis is equal to the number of nodes in the circuit minus one. This is because KCL can be applied at all nodes except for one, which can be used as a reference node with a known voltage or ground potential.

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

Yes, nodal analysis can be used for circuits with voltage sources. The voltage sources are considered as known values and can be used in the equations to solve for the unknown voltages at each node.

5. Are there any limitations to using nodal analysis?

One limitation of nodal analysis is that it can become time-consuming for larger circuits with a large number of nodes. In these cases, other methods such as mesh analysis may be more efficient. Additionally, nodal analysis assumes ideal components and does not take into account non-linear elements such as diodes and transistors.

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