Two wires of same length and thickness having specific resistances $6\, \Omega \,cm$ and $3 \,\Omega\, cm$ respectively are connected in parallel. The effective resistivity is $\rho\, \Omega \,cm$. The value of $\rho$ to the nearest integer, is ..... .
JEE MAIN 2021, Medium
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$\because$ in parallel
$R _{ net }=\frac{ R _{1} R _{2}}{ R _{1}+ R _{2}}$
$\frac{\rho \ell}{2 A }=\frac{\rho_{1} \frac{\ell}{ A } \times \rho_{2} \frac{\ell}{ A }}{\rho_{1} \frac{\ell}{ A }+\rho_{2} \frac{\ell}{ A }}$
$\frac{\rho}{2}=\frac{6 \times 3}{6+3}=2$
$\rho=4$
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