A uniform wire of length l and radius r has a resistance of 100 Ω. It is recast into a wire of radius r/2. The resistance of new wire will be: (a) 1600 Ω (b) 400 Ω (c) 200 Ω (d) 100 Ω

Answer: (a). Volume constant, so R = ρ V/A² ∝ 1/r⁴. r → r/2 ⇒ R' = 2⁴×100 = 1600 Ω. The answer is (a).

A uniform wire of length l and radius r has a resistance of 100 Ω. It… | JEE Main 2017 (9 Apr, Shift 1)

Q54JEE Main 2017 · 9 APR · SHIFT 1Medium

Ohm's Law, Resistivity & Temperature

A uniform wire of length l and radius r has a resistance of 100 $\Omega$ . It is recast into a wire of radius $\frac{r}{2}.$ The resistance of new wire will be:

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Answer: (a)

Volume constant, so $R = \rho V/A^2 \propto 1/r^4$ .
$r \to r/2 \Rightarrow R' = 2^4\times100 = 1600\ \Omega$ . The answer is (a).

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