Calculating Percent Uncertainty of Resistance at 25°C with 95% Confidence Level

[shaklove]

can you guys help me pleasee

Homework Statement

The relationship between resistance with temperature is expressed by the equation of R= R0[1+ α(T-T0)], where Ro is the resistance at the reference temp. T0 and α for the resistor material has been determined to be 0.0048 ± 0.1% oC. In the range 0 to 100* C, in which we are calibrating this resistor, temperature measurements have shown a standard deviation of 0.1* C. The systematic uncertainty of the temperature- measurement device is known to be 0.1* C.
At 0* C, the resistance is 100.00 Ω. compute the percent uncertainty of R, at a temperature of 25* C with a 95% confidence level

Homework Equations

Wx = (Bx^2 + Px^2)^ 1/5

The Attempt at a Solution

I know that the confidence level is = 1 - a (alpha)
0.95 = 1 - a >>>>>>> a = 1 - 0.95 = 0.05
a/2 = 0.025
i know that i can use this formula Px = tSx
Should i assume that "t" is 2 , then i say Px = 2 * (0.1) = 0.2
am not sure of am right !

 

[KataKoniK]

Thank you for reaching out for help with your question. It seems like you are on the right track in terms of calculating the confidence level and the standard uncertainty of the temperature measurement. However, I would like to clarify a few things:

1. The formula you have provided, Wx = (Bx^2 + Px^2)^1/5, seems to be for calculating the combined standard uncertainty, Wx, of a measurement with two components, Bx and Px. In this case, Bx represents the systematic uncertainty and Px represents the random uncertainty. However, in your problem, you only have one source of uncertainty, which is the random uncertainty of the temperature measurement. Therefore, you do not need to use this formula.

2. The value of "t" that you mentioned is the critical value for a t-distribution with a certain degrees of freedom. In this problem, you have a sample size of 1 (since you are only measuring one temperature) and you are trying to calculate the uncertainty at a 95% confidence level. Therefore, the critical value for a t-distribution with 1 degree of freedom and a confidence level of 95% is approximately 12.71. This value can be found in a t-table or by using a calculator. So, instead of assuming "t" is 2, you should use the correct critical value of 12.71.

3. The formula you need to use to calculate the uncertainty of R is R = R0[1+α(T-T0)]. This formula takes into account the uncertainty in both R0 and the temperature measurement. So, you will need to calculate the uncertainty in R0 first using the formula Wx = (Bx^2 + Px^2)^1/2, where Bx is the systematic uncertainty of R0 (which is 0.1% of R0) and Px is the random uncertainty of the temperature measurement (which is 0.1*C). Then, you can plug in this value of Wx into the formula for R to get the uncertainty in R.

4. Lastly, to calculate the percent uncertainty, you will need to divide the uncertainty in R by the value of R at a temperature of 25*C (which you can calculate using the given formula for R). Then, multiply this value by 100 to get the percent uncertainty.

I hope this helps to clarify the steps you need to take