Help me with nodal analysis equations

[BlackOps]

Nodal Analysis

Hello, i must find V2, usind Nodal Analysis here:
**broken link removed**

so..i began to write down the KCL equations:

V1/20 + (V1 - V2)/40 = 10

V2/100 + (V2 - V3)/50 = (V2 - V1)/40

(V3 - V2)/50 + (V3 - V4)/10 = 2 - 2.5

V4/200 + (V4 - V3)/10 = 5 - 2


then i solved these simultaneous equations and didnt get correct result, error is not in solving..but probably in equations. so can u help me to write down Correct equations, and say me where i was wrong when i was writing those equations?

 

[field_catcher]

Re: Nodal Analysis

The second equation is wrong, it should be:
V2/100 + (V2 - V3)/50 + (V2 - V1)/40 =0.

Be careful about current direction.

 

[BlackOps]

Re: Nodal Analysis

solved the equations..well, now the answer is correct.

but i dont understand second equation!!!

from it i can conclude that currents are only entering node from three resistors! but it is not possible... can u explain second equation to me?

 

[cedance]

Re: Nodal Analysis

solved the equations..well, now the answer is correct.

but i dont understand second equation!!!

from it i can conclude that currents are only entering node from three resistors! but it is not possible... can u explain second equation to me?[/quote

that is coz,

V1/20 + (V1 - V2)/40 = 10 ---- 1

V2/100 + (V2 - V3)/50 = (V2 - V1)/40 ------- 2

(V3 - V2)/50 + (V3 - V4)/10 = 2 - 2.5

V4/200 + (V4 - V3)/10 = 5 - 2

in 1, from the equ. written, current of V1 is downwad and that of the branch connecting V1 and V2 is from V1 to V2... so always whatever branch u are goin to take in the future.. u can not change this assumed direction.. so.. what u can say is, the current floes from left to right for branch having V1 and V2 vol. and it is V1-V2/40.

condsidering equ 2. v2/100 => downward cur. dir.

v2-v3 / 50 => from left to right.

but those 2 are outgoin currents.. and u have assumed ur direction of V1-V2 loop to be left to right whiuch says, its into the branch/node for this particulare node.. so its..

V2/100 + (V2 - V3)/50 = (V1 - V2)/40 its just the same current.. only incoming = outgoing..

Hope it helps.. in case of any confusiioons.. pls revert back..

/Am

 

[BlackOps]

Re: Nodal Analysis

Yes, that explanation helped me!
So..now i understood that for Nodal Analysis, one of the main things is to
discover the directions of all currents right.

thanx

 

[picus]

Re: Nodal Analysis

Where can I find
documentation on Nodal Analysis

 

[BlackOps]

Re: Nodal Analysis

picus, best book about circuit analysis is, Engineering Circuit Analysis, by Hayt and Kemmerly

 

[cedance]

Re: Nodal Analysis

picus, best book about circuit analysis is, Engineering Circuit Analysis, by Hayt and Kemmerly

i found the book "fundementals of electric circuits" by "alexander and sadiku" very useful for me... especially for nodal analysis and theorems...

its even available here! u could have a look at it.. also this one which icould never compromise.. right from the basics to the extreme! one of the best!



good luck!

/Am

 

[BlackOps]

Re: Nodal Analysis

Hi, can u help me to find V, using nodal analysis...well there are 3 nodes...there must be 2 equations, but i dont know which node to choose as a reference node..

can u please write down KCL equations for this circuit.

thanx
**broken link removed**

 

[cedance]

Re: Nodal Analysis

25 parallel with (17+3) is the equ resistance of upper part.. with thec urrent source.. convert to a voltage source with a series resistor and just include it at the end (may be anywhere) in the lower circuit.. andjust pull the ground upward.. so that ckt is familiar with the whole thing inverted.. look the circuit turning it 90deg. and u ll get an ordinary ckt to solve for.. hope this helps.. any thin to clarify.. reply with ur queries.

/Am

 

[field_catcher]

Re: Nodal Analysis

You can delete the upper part of the circuit, it won't affect the solution for V.

V = (R5||R3) (I3-I2)
= 50 * 2
= 100 v

 

[tyassin]

Re: Nodal Analysis

Hi

If the the voltage is calculated with the sign notation given in figure, then the equation should be:
V = (R5||R3) (I2-I3)
V = -100!

But again it depends on how you place the +\- signs on the resistor, but with the +\- given in the figure the correct answer is V=-100.

 

[BlackOps]

Re: Nodal Analysis

Hi, here is the circuit, where i want to perform Nodal Analysis. Of course this circuit can be simplified by finding equivalent resistances, and no nodal analysis needed. But i want to do it... then strange thing appears.

look at the pic
**broken link removed**

now say me, those nodal equations are right? or wrong? if they areright, then why i dont get correct answers, if they are wrong, then what is wrong with them?

 

[tyassin]

Re: Nodal Analysis

Hi the first and last equations are wrong. There should be a plus(+) instead of a minus(-).

That should do the trick.

Regards

 

[BlackOps]

Nodal Analysis

ok, i changed - to + in first and last equations!

and still dont get correct answers! whats going wrong? i dont have problem with matrix, cuz matlab does it... problem is in equations.... so whats wrong with them now>???? which mistake i did? are those equations wrong again?

 

[umairned]

Re: Nodal Analysis

The second equation is wrong, it should be:
V2/100 + (V2 - V3)/50 + (V2 - V1)/40 =0.

Now solve and chk the answer

 

[aryajur]

Re: Nodal Analysis

I solved the following equations for the circuit:

V1/1250 +(V1-V2)/250 = 0
V2 = 120
(V3-V2)/600 + V3/2000 + (V3-V4)/100 = 0
V4/400 + (V4-V3)/100 = 0


And I get the answer:
V1 = 100
V2 = 120
V3 = 48
V4 = 38.4

What do you get?
Maybe you are writing something wrong in the MATLAB program.

 

[BlackOps]

Re: Nodal Analysis

yes ur answers are correct... hmm...
ok look what i do:

from those equations i get:

V1/1250 +(V1-V2)/250 = 0 *1250
V2 = 120
(V3-V2)/600 + V3/2000 + (V3-V4)/100 = 0 *12000
V4/400 + (V4-V3)/100 = 0 *400

V1 + 5V1 - 5V2 = 0
V2 = 120
20V3 - 20V2 + 6V3 + 120V3 - 120V4 = 0
V4 + 4V4 - 4V3 = 0

6V1 - 5V2 = 0
V2 =120
-20V2 + 146V3 - 120V4 = 0
-4V3 + 5V4 = 0

then i get this matrix:

6 -5 0 0
0 120 0 0
0 -20 146 -120
0 0 -4 5

and i get determinant = 1.8 * 10^5

then i change matrix to:

0 -5 0 0
120 120 0 0
0 -20 146 -120
0 0 -4 5

and i get 1.5 * 10^5

then V1 = 1.5 * 10^5 / 1.8 * 10^5

and V1 is not 100 v... thats it..which error i could do in matlab???

 

[aryajur]

Re: Nodal Analysis

Like I said you are getting the matrices and determinants wrong. Starting from your equations:

6V1 - 5V2 = 0
V2 =120
-20V2 + 146V3 - 120V4 = 0
-4V3 + 5V4 = 0


In Matrix Form we have:

|6 -5 0 0| |V1| |0|
|0 1 0 0| |V2| |0|
|0 -20 146 -120| |V3| = |120|
|0 0 -4 5| |V4| |0|


which is like [C] [V] = [K]

where [C] is the coefficient matrix and [K] is the constant matrix

Now V1 = |C1| / |C|

where C1 is a matrix in which the 1st column has been replaced by the K matrix.

So on solving |C1| = 5(120(146x5 + 480))
|C| = 6x(146x5+480)

And so V1 = 100

Hope you get it this time.

 

[BlackOps]

Re: Nodal Analysis

ahhh.... i just did stupid error and didnt see it...

i wrote 120, instead of 1 ... how stupid.. thanks anyway!