QJEEM17Ph7793: JEE Main 2017 Physics - Class 12 JEEM17Ph7793 Solution: A uniform wire of length 1 and radius r has a resistance of 100 …

Question

Verified Solution • 2025–26 Session moderate

A uniform wire of length 1 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 :

Accepted Answer

Resistance of a wire of length l and radius r is given by

R =

\frac{ρ l}{A}

=

\frac{ρ l}{A} \times \frac{A}{A} = \frac{ρ V}{A^{2}} = \frac{ρ V}{π^{2} r^{4}}

\Rightarrow

R

\propto

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

∴

\frac{R_{1}}{R_{2}} = {(\frac{r_{2}}{r_{1}})}^{4}

Given, R₁ = 100

Ω

, r₁ = r, r₂ =

\frac{r}{2}

, R₂ = ?

∴

R₂ = R₁

{(\frac{r_{1}}{r_{2}})}^{4}

= 16R₁ = 1600

Ω

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