Q73 / 90 · JEE Main 2017 (09 Apr Online) · Physics

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

Correct answer
A
$1600 Ω$
B
$100 Ω$
C
$200 Ω$
D
$400 Ω$

Solution

R = ρ \frac{l}{A}

A l = V

R = \frac{ρ V}{A^{2}}

ρ \to

constant

V \to

constant

R \propto \frac{1}{A^{2}} \propto

\frac{1}{{(r^{2})}^{2}}

R \propto \frac{1}{r^{4}}

R_{2} = 16 R_{1} = 1600 Ω

Hence, the correct answer is option: 'A'.

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