Question

A metal wire of specific resistance $64\times {10}^{–6}\Omega$ cm and length 198 cm has a resistance of $7\Omega$. The radius of the wire will be

• A. 2.4 cm
• B. 0.24 cm
• C. 0.024 cm
• D. 24 cm

Answer 1

The correct option is C 0.024 cm

Resistivity of wire, $\rho =64\times {10}^{-6}\Omega cm$
Length of wire, I = 198 cm
Resistance of wire, $R=7\Omega$
The resistance of wire is given by:
$R=\rho \frac{l}{A}=\rho \frac{l}{\pi r^2}\text{[Area of cross-section of wire A= pi~r^2]}$
The radius of wire can be calculated as:
$r=\sqrt{\frac{\rho l}{\pi R}}=\sqrt{\frac{64\times {10}^{-6}\times 198}{3.14\times 7}}$
= 0.024 cm
Hence, the correct answer is option (3).