# 2nd Kirchhoff's law

1. Jun 8, 2014

### Jhenrique

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

Apply the 2nd Kirchhoff's law in:

2. Relevant equations
3. The attempt at a solution

$V_1 = V_3 + V_5 + V_2$

$V_7 = V_4 + V_5$

$0 = V_2 + V_4 + V_6$

$V_1 + V_7 = V_3 + V_6$

All right!?

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2. Jun 8, 2014

### dauto

No, not all right. You have to chose a direction for the Voltage drops V2, V3, etc. and then be consistent with that choice through out the equations. Some of the terms will inevitably end up with a minus sign attached to them.

3. Jun 8, 2014

### dauto

Also, Application of Kirchhoff's 2nd to that circuit produces only three independent equations. You wrote down four equations. Even after fixing the signs one of those equations will be useless. Correct but useless.

4. Jun 8, 2014

### Jhenrique

hmm... if v1 > v7 so this scheme is correct:

and if v1 < v7 so this scheme is valid:

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5. Jun 8, 2014

### Jhenrique

OR

for v1 > v7 the correct is:

and v1 < v7 is:

?

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6. Jun 8, 2014

### dauto

Don't waste time trying to guess the direction of the currents. Just chose one that seems reasonable. If you make a mistake somewhere, it is a self correcting mistake because the solution for those currents that were chosen in the wrong direction will turn out to be negative numbers indicating that the current is in the opposite direction.

7. Jun 8, 2014

### Jhenrique

Ok... so why the my equations in the 1st post are wrong?

8. Jun 9, 2014

### baby_1

Dear Jhenrique
for writeing KVL equation at first you should define the direction of current or voltage of each element.it depends on you how you can assume the element voltage or current sign or direction.for example i set the voltage sign in this form

now for first loop we write KVL
-V1+V2+V5-V3=0
and for third loop we have
-V7-V4+V5=0

above equations were an example of setting voltage signs.after set the voltage sing and write KVL equation you should solve them.i assume that we find V5=2 and V3=-1 so the circuit could be same as this

or combine the sign of voltage that specified and the sign of voltage that you obtain. redraw the circuit like this

Last edited: Jun 9, 2014
9. Jun 9, 2014

### Jhenrique

10. Jun 9, 2014

### dauto

I said don't waste time guessing the direction of the currents. Just chose one. Your 1st post is wrong because you didn't chose a direction

11. Jun 9, 2014

### Jhenrique

I found another way more easy of solve it (my ideia isn't solve the problem, is understand the dynamical of the electrical circuit)

if I apply the hydraulic analogy like this video:

and the superpostion theorem:
http://en.wikipedia.org/wiki/Superposition_theorem

together with KVL
$\oint \vec{E} \cdot d\vec{s} = 0$

in this case:

and choose a mesh and a sense of circulation, so the "ramps" (source or resistor) would have positive voltage and the declivities correspond to negative voltage!

Last edited by a moderator: Sep 25, 2014
12. Jun 9, 2014

### dauto

Yes, that's the way to solve the problem. Guess what you will get out of it. Yes, you get Kirchhoffs' laws. No kidding...

Last edited by a moderator: Sep 25, 2014
13. Jun 10, 2014

### Jhenrique

The 2nd Kirchhoff's law is quite elaborate! I never would understand the ideia, the principle, the fundament, the dynamical of the thing if I hadn't watched the caltech's video...