A 'twisted' resistor network

[Wond3rboy]

Hi, this is a homework that was given to me by a friend of mine(its actually his but he asked me to do it) and i cant seem to solve it although it seems trivial

Its a three resistor network(A,B,C or 1,2,3 whatever way one wants to name them) and i am supposed to come up with resistor values that satisfy the given conditions. Please help me out...I am missing the point somewhere..

Thanks.

 

[Nigel Goodwin]

Only one resistor has a specified value, and the result isn't specified either - a pretty useless question.

Having nothing in the middle will meet the criteria given >=10K.

 

[Wond3rboy]

Hi Nigel, thanks for your reply, there are actually 3 resistors, the values of the individual resistors are to be found with so that we get the equivalent resistances being equal to the given values.

 

[alec_t]

You can get several answers from these clues:
RB+RC <0.5k, so neither can be >= 0.5k.
RA=15k-RB, so RA > 14.5k.
RA+RC > 10k, but RA itself > 10k.

 

[Wond3rboy]

Hi Alec, thanks for the reply. You have taken the equivalent resistance to be made up of two resistors in series whereas they are to be taken in parallel. Thats whats causing the problem. Sorry to be unhelpful.

 

[alec_t]

whereas they are to be taken in parallel

You mean RAB means RA¦¦RB, RAC means RA¦¦RB, RBC means RB¦¦RC ?
In that case we have:
1) RA and RB must both be >15k.
2) RC must be >> 15k to meet the RAC requirement.
3) RC must be < ~0.6k to meet the RBC requirement.
4) Since RC can't satisfy both the RAC and RBC reqirements there is no possible set of three resistors meeting all three requirements.

 

[Wond3rboy]

Thanks. I couldn't come up with an analytical explanation for it. Thats what i had concluded but wanted someone else to confirm it too. Thanks a million.

 

[The Electrician]

Thanks. I couldn't come up with an analytical explanation for it. Thats what i had concluded but wanted someone else to confirm it too. Thanks a million.

Your diagram allows for equality in the expressions as well as "greater than" or "less than", so if RAB means RA||RB, RAC means RA||RC and RBC means RB||RC, then a solution is:

RA = -12000/11
RB = 60000/59
RC = 60000/61

However, I don't see how you could have a network with 3 terminals that would have 3 resistors RA, RB and RC, and the property that between 2 of the terminals the resistance would be RA||RB, between a second pair of terminals the resistance would be RA||RC, and between the third pair the resistance would be RB||RC.

But you could have a "TEE" network with the property that the resistance between the 3 possible pairs of terminals would be the series resistance (rather than the parallel resistance) of the resistors, two at a time as was assumed in post #4. In that case, a solution would be:

RA = 12250
RB = 2750
RC = -2250

 

[ljcox]

You are all assuming (as I did initially) that the resistors are in a T formation.

But what if they are in a delta formation?

This leads to an infinite number of answers.

See the attachment for 4 examples.

As far as I can see, this meets the stated criteria.

Perhaps I'm missing something, if so, please correct me.

Resistor a is the one between A & C, Resistor b is between A & B & of course, c is between B & C.

 

[Wond3rboy]

Thanks. Never thought of it in that line.

 

[ljcox]

Hi Alec, thanks for the reply. You have taken the equivalent resistance to be made up of two resistors in series whereas they are to be taken in parallel. Thats whats causing the problem. Sorry to be unhelpful.

Where does it say that the resistors have to be in parallel?

If that restriction is not applied (and I don't see how it can be) then the T config shown in your post #3 leads to an infinite number of solutions.

For example: If RB = RC = 200 Ohm, then RA = 14.8K.

Thus RaB = 15k, RAC = 15k & RBC = 400 Ohm thus all the criteria are satisfied.

 

[Wond3rboy]

My friends teacher said that. I was also trying to this with the T network thing before he 'corrected' me. I have since told him the result so i am done with the task. T