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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 2l have the same resistance (R) then its diameter will be _________ d.

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answer is 4.

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Detailed Solution

Each wire has resistance $= ρ \frac{4 ℓ}{{πd}^{2}} = r$

Eight wire in parallel, then equivalent resistance is $\frac{r}{8} = \frac{ρℓ}{2 {πd}^{2}}$

Single copper wire of length 2l has resistance

$\begin{array}{l} R = ρ \frac{2 ℓ \times 4}{{πd}_{1}^{2}} = \frac{ρℓ}{2 {πd}^{2}} \\ \Rightarrow d_{1} = 4 d \end{array}$

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