Two wires A and B of same material, having same lengths and diameters 0·2 mm and 0·3 mm respectively, are connected one by one in a circuit. Which one of these two wires will offer more resistance to the flow of current in the circuit ? Justify your answer.
Generated by claude-sonnet-4-6 · 2026-06-15 06:43 · grounding rag
Model Answer
Wire A will offer more resistance.
Justification: Resistance is given by $R = \rho \dfrac{l}{A}$. Since both wires have the same material and length, resistance depends inversely on area of cross-section. Wire A has a smaller diameter (0.2 mm) and hence a smaller area, so it offers more resistance.
$$R \propto \frac{1}{A} \propto \frac{1}{d^2}$$
$$\frac{R_A}{R_B} = \frac{d_B^2}{d_A^2} = \frac{(0.3)^2}{(0.2)^2} = \frac{9}{4} = 2.25$$
So wire A has 2.25 times more resistance than wire B.
Source: Chapter 11, Section 11.5 – Factors on which the resistance of a conductor depends
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Explanation
- The key formula is $R = \rho \dfrac{l}{A}$, where $A = \dfrac{\pi d^2}{4}$.
- Examiners expect you to: (1) state the correct wire, (2) cite the formula, (3) show the inverse relationship with diameter, and (4) optionally calculate the ratio for full marks.
- Don't forget: same material = same $\rho$; same length = $l$ cancels. Only $d$ differs.