How would one connect three 9Ω resistors to get 12Ω?

[bpani]

how would one connect three 9Ω resistors to get 12Ω??

Statement
-----------
how would one connect three 9Ω resistors to get 12Ω??

equations
-----------
i guess the relevant equations would be nothing more than series & parallel resistance connections..


The attempt at a solution
-------------------------
I've tried all possible ways to connect them (only 4 diff ways I guess??). There is apparently a solution since its in my nephew's textbook.

 

[berkeman]

Statement
-----------
how would one connect three 9Ω resistors to get 12Ω??

equations
-----------
i guess the relevant equations would be nothing more than series & parallel resistance connections..


The attempt at a solution
-------------------------
I've tried all possible ways to connect them (only 4 diff ways I guess??). There is apparently a solution since its in my nephew's textbook.

Hint -- you are going to have to cut the resistors in half with a fine saw...

 

[alan2]

I can do it with 4. Are you sure you read the problem correctly?

 

[alan2]

But I like Berkeman's answer better.

 

[DeeNos]

But I can't seem to get it right. Please help!!

In order to connect three 9Ω resistors to get 12Ω, you would need to connect them in a series-parallel combination. This can be achieved by connecting two of the resistors in series, and then connecting the third resistor in parallel to the combination of the first two resistors. This will result in a total resistance of 12Ω.

To further explain, let's label the resistors as R1, R2, and R3. First, connect R1 and R2 in series by connecting the positive terminal of R1 to the negative terminal of R2. The remaining positive terminal of R2 and negative terminal of R1 will then be connected to the circuit.

Next, connect R3 in parallel to the combination of R1 and R2. This can be achieved by connecting the positive terminal of R3 to the positive terminal of R1, and the negative terminal of R3 to the negative terminal of R2. The remaining positive terminal of R2 and negative terminal of R1 will then be connected to the circuit.

This configuration will result in a total resistance of 12Ω, as the resistors in series will add up to 18Ω, and then the parallel combination will reduce the overall resistance to 12Ω. This is known as a series-parallel circuit and is commonly used in electrical circuits to achieve specific resistance values.