Question

what is the resistance of a 1.3 m copper wire ($\
ho = 1.7\times10^{-8}\\ \omega\cdot m$) that has a cross - sectional area of $8.36\times10^{-6}m^{2}$? use $r = \frac{\
ho l}{a}$.
a. $2.6\times10^{-3}\\ \omega$
b. $3.8\times10^{2}\\ \omega$
c. $1.6\times10^{-3}\\ \omega$
d. $6.4\times10^{2}\\ \omega$

Explanation:

Step1: Substitute values into formula

Given \(
ho = 1.7\times10^{-8}\ \Omega\cdot m\), \(l = 1.3\ m\), \(A=8.36\times 10^{-6}\ m^{2}\), substitute into \(R=\frac{
ho l}{A}\).
\(R=\frac{1.7\times 10^{-8}\times1.3}{8.36\times 10^{-6}}\)

Step2: Calculate the value

First, calculate \(1.7\times1.3 = 2.21\). Then, use the rule of exponents \(\frac{a^{m}}{a^{n}}=a^{m - n}\), so \(\frac{10^{-8}}{10^{-6}}=10^{-8+6}=10^{-2}\).
\(R=\frac{2.21\times10^{-8 + 1}}{8.36\times10^{-6}}=\frac{2.21\times10^{- 2}}{8.36}\)
\(R\approx0.264\times10^{-2}=2.64\times10^{-3}\ \Omega\)

Answer:

A. \(2.6\times 10^{-3}\ \Omega\)