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  4. 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 :

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Q. 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 :

JEE MainJEE Main 2017Current Electricity

Solution:

$R=\frac{\rho l}{A} \,\,\,\,\,A l=V$
$R=\frac{\rho v}{A^{2}}$
$\rho \rightarrow$ constant
$v \rightarrow$ constant
$R \propto \frac{1}{A^{2}} \propto \frac{1}{r^{2}}$
$R \propto \frac{1}{r^{4}}$
$R_{2}=16 \,R_{1}=1600 \,\Omega$