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I am learning about source transformations in my circuits class and I had a couple of questions regarding them.

Question 1: Is a source transformation a law? By this, I am asking if I am able to do it at any time and still yield the same results as far as power dissipation, current measurements, voltage drops, etc.

Question 2: Why doesn't this source transformation problem yield the same results? I use source transformations until I had one source and some resistors. Then I used a source transformation and tried keeping it the same; in the end, I got different results. The voltage drops across resistors were correct though.

SourceTransformations CircuitLab

The first three images are just using source transformations to get one power source. Then from 3-4 and 3-5, I tried it with a current source and voltage source and got different results.

But, if I find the voltage across the 8ohm resistor, I find that it is 48V. (Which is what the book says is correct). Is this all that source transformations are good for?

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1) It isn't a 'Law' as much as it is a theorem, specifically Thevenin's theorem, stating that any network of resistors, voltage sources and/or current sources can be represented by a single ideal voltage source with a series resistance. There is also then the Norton equivalent circuit which represents any similar network as a current source and parallel resistance instead.

2) You can use it at any time in the types of network described earlier. The reason you get different answers in #6 and #7 is that you are looking at different things. There are a whole lot of different elements in the circuit which have been lumped together in different ways which are not necessarily related to any particular element in the original circuit. Essentially the idea of the transformation is that you don't care what is going on inside the 'black box', only what effect it has on your load.

To that end, you need to keep your load outside any transformations you do, make all transformations as if the load was just two unconnected terminals - but don't lose track of where those terminals are as at the end you will need to connect them back to your load for analysis. For analysing the 8ohm resistance, you are aiming to get circuit #5 as it essentially boils the circuit down into a potential divider.

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You are getting different answers because you are measuring different things. 'R27' and 'R31' are not the same equivalent resistance. The current path through R27 does not exist in the original circuit, but the current path through R31 is equivalent to the path through R4/R5.

If you take the 57.6V across R27 and you apply that across R22 and R23, then you see that the current through R22 and R23 is 57.6/(1.6+8) = 6 amps, which is the same as the current through R31.

The thing to remember with source transformations is that you are swapping a Thevenin and a Norton equivalent circuit. These circuits have a pair of terminals that connect the 'source' to the 'load'. If you remove the terminals (as in #6 and #7) then you get a nonsensical result because the voltage or current path does not correspond to anything in the original circuit. Basically, you need to keep R30 in #5 and R21 in #4 and not combine these with the other resistors. R22/R23 and R25/R26 correspond to R4/R5 in the original circuit. If you combine these with your Rt, then you may not get a usable result.

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