Possible resistances using 3 resistors?

[carnivalcougar]

Homework Statement

You have 3 resistors 1000ohms each. List all the resistances you can achieve using this set.

Homework Equations

R in series = R1 + R2 + R3...etc

1/R in parallel = 1/R1 + 1/R2 + 1/R3...etc

The Attempt at a Solution

If they are all in series you have 3000ohms. If they are all in parallel you have 333.333ohms. If two are in parallel while one is in series, you have 1500ohms. If one is in parallel while two are in series, then I'm getting that the Req will be 3000ohms. I'm not sure if that last part is correct. If it is, then the possible resistances are 333.33ohms, 1500ohms, and 3000ohms.

 

[ehild]

The resistance (for two series, one parallel) is not correct.

ehild

 

[NascentOxygen]

Does it specify that you must use all 3 resistors?

 

[lewando]

Or can you connect a resistor to itself?

 

[asdf12312]

I don't think you can have 1 resistor in parallel with itself. So for the last one you have one in parallel with the 2 in series.

 

[lewando]

I meant connect one terminal of a resistor to the other terminal of the same resistor. Forming a circular resistor, effectively shorting it out of existence.

 

[carnivalcougar]

How would you calculate the resistance for two series and one parallel? I'm doing it as Req = R1 + R2 + (1/R3)^-1

 

[asdf12312]

I was responding to the OP's post lol. He was trying to have 'one in parallel with 2 in series' but what he was doing was having one resistor in parallel with itself ([itex]\frac{1}{R}[/itex]^-1) or R+R+R which was wrong.

 

[asdf12312]

dfdfd

Try googling 'two resistors in series one in parallel'. Here is a good example:
http://introcs.cs.princeton.edu/java/36inheritance/images/combination.png

 

[carnivalcougar]

So two in series and one in parallel would be equal to R1 + (1/R2+1/R3)^-1 ?

So all in all you can have:

One resistor alone = 1000ohms

Two resistors in series = 2000ohms

Two resistors in parallel = 500ohms

Three resistors in series = 3000 ohms

Two in parallel, one in series = 1500ohms

Two in series, one in parallel = 1500ohms

All in parallel = 333.33 ohms

Is this all correct and am I missing any others?

 

[ehild]

So two in series and one in parallel would be equal to R1 + (1/R2+1/R3)^-1 ?

Is not that two parallel and one series with the parallel ones? Look at the figure: What is the equivalent resistance ?

ehild

 

[asdf12312]

So two in series and one in parallel would be equal to R1 + (1/R2+1/R3)^-1 ?


Two in parallel, one in series = 1500ohms

Two in series, one in parallel = 1500ohms

you are doing the same thing for both (2 in parallel, 1 series) so getting the same answer. did you see the link from my previous post? I thought it did a good job explaining it.

 

[carnivalcougar]

Is not that two parallel and one series with the parallel ones? Look at the figure: What is the equivalent resistance ?

ehild

It looks like the Req would be 3000ohms

you are doing the same thing for both (2 in parallel, 1 series) so getting the same answer. did you see the link from my previous post? I thought it did a good job explaining it.

The link brought me to a picture of the cover of a Java textbook. However, isn't this two in parallel and one in series?

Wouldn't the Req of that be 1500ohms?

 

[carnivalcougar]

Wouldn't the resistance of this also be 1500ohms? (2 in series 1 in parallel)

http://www.cheng.cam.ac.uk/research/groups/electrochem/JAVA/impedance/figure/sparal1.gif

 

[carnivalcougar]

I think I see now. For two in series and one in parallel you need to find the Req of the 2 in series which is 2000ohms. Then you do (1/2000 + 1/1000)^-1 which is 666.67 ohms.

That leaves 7 possible combinations with three resistors:

One resistor alone = 1000ohms

Two resistors in series = 2000ohms

Two resistors in parallel = 500ohms

Three resistors in series = 3000 ohms

Two in parallel, one in series = 1500ohms

Two in series, one in parallel = 666.67ohms

All in parallel = 333.33 ohms

 

[NascentOxygen]

That's looking better.

 

[asdf12312]

The link brought me to a picture of the cover of a Java textbook.

thats weird, when I see the image it is of a circuit! It must be a browser issue or something. I attached the image below that I was talking about (this link should work). anyway it looks like you already figured it out. good job.

http://s29.postimg.org/vtkoxgodz/combination.png