Science — CBSE Class 10 board question

Given: radius $r = 0.01$ cm $= 1 \times 10^{-4}$ m, length $l = 1.0$ cm $= 1 \times 10^{-2}$ m, $R = 7$ Ω

Area of cross-section: $A = \pi r^2 = 3.14 \times (10^{-4})^2 = 3.14 \times 10^{-8}$ m²

Using $R = \rho \dfrac{l}{A}$:

$$\rho = \frac{R \times A}{l} = \frac{7 \times 3.14 \times 10^{-8}}{1 \times 10^{-2}}$$

$$\rho = 21.98 \times 10^{-6} \approx 2.2 \times 10^{-5} \text{ Ω m}$$

Source: Chapter 11, Section 11.5

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• The key formula is $\rho = RA/l$ (rearranged from $R = \rho l/A$).
• Always convert all units to SI (metres) before substituting.
• Examiners award 1 mark for correct substitution and 1 mark for the final answer with correct unit (Ω m). Don't forget to write the unit.