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Refer to Exercise 14. Assume that l = 10.0 cm ± 0.5% and d

Statistics for Engineers and Scientists | 4th Edition | ISBN: 9780073401331 | Authors: William Navidi ISBN: 9780073401331 38

Solution for problem 26E Chapter 3.4

Statistics for Engineers and Scientists | 4th Edition

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Statistics for Engineers and Scientists | 4th Edition | ISBN: 9780073401331 | Authors: William Navidi

Statistics for Engineers and Scientists | 4th Edition

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Problem 26E

Refer to Exercise 14. Assume that l = 10.0 cm ± 0.5% and d = 10.4 cm ± 0.5%.

a. Estimate R, and find the relative uncertainty in the estimate. Does the relative uncertainty depend on k?

b. Assume that either l or d can be remeasured with relative uncertainty 0.2%. Which should be remeasured to provide the greater improvement in the relative uncertainty of the resistance?

EXERCISE 14: The resistance  (R in ohms) of a cylindrical conductor is given by r = kl / d2, where l is the length, d is the diameter, and k is a constant proportionality. Assume that

Estimate R, and find the uncertainty in the estimate. Your answer will be in terms of the proportionality constant k.Which would provide the greater reduction in the uncertainty R: reducing uncertainty in l to 0.05 cm or reducing the uncertainty in d to 0.05 cm?
Step-by-Step Solution:

Step 1 of 5</p>

Here we have to find the uncertainty of the resistance

Given resistance R=

The length is

From this =10,

The diameter is

From this =10.4, 

Step 2 of 5</p>

Now R=

         R=k10/(10.4)2 

           =0.09k

Step 3 of 5</p>

Now differentiate R with respect to and d

2

      = 0.009k

 3

      = -k(2(10)/10.43)

      =-20k/1092.727

      = -0.0183k

Step 4 of 5

Chapter 3.4, Problem 26E is Solved
Step 5 of 5

Textbook: Statistics for Engineers and Scientists
Edition: 4
Author: William Navidi
ISBN: 9780073401331

The answer to “Refer to Exercise 14. Assume that l = 10.0 cm ± 0.5% and d = 10.4 cm ± 0.5%.a. Estimate R, and find the relative uncertainty in the estimate. Does the relative uncertainty depend on k?________________b. Assume that either l or d can be remeasured with relative uncertainty 0.2%. Which should be remeasured to provide the greater improvement in the relative uncertainty of the resistance?EXERCISE 14: The resistance (R in ohms) of a cylindrical conductor is given by r = kl / d2, where l is the length, d is the diameter, and k is a constant proportionality. Assume that 1. Estimate R, and find the uncertainty in the estimate. Your answer will be in terms of the proportionality constant k.2. Which would provide the greater reduction in the uncertainty R: reducing uncertainty in l to 0.05 cm or reducing the uncertainty in d to 0.05 cm?” is broken down into a number of easy to follow steps, and 147 words. Since the solution to 26E from 3.4 chapter was answered, more than 254 students have viewed the full step-by-step answer. Statistics for Engineers and Scientists was written by and is associated to the ISBN: 9780073401331. This full solution covers the following key subjects: uncertainty, relative, estimate, proportionality, assume. This expansive textbook survival guide covers 153 chapters, and 2440 solutions. This textbook survival guide was created for the textbook: Statistics for Engineers and Scientists , edition: 4. The full step-by-step solution to problem: 26E from chapter: 3.4 was answered by , our top Statistics solution expert on 06/28/17, 11:15AM.

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Refer to Exercise 14. Assume that l = 10.0 cm ± 0.5% and d

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