Network analysis using the superposition theorem?

In the superimposition process, the flows of the individual sources are calculated. For this, only one source is always activated or the remaining disabled.

In this case, the voltage source is short-circuited or replaced by a short-circuit bridge, while the current source is switched to idling or is operated open, but all stepwise and individually.

The task is to determine the voltage U between AB, i.e. U_AB.

In the first step (photo), as you can see, you decided to remove the power source first. Now only Uq1 is active. The desired voltage is obtained in this circuit:

You simply get the total current out by determining the overall resistance of the circuit:

The indices of resistance may be helpful to you for understanding, but without indices the equation is simplified as there are only “R” or multiple of it. Here only as an example:

Now you have all known sizes and can calculate U_AB. This is U_AB_1. The 1 is active for the network 1 with only Uq 1 .

Now you start the circuit in the same way, only that now Uq1 is replaced by a short circuit and the current source Iq2 is activated.

Here, the desired voltage U_AB_2 results as follows:

Reminder: R2 = R

So you lack the current I2 and you gave the total current Iq2. Here you can work with the power divider. For thought help:

viewed from the right, a part of the current flows through the first resistor R4, the other part flows through R3. This current flowing through R3 is the total current for the left current divider consisting of R1 and R2.

Used on the circuit:

After conversion:

How do you get to I3? By applying the same principle and combining resistors R1, R2 and R3. This results in a parallel connection of R123 and R4. Here you turn on the power divider again.

With the power divider, where now Iq2 is the total current:

Now, if you put Iq2 in your equation for I2, you will come up with:

You can now use this in your equation for U_AB_2.

With this, you have now determined the voltage U_AB once originating from Uq1 and once originating from Iq2.

You’re overlaying these tensions.