Question

You have a metal wire of length $1000m$, radius of $0.7mm$ 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).
$R=\frac{\rho L}{A}\rho =153.86\times {10}^{-6}\Omega mL=1000mR=0.7mm=7\times {10}^{-4}mArea=3.14\times 7\times {10}^{-4}m\times 7\times {10}^{-4}mR=\frac{153.86\times {10}^{-6}\Omega m\times 1000m}{3.14\times 7\times {10}^{-4}m\times 7\times {10}^{-4}m}R=100k\Omega$