Question

You have a metal wire of length 1000 m, radius of 0.7 mm and resistivity of the metal is given as $153.86\times {10}^{-6}\Omega m$. Find the resistance of the wire.

• A. $100k\Omega$
• B. $40k\Omega$
• C. $18k\Omega$
• D. $250k\Omega$

Answer 1

The correct option is A $100k\Omega$

Resistance of the conductor depends on
(i) its length
(ii) its area of cross-section and
(iii) the nature of its material.
Measurements have shown that resistance of a uniform metallic conductor is directly proportional to its length, $L$ and inversely proportional to the area of cross-section, $A$.
$R=\frac{\rho L}{A}\text{Given, resistivity},\rho =153.86\times {10}^{-6}\Omega mL=1000m\text{radius},r=0.7mm=7\times {10}^{-4}m\Rightarrow \text{Area}=3.14\times (7\times {10}^{-4}{)}^2\Rightarrow \text{Resistance},R=\frac{153.86\times {10}^{-6}\times 1000}{3.14\times 7\times {10}^{-4}\times 7\times {10}^{-4}}=100k\Omega$