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Science · 2022 · 3 marks
CBSE 2022 · Region 4 · Set 3 · Q8
(a) Write the relationship between electrical resistance and electrical resistivity for a metallic conductor of cylindrical shape. Hence derive the…
(a)
Write the relationship between electrical resistance and electrical resistivity for a metallic conductor of cylindrical shape. Hence derive the SI unit of electrical resistivity.
(b)
Find the resistivity of the material of a metallic conductor of length $\displaystyle 2$ m and area of cross-section $\displaystyle 1.4 \times 10^{-6} \mathrm{~m}^{2}$. The resistance of the conductor is $\displaystyle 0.04$ ohm.
Marking-scheme solution
(a)
\(\displaystyle \rho=R \frac{A}{l}\)
SI unit of \(\displaystyle \rho=\mathrm{ohm} \times \frac{m^{2}}{m}\)
\[=\text { ohm × metre } / \Omega \mathrm{m}
\]
(b)
\[\begin{aligned}
\rho & =R \frac{A}{l} \\
& =\frac{0 \cdot 04 \Omega \times 1 \cdot 4 \times 10^{-6} \mathrm{~m}^{2}}{2 \mathrm{~m}} \\
& \quad=2 \cdot 8 \times 10^{-8} \Omega \mathrm{~m}
\end{aligned}
\]
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CBSE Class 10 Science past-paper question from the 2022 board exam, with the answer as CBSE’s own marking scheme gives it. Where our answers come from.