Solution Found!
The resistance R (in ohms) of a cylindrical conductor is
Chapter 3, Problem 14E(choose chapter or problem)
The resistance \(R\) (in ohms) of a cylindrical conductor is given by \(R=k l / d^{2}\), where \(l\) is the length, \(d\) is the diameter, and \(k\) is a constant of proportionality. Assume that \(l=14.0\pm0.1\mathrm{\ cm}\) and \(d=4.4\pm0.1\mathrm{\ cm}\).
a. Estimate \(R\), and find the uncertainty in the estimate. Your answer will be in terms of the proportionality constant \(k\).
b. Which would provide the greater reduction in the uncertainty in \(R\): reducing the uncertainty in \(l\) to 0.05 cm or reducing the uncertainty in \(d\) to 0.05 cm?
Equation Transcription:
Text Transcription:
R
R=kl/d^2
l
d
k
l = 14.0 pm 0.1 cm
d = 4.4 pm 0.1 cm
Questions & Answers
QUESTION:
The resistance \(R\) (in ohms) of a cylindrical conductor is given by \(R=k l / d^{2}\), where \(l\) is the length, \(d\) is the diameter, and \(k\) is a constant of proportionality. Assume that \(l=14.0\pm0.1\mathrm{\ cm}\) and \(d=4.4\pm0.1\mathrm{\ cm}\).
a. Estimate \(R\), and find the uncertainty in the estimate. Your answer will be in terms of the proportionality constant \(k\).
b. Which would provide the greater reduction in the uncertainty in \(R\): reducing the uncertainty in \(l\) to 0.05 cm or reducing the uncertainty in \(d\) to 0.05 cm?
Equation Transcription:
Text Transcription:
R
R=kl/d^2
l
d
k
l = 14.0 pm 0.1 cm
d = 4.4 pm 0.1 cm
ANSWER:Answer :
Step 1 of 3
The question is asking to estimate the resistance R (in ohms) of cylindrical conductor and uncertainty in the estimate in terms of the proportionality constant k.
Given parameters
Equation of resistance R (in ohms) of cylindrical conductor R = k l/d2
l is the length, d is the diameter, and k is proportionality constant.
Given l = 14.0 ± 0.1 cm and d = 4.4 ± 0.1 cm.
The quantity which we are estimating has several measurements. In this question we are measuring the length l and diameter d of a resistance R (in ohms). The both quantity mentioned here is uncertain and independent measurements.
So here we can use the following basic formula.
……………...(1)
Where ,
,........,
are independent measurements and uncertainties are
,
,.........,
Equation 1 is called the multivariate propagation of error formula.