bob012345 said:
I tried this several times. It’s three times the work and I never got the right answers! I think it’s better to include the sources in the original loop equations.
There are several different methods to solve circuits like this. So EEs use the ones they are most comfortable with. You may need to practice other methods to become proficient. The "best" method depends on the problem, the methods you know, and your preferences.
The superposition method is shown below. It looks a bit laborious because I drew out every step. In practice we would do most of this in our head since each case is simply a voltage divider. Especially in this case since we can combine R2 and R3 and move the voltage sources all to the bottom which results in symbolically identical branches. You really only need to solve 1 case and then interchange the component names for the others (always look for and exploit symmetry if you find it).
I usually prefer source transformations, depending on the network, of course. That method looks like this. I've drawn this one the way I actually would in practice, skipping steps.
I usually prefer these more graphical transformations to purely algebraic solutions because shorter equations are less error prone, common terms often appear that make calculation easier, and (most importantly) you get a little insight into how the network works, not just what the answers are. This latter point is important in the real world of design where the process works in reverse; you know what you need and have to choose the network/values to achieve that.
For example, this network is part of the most common summing amplifier circuits and these methods yield the easy approach to understanding and designing them. So how hard would it be if I asked you to add a 6th input to the summer below, or increase the gain in channel 4 by 20% without changing the other channels? Would you have to start over, or just adjust a few things?
