Creating Circuits with equivalent resistances

In summary, the problem is to find 9 different arrangements of four identical 300 ohm resistors that result in unique equivalent resistances using all four resistors in each configuration. So far, two arrangements have been shown: 4R = R + R + R + R and R = R/2 + R/2. The connection points for the resistors do not need to include a battery, unless specified by the problem.
  • #1
ragsz
3
0

Homework Statement


Given 4 Identical resistors, I need to be able to find the 9 combinations of circuits with equivalent resistances


Homework Equations


Do I just keep flipping between parallel resistor sequences?



The Attempt at a Solution


I drew 3 different circuits that I believe to be correct, but cannot seem to come up with 9 different ones.
 
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  • #2
ragsz said:

Homework Statement


Given 4 Identical resistors, I need to be able to find the 9 combinations of circuits with equivalent resistances


Homework Equations


Do I just keep flipping between parallel resistor sequences?



The Attempt at a Solution


I drew 3 different circuits that I believe to be correct, but cannot seem to come up with 9 different ones.

Welcome to the PF.

Could you clarify the problem statement some? What do you mean by "equivalent resistances"? Equivalent to what? To one of the single R values? Or equivalent to some other value, and all 9 combinations are equivalent to that value?
 
  • #3
Maybe I should have typed it word for word... my bad. And thanks for the reply
You are given for identical 300 ohm resistors. Find as many ways of connecting all four resistors that give unique equivalent resistances. Then my professor gives us a hint that we should get 9 different arrangements using all four resistances that will give unique equivalent resistances.
Thanks
 
  • #4
ragsz said:
Maybe I should have typed it word for word... my bad. And thanks for the reply
You are given for identical 300 ohm resistors. Find as many ways of connecting all four resistors that give unique equivalent resistances. Then my professor gives us a hint that we should get 9 different arrangements using all four resistances that will give unique equivalent resistances.
Thanks

Oh, unique equivalent resistances. So each configuration will result in a different equivalent resistance, and you have to use all 4 resistors in each configuration. Got it.

Show us what you have so far, and maybe we can offer some hints...
 
  • #5
I'm at 5 right now... Interesting problem. :smile:
 
  • #6
berkeman said:
I'm at 5 right now... Interesting problem. :smile:

7...
 
  • #7
9. :smile:

How's it going on your end?
 
  • #8
  • #9
ragsz said:
Ok well here are my two... I know that's not much, but I think I am lost with this stuff.
http://imgur.com/ZyxobN4

You probably don't have to draw the battery, just show the resistors with the connection points at the ends of the configuration. Unless the problem asks for you to show the battery for some reason.

So what you have shown so far is:

4R = R + R + R + R

R = R/2 + R/2

Now keep going. Try different combinations and connections, and see if they result in a different equivalent resistance. It's actually kind of fun... :smile:
 

FAQ: Creating Circuits with equivalent resistances

What is the concept of equivalent resistances?

Equivalent resistances refer to a single resistance value that can replace a combination of multiple resistors in a circuit without changing the overall current or voltage.

How do you calculate the equivalent resistance of series circuits?

In a series circuit, the equivalent resistance is the sum of all individual resistances. This can be calculated by adding all the resistance values together.

How do you calculate the equivalent resistance of parallel circuits?

In a parallel circuit, the equivalent resistance is calculated using the formula 1/Req = 1/R1 + 1/R2 + 1/R3 + ..., where R1, R2, R3, etc. are the individual resistance values.

What is the difference between series and parallel circuits in terms of equivalent resistance?

In a series circuit, the equivalent resistance is always greater than the individual resistances, while in a parallel circuit, the equivalent resistance is always less than the individual resistances.

How can the concept of equivalent resistances be applied in practical circuits?

The concept of equivalent resistances is used in circuit analysis and design to simplify complex circuits and make calculations easier. It is also important in ensuring the correct amount of current and voltage is distributed throughout a circuit.

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