✓ Board-verified
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 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.
(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)
\[\begin{aligned}
\rho & =R \frac{A}{l} \\
& =\frac{0 \cdot 04 \Omega \times 1 \cdot 4 \times 10^{-6} \mathrm{~m}^{2}}{2 \mathrm{~m}} \\
& \quad=2 \cdot 8 \times 10^{-8} \Omega \mathrm{~m}
\end{aligned}
\]
More from Electricity
- In domestic electric circuits the wiring with 15 A current rating is for the electric devices which have2023 · asked 3×
- Assertion: Electrons move from lower potential to higher potential in a conductor. Reason (R): A dry cell…2024 · asked 3×
- The resistance of a wire of 0.01 cm radius and 1.0 cm length is 7 Ω. Calculate its resistivity. OR An…2026 · asked 3×
- Four identical resistors of 12 Ω each are connected in series to form a square ABCD as shown in the figure.…2025 · asked 3×
- The resistance of a wire of 0.01 cm radius is 7 ohms. If the resistivity of the material of the wire is 44 ×…2025 · asked 3×
- Read the following passage and answer the questions that follow: Swati, a class 10 student, observes that…2026 · asked 3×
- For verifying Ohm's law, we design an electric circuit diagram in which we show the arrangement of different…2023 · asked 3×
- The minimum number of identical bulbs of rating 4V; 6W, that can work safely with desired brightness, when…2025 · asked 3×
CBSE Class 10 Science past-paper question from the 2022board exam, with the answer as CBSE’s own marking scheme gives it. Where our answers come from.