Wye-Delta and Series-Parallel Circuit Problem

[terryds]

Homework Statement

Determine the equivalent resistance and the total current!

Homework Equations

Ohm's Law
Wye-Delta Transformation

The Attempt at a Solution

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I do the series on 10 ohm, 5 ohm, 3 ohm resistors, because it is node e-g,g-h,h-f, so it becomes 18 ohms (e-f). Then I do the parallel 18 ohms // 4 ohms = 3.272 ohms (node e-f).

Then, I do the series 8 ohms with 3.272 ohms then parallel it with 0.0263 ohms. Let's call this result R_a (node d-f)
Also, I do the series 2 ohms with 60 ohms then parallel it with 0.0526 ohms. Let's call this result R_b (node c-d)

Then, I do the series R_b with R_a = R_c (node c-f) which is parallel to 0.3157 ohms.

After doing the parallel calculation, I do the series with 4 ohms.
But, it turns out that it is wrong answer.

The question is: Where did I get wrong? Please help. (I already know the correct answer and the correct step; but I still couldn't understand where I got wrong)

 

[lewando]

I do the series on 10 ohm, 5 ohm, 3 ohm resistors...

These three resistors are not in series. The 5 ohm and 3 ohm are in series.

 

[terryds]

These three resistors are not in series. The 5 ohm and 3 ohm are in series.

Alright, I understand!
It seems that I can't make it series because the current at 10 ohm is different than 5 ohm and 3 ohms!

 

[scottdave]

To start, yes the 3Ω and 5Ω are in series, because at node h, ther is only one way for current to flow, but you cannot say the same about these two and 10Ω, because at node g, current has two directions it can flow. That is how you can make decisions if a resistor (or equivalent resistance) is in series with another resistor.

 

[scottdave]

One option, would be to treat the 4Ω, 8Ω and 10Ω a Y, and turn that into an equivalent Delta, then proceed with those equivalents.