Resistors in Series Calculations including Uncertainties

[daveco-inc]

Hey, this is my first post ever on PF, and I have done my best to follow the guidelines on posts asking for help with homework. Please know that I am not after the answer just to cheat and get the questions right, I am after the method so that I could do a similar question myself in the future.

Homework Statement

Three resistors in series are 4.0 Ohms, 9.4 Ohms and again 4 Ohms.
They all have a tolerance or uncertainty of 10%. What is the total resistance including uncertainties?

Homework Equations

Total resistance in series = R(1) + R(2) + R(3)

The Attempt at a Solution

The first part is easy, 4.0+9.4+4.0= 17.4

Now, I believe that when calculating uncertainty in this situation, you are meant to calculate the uncertainty for each resistor, and then add.

10% of 4 = 0.4
10% of 9.4 = .94
10 % of 4 = 0.4

Total uncertainty of all resistors combined = 1.74.

So am I correct in saying that the total resistance in series = 17.4 Ohms + or - 1.74 Ohms, correct? The thing I am worried about is whether it is +- 1.74, or half; 0.84.

Again, thanks for the help, and please let me know if I have broken any rules or how I can improve my post.

Thanks.

 

[wukunlin]

if i remember correctly, when the quantities are added of sutracted,

the absolute error values (I mean the actually error values, not the percentages) are added together like calculating the hypotenuse of a triangle,

ie say your error values are x,y,z, the final error value should be:
sqrt(x^2 + y^2 + z^2)

 

[daveco-inc]

Hmm. That's interesting. I will ask my teacher about the best approach in this situation. Thank you very much for your reply.

 

[phinds]

does the 10% uncertainty mean "plus or minus 5%" or does it mean "plus or minus 10%" ?

Seems to me it has to mean plus or minus 10%, so I believe your calculations are the right way to do it AND have the right answer.

 

[daveco-inc]

The exact questions says: Three resistors are in series. They have values of 4.0 ohms, 9.4 ohms, and 4.0 ohms. All values have an uncertainty of 10%. What is the total resistance including uncertainties?

I believe that it means "plus or minus 10%", but I am not sure.

Thank you for your help.

 

[vela]

Wukunlin is correct. The idea here is that the value of each resistor is a random variable, and when you sum them, you form a new random variable. The variance of the new random variable is the sum of the individual variances, where the variance is equal to the uncertainty squared.

An uncertainty of 10% means "plus or minus 10%".

 

[Dick]

does the 10% uncertainty mean "plus or minus 5%" or does it mean "plus or minus 10%" ?

Seems to me it has to mean plus or minus 10%, so I believe your calculations are the right way to do it AND have the right answer.

Tolerance in this case refers to the standard deviation in a normal distribution of the component values. Not the extreme values. You add standard deviation just like wukinlin said. It's a square root of the sum of the squares.