Q1. [4]
Three students Shweta, Ayesha and Samridhi were performing an experiment to understand the factors on which the resistance of a conductor depends. Each one of them completed electric circuit with the help of a cell, an ammeter, a plug key and wire.
Shweta put nichrome wire of length 'l' in the circuit and after plugging the key, noted current in the ammeter.
Ayesha put nichrome wire of same thickness but twice the length i.e. '2l' in the circuit and after plugging the key, noted current in the ammeter.
Samridhi took copper wire of length 'l' and same thickness in the circuit and after plugging the key, noted current in the ammeter.
Answer the following questions based on the passage:
- (a) If the ammeter reading is X ampere with nichrome wire of length 'l', then what will be the ammeter reading if the length of nichrome wire is doubled with same area of cross-section ? [1]
- (b) What happens to the ammeter reading if the area of cross-section of nichrome wire is doubled, keeping the length of wire 'l' the same ? [1]
- (c) Define 'resistivity'. Write its SI unit. Compare the resistivity of an alloy with its constituents metals. [2]
Previously asked in CBSE board exam
2026 31/5/1 Q38
Generated by claude-sonnet-4-6 · 2026-06-15 06:42 · grounding stimulus
Model Answer
(a) When length is doubled, resistance doubles (R ∝ l). By Ohm's law, current halves.
∴ Ammeter reading = X/2 ampere
(b) When area of cross-section is doubled, resistance halves (R ∝ 1/A). Therefore, current doubles.
∴ Ammeter reading increases (becomes 2X ampere).
(c) Resistivity is defined as the resistance of a conductor of unit length and unit area of cross-section.
$$\rho = \frac{R \cdot A}{l}$$
SI unit: Ohm-metre (Ω·m)
Comparison: The resistivity of an alloy is generally higher than that of its constituent metals. For example, nichrome (an alloy) has much higher resistivity than nickel or chromium alone.
Source: Chapter 11 – Electricity, Resistance of a System of Resistors / Resistivity
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Explanation
- For (a) and (b), use R ∝ l and R ∝ 1/A directly, then apply V = IR (V constant from cell).
- For resistivity, examiners expect: definition, formula, SI unit, and the key comparison point (alloy > constituent metals). All four elements together fetch full 2 marks.
- Write "Ω·m" correctly — a common mistake is writing Ω/m.
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