Science (086) — AI-generated practice question

Since P and Q are made of the same material, their resistivity (ρ) is the same. Let length = $l$ and area of P = $A$, so area of Q = $2A$.

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

$$R_P = \rho \frac{l}{A}, \quad R_Q = \rho \frac{l}{2A} = \frac{1}{2} R_P$$

So $R_Q$ is half the resistance of $R_P$.

Since both are connected to the same battery (same V), by Ohm's law $I = V/R$:

$$\frac{I_Q}{I_P} = \frac{R_P}{R_Q} = 2$$

Conclusion: The current through Q is twice the current through P.

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

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• The key formula is $R = \rho l/A$. Same material → same ρ; same length → only area differs.
• Q has double the area, so half the resistance.
• Same voltage, half the resistance → double the current (Ohm's law: $I = V/R$).
• Examiners award marks for: writing the formula, substituting correctly for both resistors, stating the ratio of resistances, and applying Ohm's law to get the current ratio. Don't skip steps.