Nodal analysis problem

1. Nov 14, 2015

terryds

1. The problem statement, all variables and given/known data

3. The attempt at a solution

At node B,

$i_s + 3 = i_2$
$3 + 3 = i_2$
$i_2 = 6A$
$V_2 = i_2/R_2 = 3V$

But, it seems that the answer is wrong. Using superposition method, the voltage is 4V
Please tell me where I got wrong

2. Nov 14, 2015

Staff: Mentor

I can't understand your node equation. Can you explain the terms in detail? The current source term is clear, it's a fixed 3 A source, but I don't see any influence from the resistor values.

3. Nov 14, 2015

terryds

The resistor 2 kilo ohms is at the right. Of course, it doesn't influence the independent current source.

I label the three points at the top as A , B , and C. Forget about what Va means. Let's call it Vb since it is on the point B.

At the point B, the current which goes in are the current generated by Vs and $R_1$ and the independent current source. The current goes out from point B is $I_2$.
So,
in=out
$Vs/R_1 + 3 A = I_2$
$3 V / 1 k ohms + 3 A = I_2$
$I_2 = 3 + 3 * 10^-3 A = 3.003 A$
$V_2 = 3.003 A * 2 * 10 ^ 3 = 6006 A$

Which seems a wrong answer... In the book which use the superposition method, the $I_2$ is 1 mA and the voltage $V_2$ is 4 V... Please help me where I got wrong

4. Nov 14, 2015

ehild

The source current is not VsR1. What is the potential difference across R1? Does it not depend on the potential of the node B?

5. Nov 14, 2015

terryds

Hmm.. You're right..

$\frac{V_B-V_A}{R_1}+3=i_2$
$\frac{V_B-V_s}{R_1}+3=i_2$
$\frac{V_B-3}{1000}+3=i_2$
$V_B - 3 + 3000 = i_2$
$V_B - i_2 = -2997$
$V_B -\frac{V_2}{2000} = -2997$

I'm stuck here

How to relate $V_2$ and $V_B$ ?

If I'm not wrong, $V_A$ = $V_B$ = $V_C$ because they are parallel, right ?
And, $V_C$ is $V_2$, so $V_B$ = $V_2$ ???

6. Nov 14, 2015

ehild

If I'm not wrong, $V_A$ = $V_B$ = $V_C$ because they are parallel, right ?
And, $V_C$ is $V_2$, so $V_B$ = $V_2$ ???

No, that is right, VB=V2.

7. Nov 14, 2015

terryds

If it's right, then $V_2 = V_B =V_A = V_S = 3 V$?? But, the answer is 4V

However, by substituting $V_2$ = $V_B$, I get
$V_B - \frac{V_B}{2000} = -2997$
$2000V_B-V_B = -5994000$
$1999V_B = -5994000$
$V_B = \frac{-5994000}{1999} = -2998.49$

which seems to be an impossible answer..

8. Nov 15, 2015

ehild

You have a sign error in the first line. You assumed the current flowing from left to right, that means it is (VA-VB)/R1. The current flows in the direction of decreasng potential.
I think the current is given in mA instead of A, it is 3 mA instead of 3 A.

9. Nov 15, 2015

mpresic

You sure the ammeter is measuring 3 Amperes and not 3 milliamperes

10. Nov 15, 2015

terryds

$\frac{3-V_B}{1000} + 3 * 10^-3 = \frac{V_B}{2000}$
$3-V_B+3=\frac{V_B}{2}$
$V_B = 4 Volt$

Anyway, you haven't answered my question :
Why $V_B$ is not equal to $V_S$ since it is parallel ??

11. Nov 15, 2015

terryds

Maybe it is an error in the book.. It should be 3 miliamps not 3 amps

12. Nov 15, 2015

ehild

V2=VB, but not equal to VA. The source and the R2 resistors are not parallel. When are two elements connected in parallel?

13. Nov 15, 2015

terryds

I think $V_S$ and $I_S$ are in parallel. So, I think VA = VB..
I think two elements connected in parallel means that they are opposite direction..
But, Hmm...
So, the better definition is parallel-connection means that the currents are divided to sections, right ?
So, the voltage source is neither parallel to the current source (vertical line B) nor the R2 (vertical line C), right ?

14. Nov 15, 2015

ehild

Parallel connection of two element means that both terminals of one of them is common with the other one.The voltage is the same across both elements.
Series connection means one common terminal, and nothing else is connected to that. The same current flows through both elements.