Question

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 _______.

Answer 1

$R _{ net }=\frac{ R _{1} R _{2}}{ R _{1}+ R _{2}}$
$\frac{\rho \ell}{2 A }=\frac{\rho_{1} \frac{\ell}{ A } \times \rho_{2} \frac{\ell}{ A }}{\rho_{1} \frac{\ell}{ A }+\rho_{2} \frac{\ell}{ A }}$
$\frac{\rho}{2}=\frac{6 \times 3}{6+3}=2$
$\rho=4$