Question

A wire of resistance 20 ohm has a radius of 1 x 10-3 m and the resistivity of its material is 2 x 10-6 ohm-m. The length of the given wire is................... m

A) 62.8
B) 31.4
(c) 16.6
(D) 125.6​

Answer 1

Given :

• Resistance of wire (R) = 20Ω
• Radius of wire (r) = 1 × $\rm{10^{-3}}$m
• Resistivity of material ${\sf \rho = 2 \times 10^{-6}\:ohm.m}$

To Find :

• Lenght of wire $(\ell)$

Formula Used :

$\implies\underline{\boxed{\sf R = \rho\dfrac{\ell}{A}}}$

Solution :

Area of Cross-section of wire (A) = πr²

$\implies{\sf A = \pi \times (10^{-3})^2}$

$\implies{\bf A = \pi \times 10^{-6} m}$

______________________________

$\implies{\sf 20 = 2 \times 10^{-6} \times \dfrac{\ell}{3.14 \times 10^{-6}} }$

$\implies{\sf \ell = \dfrac{20 \times 3.14 \times 10^{-6}}{2 \times 10^{-6}}}$

$\implies{\sf \ell = 10 \times 3.14}$

$\implies{\bf \ell = 31.4 \: m }$

Answer :

Option (B) 31.4m

Lenght of wire is 31.4m