A black box with three terminals contains three equal resistors of unknown value, connected either as a delta or as a wye.

physics/black.box New

New entry, edited from material collected for the archive and not yet in a released version.

Problem

A black box with three terminals contains three equal resistors of
unknown value, connected either as a delta or as a wye.  Can you tell
which by measuring resistances at the terminals?

[ Editor: problem statement reconstructed from the postings. ]

Show solution

"Fritz Whittington" <fritz@ti.com> wrote:

>This has gone on so long with so many conflicting answers, and I can't
>understand why it's so difficult.

It's not difficult, it's impossible.

>It takes two simple resistance measurements, and for sake of example
>I'm going to assume a resistance value of 10 ohms.  This doesn't
>invalidate the method, just makes it easier to follow along.  In fact,
>after determining the configuration, you will also have determined the
>resistance value used.

>MEASUREMENT 1:  Measure the resistance between any two terminals.  If
>it's a Wye, this will be 20 ohms,

Right. Two ten ohm resistors in series with the third resistor out of
the circuit = 20 ohms.

>if a Delta, 10 ohms.

Wrong. This is where your argument falls to pieces. If a delta, 10 ohms
is in parallel with 20 ohms. The product over the sum = (20 x 10)/30 =
6.667 ohms (six and two thirds ohms).

>MEASUREMENT 2:  Short any two terminals together, and measure the
>resistance to the third terminal.  If it's a Wye, this will be 15 ohms,

Right. Two 10 ohm resistors in parallel = 5 ohms. This in series with 10
ohms = 15 ohms.

>if a Delta, 5 ohms.

Right. Two 10 ohm resistors in parallel = 5 ohms, with the third
resistor out of the circuit.

>Examine the ratio of measurement 1 to 2.  It must be either 4/3, or
>2/1.  If 4/3, then it's a Wye; if 2/1, a Delta.

The ratio will be 4/3 either way. 20/15 = 4/3, and 6.6667/5 = 4/3.

>So, not knowing the resistance beforehand is no problem.

Believe me, it is. I even built a pair of these just for fun, using
three 30 ohm resistors in a delta, and three 10 ohm resistors in a wye.
I then hid the resistors under some tape so that only the three leads
were accessable in each case. They are identical in every respect - 20
ohms resistance between any two leads. Short any two leads and you get
15 ohms.

-- Mike Naylor <mike.naylor@mail.serve.com>