Is my method of solving this correct? Superposition theorem

[arhzz]

Homework Statement

Solve for the current Ik

Relevant Equations

Superposition theorem

Hello! Consider this circuit

Now I want to calculate the current Ik. The values are given as follows;

Uq1 = 12 V
Uq2 = 18V
R1 = R2 = 8 Ohm
R3 = R4 = 20 Ohm

My approach was using the Superposition theorem. First I deactived Uq2 and left Uq1 active.

Now if I am not mistaken the resistors R2 R3 and R4 should be short circuited since the current will go through the 0 Ohm wire. That would mean that the current can simply be calculated

$$ I_k' = \frac{U_{q1}}{R1} $$ that should be $I_k' = 1,5A$

Now if we deactivate Uq1 and leave Uq2 only R2 should remain,the rest should be short circuited.

$$ I_k'' = \frac{U_{q2}}{R2} $$ that should be $I_k'' = 2,5 A$

Now we can simply add these two together but I think that the direction of $I_k''$ is opposite of Ik since drawn in the picture,since the current is flowing in the opposite direciton of where the arrow at Uq2 is pointing,that will mean that they will colide so it should be -2,5A

That gives us $I_k = 1,5 - 2,5 = 1,5 A$

Now I am not sure if the way I solved it was correct.Are my assumptions that the resistors are short circuited correct?
If not how could I solve this otherwise?

Many thanks!

EDIT: I just realized that I input the wrong value for Uq2; its not 18V but rather 20V.

Also the value for $I_k$ is also wrong it should be $I_k = -1A$.

 

[gneill]

Your method is correct, but verify your calculation of the value for $I_k''$ .

 

[anuttarasammyak]

Kirchhoff’s law would verify your method.

 

[arhzz]

Okay I've made a few errors I need to clear up; I edited my post(1st one) I input the wrong value for Uq2 and also 1,5-2,5 is -1 not 1,5.

For clarification, which Kirchofff's law are you implying? The one for currents one for voltages?

 

[anuttarasammyak]

We need the both to explain your method.

 

[lewando]

What is the significance of the arrows on your voltage sources?

I assume they indicate polarity, but I am unfamiliar with this notation. Which terminals of the sources have the higher potential?

 

[DaveE]

What is the significance of the arrows on your voltage sources?
View attachment 293203
I assume they indicate polarity, but I am unfamiliar with this notation. Which terminals of the sources have the higher potential?

I assumed they were current sources because of those arrows. Clearly they are voltage sources by the values. That notation means the positive side is at the pointy end of the arrow. I HATE that style, but it is out there.

 

[lewando]

That notation means the positive side is at the pointy end of the arrow.

If that is the case, then I question the direction of $I_k'$ result.

 

[arhzz]

That style is common in the country I live in.Basically it means that the current flowing out of that voltage source is going in the opposite direction of where the arrow is pointing.That would mean that in #I_k'## scenario the current would flow in the same direction as Ik is drawn in the circuit.Should be positive right?

Also what does both mean? I've never heard that word before

 

[lewando]

I am trying to find an independent reference for this symbol convention--in which countr(y/ies) is this symbol common? Also can you respond to the following question?

Which terminals of the sources have the higher potential?

"Both" is a way of emphasizing or referring to a union of two things. As in "both A and B". It can seem superfluous sometimes. In this case:

We need the both to explain your method.

They mean simply "both" or "the both of them". Possibly a typo for "them both".

 

[lewando]

it means that the current flowing out of that voltage source is going in the opposite direction of where the arrow is pointing.

What confuses me with this convention is how one would know which way the current is flowing through a voltage source unless one figures it out by actual circuit analysis. It is especially not obvious in multi-source circuits. Out of pure curiousity, what symbolic convention do you use for a current source?

 

[gneill]

While at school I was introduced to several conventions for source representations. This "arrow beside a circle" was one such. The arrow is meant to represent the direction of increasing electric potential, and is not necessarily indicative of the direction of current flow.

We've all seen cases where in a given circuit the current is made to flow into the "positive" terminal of a voltage source due to influence of other sources. In fact, this is how (appropriate types of) batteries are recharged.

 

[anuttarasammyak]

Please find attached the sketch for the investigation.

$$-U_{q1}+R_1I_1+0I_k=0$$
$$-U_{q2}+R_2I_2-0I_k=0$$
$$I_1-I_2=I_k$$
with upward direction positive for $I_k$ .

 

[The Electrician]

That style is common in the country I live in.Basically it means that the current flowing out of that voltage source is going in the opposite direction of where the arrow is pointing.That would mean that in #I_k'## scenario the current would flow in the same direction as Ik is drawn in the circuit.Should be positive right?

Also what does both mean? I've never heard that word before

There was quite a discussion about the arrow meaning here: https://www.eevblog.com/forum/beginners/mesh-analysis/msg1106528/#msg1106528

 

[DaveE]

The more you look into this, the better you'll understand why I HATE this convention. Arrows for current, and +/- for voltage works pretty well. Anything else and your likely to have to explain it to someone (like me). Also, thanks to Ben Franklin, the current arrow points in the direction the electrons do not go, everyone agrees with that convention.

Also, I retract my previous vote. I'm now convinced that there is no standard for polarity of voltage sources labeled only with arrows. I can pretend to know the answer, but if enough people disagree, then I think there is no standard. You'll just have to ask.

 

[arhzz]

Well I hope everything is cleared up.I've asked my professor since I really was not sure and he says that all of my steps were legit.

As for what countries is that symbol common? Austria (where I live) and I think in Germany as well as Switzerland (so German speaking countries mainly)

What symbol we use for a current source? If its DC this one;

If its Ac than the straight line across the circle is wavy.

Thanks for the help as always!