Q1. [1]
In case of four wires of same material, the resistance will be minimum if the diameter and length of the wire respectively are
- A D/2 and L/4
- B D/4 and 4L
- C 2D and L
- D 4D and 2L
Previously asked in CBSE board exam
2024 31/3/1 Q14
Generated by claude-sonnet-4-6 · 2026-06-15 06:46 · grounding rag
Model Answer
Option D: 4D and 2L
Using $R = \rho \dfrac{l}{A} = \rho \dfrac{l}{\pi d^2/4}$, resistance is minimum when length is minimum and diameter is maximum. Option D (diameter = 4D, length = 2L) gives the largest diameter and a relatively short length, hence minimum resistance.
Explanation
- $R \propto l$ and $R \propto \dfrac{1}{d^2}$ (since $A = \pi d^2/4$).
- To minimise R: maximise diameter, minimise length.
- Compare all options: Option D has the largest diameter (4D), making $d^2$ largest, which dominates over the longer length (2L). This gives the smallest resistance among all four choices.
- Source: Chapter 11, Section 11.5 (Factors on which resistance depends).
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