Electric Circuits (resolving them)

[bobnojio]

"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

 

[John Creighto]

"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.