Question 76 of 380

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 ___ .

Your answerCheck answer

Show answer and solution▾

Answer: 4

$∵$ in parallel, ${R}_{net}=\dfrac{{R}_{1}{R}_{2}}{{R}_{1}+{R}_{2}}$

$\Rightarrow \dfrac{\rho l}{2A}=\dfrac{{\rho }_{1}\dfrac{l}{A}\times {\rho }_{2}\dfrac{l}{A}}{{\rho }_{1}\dfrac{l}{A}+{\rho }_{2}\dfrac{l}{A}}$
$\Rightarrow \dfrac{\rho }{2}=\dfrac{6\times 3}{6+3}=2$$\Rightarrow \rho =4$