Science (086) — AI-generated practice question

The resistance of a conductor is given by:

$$R = \rho \frac{l}{A}$$

where $l$ is length, $A$ is area of cross-section, and $\rho$ is the resistivity of the material.

Effect of length: Since $R \propto l$, doubling the length doubles the resistance. A longer wire means electrons must travel farther, encountering more opposition.

Effect of area: Since $R \propto \dfrac{1}{A}$, doubling the cross-sectional area halves the resistance. A wider wire provides more paths for electrons to flow, reducing opposition to current.

Thus, resistance depends directly on length and inversely on area of cross-section.

Source: Chapter 11, Section 11.5 – Factors on which the resistance of a conductor depends.

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• Examiners expect the formula $R = \rho \frac{l}{A}$ to be written — this is the core of the answer and earns a mark directly.
• One mark each for explaining the effect of length and area using the proportionality relationships ($R \propto l$ and $R \propto 1/A$).
• Avoid lengthy analogies; state the relationship, then give a brief physical reason. That's all that's needed for 3 marks.