Help please! I am so confused! How can i find Rtotal in this circuit??


Joined Mar 31, 2012
The Δ↔Y transforms can certainly be useful, but unless you happen to be doing things that involve using them on a very regular basis you are unlikely to remember them accurately and so will usually have to look them up when you want to use them. That, plus the fact that that there is a non-trivial amount of overhead involved in applying them (with the consequent opportunities for making silly mistakes), they are seldom worth using for the types of simple circuits you will normally need to deal with.

In general, you will be better served by cementing the basic, fundamental analysis techniques so that when you see a problem like this your natural thought processes might be something like:

1) Can I reduce this exploiting symmetry arguments?
2) Can I reduce this using series-parallel combinations?
3) Can I analyze it by applying a test source, calculating the resulting test current, and taking the ratio?
4) Can I reduce it using Δ↔Y transforms.

In this case, with arbitrary resistor values, the answers to #1 and #2 are no. But the answer to #3 is a resounding Yes and there are several techniques that can be used, including a rather slick approach using Thevenin's Theorem. Only after you conclude that none of these are reasonable alternative, should you normally resort to the transforms.

Which is NOT to say that you shouldn't understand where those transforms come from and how to use them, just that you will be better served by being able to draw upon a sound foundational understanding of the fundamentals rather than looking up recipes for how to solve specific problems.