Question

Two wires of same length and thickness having specific resistances $6\Omega \text{-cm}$ and $3\Omega \text{-cm}$ respectively are connected in parallel. The effective resistivity of the combination is $\rho \Omega \text{-cm}$. The value of $\rho$, to the nearest integer, is ________.

Answer 1

We know that, in parallel combination,
$R_{\text{eq}}=\frac{R_1{R}_2}{R_1+R_2}$

$\Rightarrow \frac{\rho l}{2A}=\frac{{\rho }_1\frac{l}{A}\times {\rho }_2\frac{l}{A}}{{\rho }_1\frac{l}{A}+{\rho }_2\frac{l}{A}}(\because R=\rho \frac{l}{A})$

$\Rightarrow \frac{\rho }{2}=\frac{6\times 3}{6+3}=2$

$\Rightarrow \rho =2\times 2=4\Omega \text{-cm}$