Using the value in Table . Can someone help me answer the these question? OBS: y

Question

Using the value in Table . Can someone help me answer the these question?

OBS: you don't have to answer from #1 to #5. You can just answer #1 and put the formula, and I will be able to do the rest.

Question 1: Compare each of your Wheatstone bridge values of the five unknown resistors with its coded value by calculating the percentage error assuming the coded values as correct. State the precision of the resistors based on the resistor color coding.

#1—Error = ____________% #2—Error = ____________% #3—Error =____________% #4—Error = ____________% #5—Error =____________% Precision = ____________%

Are the percentage errors of the measurements within the precision of the resistors?

Question 2: Express the values of the standard error for each of the five unknown resistors as a percentage of the mean value.

#1 % std err 1?4 ____________% #2 % std err 1?4 ____________% #3 % std err 1?4 ____________% #4 % std err 1?4 ____________% #5 % std err 1?4 ____________%

Question 3. Compare your Wheatstone bridge values of the five unknown resistors with the values in DataTable2 determined by using the resistance meter. Calculate the percentage errors for each resistor assuming Data Table 2 as correct. For each resistor, is the agreement better or worse than the agreement with the coded values?

#1—Error = ____________% #2—Error =____________% #3—Error = ____________% #4—Error =____________% #5—Error = ____________%

Question 4. Considering the stated precision of the coded values and the various comparisons that have been done above, state whether or not your Wheatstone bridge measurements of these resistors represent more reliable values for the actual values of these resistors than the coded values. Be very specific about the facts upon which your opinion is based.

Data Table 1. Rk (2) JB (cmBK (cm) Unknown #1 470 5 GOO Coded Value Q ) 4D OS LO. 5 Unknown #2 Coded Value 2 ) Unknown #3 | 33 Coded Value 33 Q ) Unknown #4 Coded Value 50-5 2 ) 68 L9 Unknown #5 Coded Value AOOO | 50 by OO . Data Table 2

Explanation / Answer

Hi,

According to your request I will only show you how to do the first question.

In a wheatstone bridge you have four resistances arranged in a diamond. In that configuration the electric potential of the upper and inferior points are equal, while the points at the sides are at the same electric potential than the battery.

This special configuration can be used to find the value of an unkown resistance if we know the value of the other resistances in the arrangement. In a wheatstone bridge the relation between resistances is:

R1/R2 = R3/R4 ; where R1 is the resistance between left and the upper point, R2 is the resistance between the upper point and the point at the right, R3 is the resistance between the left and the inferior point while R4 is the resistance between the inferior and the point at the right.

If the are no resistors in the inferior and superior parts and the wheatstone bridge and we have a wire of constant cross section, then the relation shown above is maintained but now we use the length of the wires instead of resistances:

L1/L2 = L3/L4

Assuming that you have a wheatstone bridge where the points J and K are conected to the battery (this means they are the points at the left and right side, respectively) while the points A and B are conected to the points J and K (this means that points A and B are the upper and inferior points respectively), and that the resistances in the inferior part of the arrangement have been replaced by wires of constant cross section then we have the following:

R1/R2 = JB/KB

Besides, if the unknown resistor was put between the points J and A, then that resistor would be Ru and the other one, should be the known resistor (Rk). If all this is true then the formula to find the unknown resistance should be:

Ru/Rk = JB/KB ::::::::: Ru = Rk*(JB/KB)

In this case, we have a table wit many values. If we replace the data in the formula above we will get different values for the unknown resistance. Besides as we have a group of values that were determine to measure the same thing, we should also find the mean value in each case, which we assume is an arithmetic average:

Unknown 1     

Ru = 470 ; Ru = 489 ; Ru = 480 ; mean value = 480

Unknown 2  

Ru = 9.6 ; Ru = 9.6 ; Ru = 9.6 ; mean value = 9.6

Unknown 3

Ru = 34 ; Ru = 34 ; Ru = 34 ; mean value = 34

Unknown 4   

Ru = 69 ; Ru = 69 ; Ru = 69 ; mean value = 69

Unknown 1     

Ru = 1884 ; Ru = 2000 ; Ru = 2347 ; mean value = 2077

Once you have all this data you can compare individually each particular value for each unknown resistance with the 'real' value, or you can make that comparison using the mean value in each case.

Whatever path you choose the formula to use is:

e = abs( (fr - f)/fr)*100 ; where fr is the real value and f is the experimental one. The function 'abs' is the absolute value.

It is important to notice that we don't know the 'real' value, but the problem says we can assume this value is equal to the coded one. However as it is not giving in the question I can't give you a numerical answer.

One last thing is that an acceptable error should be inferior to 5%, but that depends on the study you are doing.

I hope it helps.

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