Electric Circuits (resolving them)

AI Thread Summary
Four identical resistors, each with resistance R, can be configured to achieve an equivalent resistance of R through multiple combinations. One method involves connecting two pairs of resistors in parallel, which are then placed in series with each other. Another approach is to connect two resistors in series and then place that combination in parallel with the other two resistors in series. The discussion emphasizes that the definition of a unique circuit can influence the number of valid configurations. Overall, there are indeed several ways to arrange the resistors to achieve the desired equivalent resistance.
bobnojio
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"you have four identical resistors, each with a resistance of R. You are asked to connect these four together so that the equivalent resistance of the resulting combination is R, How many ways can you do it? There is more than one way. Justify your answer"

I can only think of ONE way to do this. (you can neglect a voltage or current source, as its equivalent resistors), but for good measure, let V be the voltage source, ignore the .'s

|----|----|
|...|...|
V...R...R
|...|...|
|...R...R
|----|----|

Can anyone help me find any other combinations of these four identical resistors that gives the same resistance as the equivalent?

as far as I know, i am not allowed to have any of the resistors being 'open circuited' so that they do not affect the circuit.

any help is greatly appreciated
 
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bobnojio said:
"you have four identical resistors, each with a resistance of R. You are asked to connect these four together so that the equivalent resistance of the resulting combination is R, How many ways can you do it? There is more than one way. Justify your answer"

I can only think of ONE way to do this. (you can neglect a voltage or current source, as its equivalent resistors), but for good measure, let V be the voltage source, ignore the .'s

|----|----|
|...|...|
V...R...R
|...|...|
|...R...R
|----|----|

Can anyone help me find any other combinations of these four identical resistors that gives the same resistance as the equivalent?

as far as I know, i am not allowed to have any of the resistors being 'open circuited' so that they do not affect the circuit.

any help is greatly appreciated

I suppose it depends on what constitutes a unique circuit. For instance you can put in series two parallel combinations. Equivalently you can put in parallel two series combinations.
 
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