Q1. [1] § 11.6 RESISTANCE OF A SYSTEM OF RESISTORS
A piece of wire of resistance 'R' is cut lengthwise into three identical parts. These parts are then connected in parallel. If the equivalent resistance of this combination is R′, then the value of R/R′ is :
- (a) 1/9
- (b) 1/3
- (c) 3
- (d) 9
Previously asked in CBSE board exam
2025 31/4/1 Q12
Generated by claude-sonnet-4-6 · 2026-06-15 06:45 · grounding rag
Model Answer
(d) 9
Cutting wire lengthwise into 3 parts: each part has resistance R/3. In parallel: 1/R′ = 3/(R/3) = 9/R, so R′ = R/9. Therefore R/R′ = 9.
Source: Chapter 11, Section 11.6.2
---
Explanation
- Cutting lengthwise into 3 identical parts means each part has one-third the original resistance (R/3), since resistance ∝ length (and cross-section stays same per part here — note: lengthwise cut keeps length same but reduces cross-section, but the question treats them as identical parts each of resistance R/3 by analogy with the textbook's Exercise Q1).
- For 3 equal resistors (R/3) in parallel: R′ = (R/3)/3 = R/9.
- So R/R′ = 9. This mirrors the textbook Exercise Q1 (5 parts → ratio 25); here with 3 parts the ratio is 3² = 9.
If a question refers to an image, map, graph or diagram that is not shown here, find the actual CBSE question paper on the CBSE website:
cbse.gov.in.