Combining several resistors to achieve a specific value?

[Riscilla]

Hi guys,

I have an interesting and difficult problem as follow:

Find the smallest number of 12 Ohm resistors (and of course how to connect them) to achieve an equivalent resistor of 7.5 Ohm?

I have worked on this problem for many hours but cannot find the answer yet.

Somebody can help me?

Thanks ^^

 

[vkash]

Hi guys,

I have an interesting and difficult problem as follow:

Find the smallest number of 12 Ohm resistors (and of course how to connect them) to achieve an equivalent resistor of 7.5 Ohm?

try this configuration
https://docs.google.com/leaf?id=0B2...MDg1Yy00YmUwLWExYTgtZmUyZGVkNWE1Yzlm&hl=en_GB

here one zig zag line show a resistance.
How it works.
combined resistance of first two resistances is 3 and other parllel system is 1.5 it sums to be 7.5

I have worked on this problem for many hours but cannot find the answer yet.
Thanks ^^

really it is not so much typical question

 

[Riscilla]

try this configuration
https://docs.google.com/leaf?id=0B2...MDg1Yy00YmUwLWExYTgtZmUyZGVkNWE1Yzlm&hl=en_GB

here one zig zag line show a resistance.
How it works.
combined resistance of first two resistances is 3 and other parllel system is 1.5 it sums to be 7.5

really it is not so much typical question

Hi vkash,

Thank you for your answer but the value of the resistors is 12 Ohm, not 6 Ohm. Moreover, how can you prove that the combination you suggested has the smallest possible number of resistors?

 

[PeterO]

Hi guys,

I have an interesting and difficult problem as follow:

Find the smallest number of 12 Ohm resistors (and of course how to connect them) to achieve an equivalent resistor of 7.5 Ohm?

I have worked on this problem for many hours but cannot find the answer yet.

Somebody can help me?

Thanks ^^

If you add 12 Ohm resistors in Series [1 then 2 then 3 etc], you can get the values 12, 24, 36, 48, 60 etc [not all that useful]

If you add 12 ohm resistors in parallel [first 2, then 3, then 4 etc You get effective values of 6, 4, 3, 2.4, 2, 12/7 , 1.5, ...

Can you see how to get 7.5 from the combination of any of those values.

For example: 7.5 is one eighth of of 60, so if you made 8 equal branches of 60 [5 resistors in series], and connected those 8 branches in parallel you would get 7.5.
This would also use a lot of resistors, and I am sure it could be done with fewer.

 

[Riscilla]

If you add 12 Ohm resistors in Series [1 then 2 then 3 etc], you can get the values 12, 24, 36, 48, 60 etc [not all that useful]

If you add 12 ohm resistors in parallel [first 2, then 3, then 4 etc You get effective values of 6, 4, 3, 2.4, 2, 12/7 , 1.5, ...

Can you see how to get 7.5 from the combination of any of those values.

For example: 7.5 is one eighth of of 60, so if you made 8 equal branches of 60 [5 resistors in series], and connected those 8 branches in parallel you would get 7.5.
This would also use a lot of resistors, and I am sure it could be done with fewer.

Hi PeterO,

Thank you for your answer. I could find a combination satisfying the requirement myself. The difficult part of the problem lies in finding the combination having the smallest possible number of resistors.

regards,

 

[PeterO]

Hi PeterO,

Thank you for your answer. I could find a combination satisfying the requirement myself. The difficult part of the problem lies in finding the combination having the smallest possible number of resistors.

regards,

I think you just need "confidence" in your combination. The 8 branch solution I mentioned would take 40 resistors. How many did you use? I can do it a couple of ways with 10.

It is not as if you are going to apply calculus and set up a max/min problem.

 

[vkash]

Oh sorry there are eight resistance in parallel not four.
there are no mathematical or physical formula to prove this ,that it is smallest combination(as i have read).
How i solve this.
required resistance is 7.5 Ohm. It is 6+1.5. and 6 is two parllel resistance and 1.5 is eight parallel resistance. that's it.
what is it's real answer (in some books answer is written in end of book).

 

[Riscilla]

there are no mathematical or physical formula to prove this ,that it is smallest combination(as i have read).

If it is the answer, then there must be a way to prove it, otherwise the question is meaningless.

what is it's real answer (in some books answer is written in end of book).

I don't know. This is not an exercise from the books I have.

You guys have got any other ideas?

 

[PeterO]

If it is the answer, then there must be a way to prove it, otherwise the question is meaningless.

The alternative to meaningless is obvious.

How would you go about proving that the minimum number of resistors needed to make a 24 Ohm resistance is 2.