Applying 2nd Kirchhoff's Law in Electrical Circuits - Homework Practice

[Jhenrique]

Homework Statement

Apply the 2nd Kirchhoff's law in:

Homework Equations

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!?

 

[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.

 

[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.

 

[Jhenrique]

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

and if v₁ < v₇ so this scheme is valid:

 

[Jhenrique]

OR

for v₁ > v₇ the correct is:

and v₁ < v₇ is:

?

 

[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.

 

[Jhenrique]

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.

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

 

[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

 

[Jhenrique]

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

Your approach is very interesting!

 

[dauto]

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

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

 

[Jhenrique]

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

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!

 

[dauto]

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!

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

 

[Jhenrique]

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

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...