Calculating Total Resistance in a Circuit: Delta - Y Formula or Simpler Method?

[songoku]

Homework Statement

(See picture below)

Find current flowing through 14 - ohm resistor

Relevant Equations

V = I.R

Series and parallel combination

Delta - Y configuration?

To find total resistance between 22 Ω, 14 Ω and 4.5 Ω should I use delta - Y formula? Or there is other simpler way?

Thanks

 

[BvU]

Don't let yourself be fooled: Redraw with the 22 $\Omega$ and 14 $\Omega$ upright.

 

[haruspex]

Don't let yourself be fooled: Redraw with the 22 $\Omega$ and 14 $\Omega$ upright.

... which can be done by a combination of shrinking a zero resistance wire down to a node and expanding a node into a zero resistance wire, both of which are always legal.

 

[songoku]

Don't let yourself be fooled: Redraw with the 22 $\Omega$ and 14 $\Omega$ upright.

... which can be done by a combination of shrinking a zero resistance wire down to a node and expanding a node into a zero resistance wire, both of which are always legal.

My god, it will only be parallel then series then parallel again.

Let say I want to continue my foolish idea. Can it be done using delta - Y formula?

Thanks

 

[BvU]

You can always try -- and checking the answer is easy now that you have it

 

[songoku]

You can always try -- and checking the answer is easy now that you have it

I got different answers. Why can't I use delta - Y formula?

Thanks

 

[DaveE]

The problem with a wye-delta transform is that you are transforming the resistor in question, the 14 ohm resistor will no longer be 14 ohms and it's current will be different. You will get a solution to the equivalent network, and the currents in the branches outside of the delta will be correct. But you will then have to transform back to delta to find the current in the 14 ohm resistor.

Plus, it's not clear to me the one version is any easier to solve than the other.

 

[cnh1995]

Why can't I use delta - Y formula?

You can. We can't see what went wrong unless you post your work.

Also, your original series-parallel reduction method is much easier and less error-prone than the delta-Y method.
Nevertheless, it is good to try different methods and verify your answer.
Please post both your solutions so we can point out the error.

 

[songoku]

I understand.

Thank you very much for the help BvU, haruspex, daveE, cnh 1995