Question:
A cylindrical conductor of length l and uniform area of cross-section A has resistance R. Another conductor of length 2l and resistance R of the same
material has area of cross-section.
(a) A/2
(b) 3A/2
(c) 2A
(d) 3A
Solution:
(c).
Explanation : $\mathrm{R}=\rho \frac{l}{\mathrm{~A}}$ $\ldots(i)$
Also $\mathrm{R}=\frac{\rho(2 l)}{\mathrm{A}^{\prime}}$ $\ldots(i i)$
From eqns. $(i)$ and $(i i)$
$\frac{1}{\mathrm{~A}}=\frac{2}{\mathrm{~A}^{\prime}}$ or $\mathrm{A}^{\prime}=2 \mathrm{~A}$
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