Question

The resistance RRR of a copper "gauge 10" jumper cable with diameter d=0.259d=0.259 cmcm is 0.0124 ΩΩ. Find the length LLL of the cable. Express your answer in mm. Use three significant figures.

Answer 1

Answer:

The length will be "3.89 m".

Explanation:

The given values are:

Diameter,

d = 0.259 cm

On converting it in m, we get

d = 0.259 × 10⁻²            

Resistance

R = 0.0124 Ω      

As we know,

⇒  $A=\pi (\frac{d}{2})^2$

On putting the estimated values, we get

        $=3.14(\frac{0.259\times 10^{-2}}{2})^2$

        $=5.266\times 10^{-6} \ m^2$

If, $\rho = 1.68\times 10^{-8} \ \Omega.m$

then, $R=\frac{\rho L}{A}$

         $L=\frac{RA}{\rho}$

On substituting the values, we get

            $=\frac{(0.0124)(5.266\times 10^{-6})}{1.68\times 10^{-8}}$

            $=3.89 \ m$