A-Level Physics May/June 2024 Q3(c)(i): The resistance of the lightning rod is 9.6Ω. The resistivity of copper is 1.7 × 10⁻⁸Ωm.…

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  The relationship between resistance $R$, resistivity $\rho$, length $L$ and cross-sectional area $A$ is: $R = \frac{\rho L}{A}$

  The cross-sectional area of the rod is a circle, so $A = \pi r^2$. $R = \frac{\rho L}{\pi r^2}$

  Rearrange the formula to make radius $r$ the subject: $r^2 = \frac{\rho L}{\pi R}$ $r = \sqrt{\frac{\rho L}{\pi R}}$

  Substitute the values into the equation. The length $L$ is assumed to be 95 m from the context of the full question paper. $r = \sqrt{\frac{(1.7 \times 10^{-8}) \times 95}{\pi \times 9.6}}$ $r = \sqrt{\frac{1.615 \times 10^{-6}}{30.159...}}$ $r = \sqrt{5.3546... \times 10^{-8}}$ $r = 2.314... \times 10^{-4} \text{ m}$

  Rounding to 2 significant figures (as per the data provided): $r = 2.3 \times 10^{-4} \text{ m}$

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  How the marks are awarded

  • C1 — Correctly stating the formula for resistance in terms of resistivity, length and area, $R = \rho L / A$.
  • C1 — Correct substitution of all values into the formula, including the use of $A = \pi r^2$. This is demonstrated by the line 9.6 = 1.7 x 10^-8 × 95 / πr² or the subsequent rearrangement and substitution.
  • A1 — Calculating the correct final answer of $2.3 \times 10^{-4}$ m, rounded to an appropriate number of significant figures (2 s.f.).

  Common mistakes

  • Forgetting to use the formula for the area of a circle ($A = \pi r^2$) and instead just using the radius in the main equation.
  • Calculating the cross-sectional area ($A$) correctly but then forgetting to take the square root to find the radius.
  • Incorrectly rearranging the formula, for example by having $\pi$ or $R$ in the numerator instead of the denominator.
  • Calculating the diameter ($d=2r$) and presenting that as the final answer instead of the radius.

  Examiner tip: Always start by writing down the base formula, then rearrange it algebraically to make your target variable the subject before substituting any numbers to minimise calculation errors.

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