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 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