Current Source and Short Circuit
Is it correct to split the circuit in the following way (I always did it when there was a short circuit, but I do not know if it works with current sources)

I was always told that when two circuits are connected with only a node (and this is the case, since there is the short circuit), they can be separated because the current of the first does not go to the second and vice versa

Lets check some scenarios in ideal conditions.

CIRCUIT WITH TWO VOLTAGE SOURCES:


Suppose the circuit looked like this:








simulate this circuit &ndash; Schematic created using CircuitLab

Since V1 has one node unconnected, it drives no current in this circuit because the current can have no closed path for that source. Only V2 wil be driving current in the circuit.

So, you can remove it and analyse the rest of the circuit:







simulate this circuit

You can remove R3 as well from here while analysis because no current passes through it.


Consider the case when the same source was shorted instead of open:








simulate this circuit

Here, V1 gets shorted and therefore the equivalent circuit becomes:







simulate this circuit

V1 drives no current on those resistors, only V2 does. 

Seems like your taught idea of 'separating the source' works in both cases. However it is better to understand - why it works. 

Next set of scenarios.

VOLTAGE SOURCE V1 REPLACED WITH CURRENT SOURCE:


Case where current source has one node unconnected:








simulate this circuit

Here, the current source will drive no current in the circuit and hence it can be removed and analysed:







simulate this circuit

R3 can be removed too. This is similar to the first case we discussed before.


Case when current source is shorted (which you are interested in):








simulate this circuit

Here, whatever current is generated by the current source will pass only through the short, which is being the least resistance or ideally zero resistance path. The current source hence doesn't drive any current in any of those resistors. However V2 is driving them. So if you want to analyse currents or voltages across those resistors, you can 'separate' the current source away and analyse with the seemingly equivalent circuit:







simulate this circuit

But what if you were asked to calculate the current \$I_{sc}\$ through the 'short' ? Do we need to consider only the seemingly equivalent circuit ?







simulate this circuit

If you calculate it only using our seemingly equivalent circuit, you will get only a part of current driven through it. The part driven by V2.
Or in other words, you cannot just remove current source away from the picture. Because the current through that 'short' is driven by current source as well as V2 source. You have to consider the part driven by the current source as well. The net current \$I_{sc}\$ will be the sum of currents driven by both the sources.

This is what superposition theorem is all about. You can use KVL to analyse the whole circuit, however superposition theorem greatly simplifies these linear circuits with multiple sources.