Question

A resistance of $2 \Omega$ is to be made from a copper wire (specific resistance $1.7 \times 10^{-8} \Omega m$ ) using a wire of length $50\, cm .$ The radius of the wire is

• A. 0.0116 mm
• B. 0.0367 mm
• C. 0.116 mm
• D. 0.367 mm

Answer 1

Answer: (B)

Resistance of a wire, $R=\frac{\rho l}{A}$
or $A=\frac{\rho l}{R}$ or $\pi r^{2}=\frac{\rho l}{R}$
or $r=\left(\frac{\rho l}{\pi R}\right)^{1 / 2}$
Substituting the given values, we get
$r=\left(\frac{1.7 \times 10^{-8} \times 0.5}{2 \times 3.14}\right)^{1 / 2}$
$=0.367 \times 10^{-4}\, m=0.0367\, mm$