A nichrome wire of length l has a resistance R. It is replaced by another nichrome wire of the same cross-sectional area but of length 2l. What will be the new resistance? Give a reason for your answer.
Generated by claude-sonnet-4-6 · 2026-06-26 01:07 · grounding rag
Model Answer
The new resistance will be 2R.
Reason: Resistance is directly proportional to the length of the conductor, i.e., $R \propto l$. When the length is doubled (from $l$ to $2l$) while the cross-sectional area remains the same, the resistance also doubles. Therefore, new resistance = 2R.
Source: Chapter 11, Section 11.5 – Factors on which the resistance of a conductor depends.
Explanation
- The key formula is $R = \rho \dfrac{l}{A}$. Since $\rho$ (resistivity, same material) and $A$ (same cross-section) are unchanged, $R \propto l$.
- Examiners expect: the answer (2R) and a reason citing the direct proportionality between resistance and length. Both parts are needed for full 2 marks.
- Do not simply state the formula — briefly explain what it means in context.