Q 12-03-199JEE MainJEE Main 2021 (18 Mar, Shift 2)Medium
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 ______.
Numerical value type. Enter your answer.
Answer: 4
Each wire has length $l$ and area $A$. In parallel:
$$R = \frac{(6l/A)(3l/A)}{(6l/A) + (3l/A)} = \frac{2l}{A}$$
The combination is equivalent to one wire of length $l$ and area $2A$: $\rho\dfrac{l}{2A} = \dfrac{2l}{A} \Rightarrow \rho = 4\ \Omega$ cm.
Solution by Sreeraj P, M.Sc Physics