A wire of length 10 cm and radius √(7) × 10⁻⁴ m is connected across… | JEE Main 2024 (27 Jan, Shift 1)

Q35JEE Main 2024 · 27 JAN · SHIFT 1Medium

Wheatstone Bridge & Metre Bridge

A wire of length $10\text{ cm}$ and radius $\sqrt{7} \times 10^{-4}\text{ m}$ is connected across the right gap of a meter bridge. When a resistance of $4.5\ \Omega$ is connected on the left gap by using a resistance box, the balance length is found to be at $60\text{ cm}$ from the left end. If the resistivity of the wire is $\text{R} \times 10^{-7}\ \Omega\text{ m}$ , then value of $\text{R}$ is:

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Answer: (c)

$\dfrac{4.5}{R_w} = \dfrac{60}{40} \Rightarrow R_w = 3\ \Omega$ .
$\rho = \dfrac{R_w \pi r^2}{L} = \dfrac{3 \times \frac{22}{7} \times 7 \times 10^{-8}}{0.1}$ .
$\rho = 66 \times 10^{-7}\ \Omega\text{ m}$ .
So the answer is (c) 66.

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