Eight copper wire 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 $2\,l$ have the same resistance $(R)$ then its diameter will be $.....d$.
JEE MAIN 2022, Easy
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Each wire has resistance $=\rho \frac{4 \ell}{\pi d ^{2}}=r$
Eight wire in parallel, then equivalent resistance is $\frac{ r }{8}=\frac{\rho \ell}{2 \pi d ^{2}}$
Single copper wire of length $2 l$ has resistance
$R =\rho \frac{2 \ell \times 4}{\pi d _{1}^{2}}=\frac{\rho \ell}{2 \pi d ^{2}}$
$d _{1}=4 d$
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