# Possible resistances using 3 resistors?

• carnivalcougar
In summary, the possible resistances are:One resistor alone = 1000ohmsTwo resistors in series = 2000ohmsTwo resistors in parallel = 500ohmsThree resistors in series = 3000 ohmsTwo in parallel, one in series = 1500ohmsTwo in series, one in parallel = 1500ohmsAll in parallel = 333.33 ohms
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.

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

ehild

Does it specify that you must use all 3 resistors?

Or can you connect a resistor to itself?

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.

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.

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

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 ($\frac{1}{R}$-1) or R+R+R which was wrong.

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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?

carnivalcougar said:
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

#### Attachments

• 2series1parallel.jpg
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carnivalcougar said:
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.

ehild said:
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

asdf12312 said:
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?

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

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

That's looking better.

carnivalcougar said:
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

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## 1. What is the maximum resistance that can be achieved using 3 resistors?

The maximum resistance that can be achieved using 3 resistors is equal to the sum of the individual resistances. For example, if the resistors have values of 10 ohms, 20 ohms, and 30 ohms, the maximum resistance that can be achieved is 10+20+30 = 60 ohms.

## 2. How do I calculate the equivalent resistance of 3 resistors in series?

To calculate the equivalent resistance of 3 resistors in series, simply add the individual resistances together. For example, if the resistors have values of 10 ohms, 20 ohms, and 30 ohms, the equivalent resistance would be 10+20+30 = 60 ohms.

## 3. What is the formula for calculating the equivalent resistance of 3 resistors in parallel?

The formula for calculating the equivalent resistance of 3 resistors in parallel is 1/Req = 1/R1 + 1/R2 + 1/R3, where Req is the equivalent resistance and R1, R2, and R3 are the individual resistances. To solve for Req, simply take the reciprocal of both sides of the equation.

## 4. Can 3 resistors of different values be connected in parallel?

Yes, 3 resistors of different values can be connected in parallel. The equivalent resistance will be less than the smallest individual resistance and can be calculated using the formula mentioned in the previous question.

## 5. How do I determine the power rating for 3 resistors connected in series?

The power rating for 3 resistors connected in series is equal to the power rating of the individual resistors. This is because the current passing through each resistor is the same, so the power dissipated by each resistor will also be the same.

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