Question

What length of copper wire of resistivity $1.7\times {10}^{-8}\Omega m$ and radius 1 mm is required so that its resistance is $1\Omega$?

• A. $184.7m$
• B. $200m$
• C. $190.5m$
• D. $150m$

Answer 1

Answer: (A)

$\text{Step 1: The resistance of wire is expressed as}$

$R=\frac{\rho L}{A}$ $....\left(1\right)$

Given, $R=1\Omega ,$

The area of cross section, $A=\pi r^2=3.14\times {0.001}^2=3.14\times {10}^{-6}$.

Resistivity $\rho =1.7\times {10}^{-8}$ ohm-meter

$\text{Step 2: Putting above values in equation}$ $\left(1\right)$

We get

$1=\frac{1.7\times {10}^{-8}\times L}{3.14\times {10}^{-6}}$

$\Rightarrow L=\frac{1\times 3.14\times {10}^{-6}}{1.7\times {10}^{-8}}=\frac{3.14\times {10}^{-6}}{1.7\times {10}^{-8}}=1.847\times {10}^{2}m$.

Therefore, the length of the wire is 184.7 meters.

Hence, Option A is correct.