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.

 

[Moetasim]

There are actually multiple ways to connect four identical resistors together to achieve an equivalent resistance of R. Here are a few examples:

1. Series Connection: In this arrangement, all four resistors are connected in a straight line, with one end of the first resistor connected to one end of the second resistor, and so on. The equivalent resistance in this case would be R + R + R + R = 4R.

2. Parallel Connection: In this arrangement, all four resistors are connected side by side, with one end of each resistor connected to one end of the others. The equivalent resistance in this case would be 1/(1/R + 1/R + 1/R + 1/R) = R/4.

3. Combination of Series and Parallel Connection: In this arrangement, two resistors are connected in series, and then this combination is connected in parallel with another two resistors connected in series. The equivalent resistance in this case would be (R + R) || (R + R) = (2R)(2R)/(2R + 2R) = R.

There are also other possible combinations, such as connecting all four resistors in a diamond shape, or connecting three resistors in series and one in parallel, etc. The key is to understand the concept of series and parallel connections and use them in different combinations to achieve the desired equivalent resistance.