Q 12-03-168JEE MainJEE Main 2022 (25 Jul, Shift 1)Easy
Eight copper wires of length $l$ and diameter $d$ are joined in parallel to form a single composite conductor of resistance $R$. If a single copper wire of length $2l$ has the same resistance $R$, then its diameter will be ______ $d$.
Numerical value type. Enter your answer.
Answer: 4
Parallel: $R = \dfrac18\cdot\dfrac{\rho l}{\pi d^2/4}$. Single wire: $R = \dfrac{\rho(2l)}{\pi D^2/4}$.
$$\frac{2}{D^2} = \frac{1}{8d^2}\ \Rightarrow\ D^2 = 16d^2\ \Rightarrow\ D = 4d$$
Solution by Sreeraj P, M.Sc Physics