Question

Calculate the resistance of 1 km long copper wire of radius 1 mm. (Take specific resistance of copper $=1.72\times {10}^{-8}\Omega m$)

• A. $4.5\text{ohm}$
• B. $5.5\text{ohm}$
• C. $6.5\text{ohm}$
• D. $7.5\text{ohm}$

Answer 1

The correct option is (C) $5.5\text{ohm}$

Step 1, Given

Length, $l=1km=1000m$

Radius, $r=1mm={10}^{-3}m$

Specific resistance of copper, $\rho =1.72\times {10}^{-8}$

Step 2, Finding resistance

Area of cross-section, $A=\pi \times r^2=3.14\times {10}^{-6}{m}^2$

Let the resistance be $R$.

As we know, $R=\rho \frac{l}{A}$

On substituting values, $R=\frac{1.72\times {10}^{-8}\times {10}^3}{3.14\times {10}^{-6}}=5.5\text{ohm}$

$\Rightarrow$ Resistance of the copper wire, $R=5.5\text{ohm}$.

Hence the resistance of the wire is 5.5 ohm.