Q1. [3] medium thorough-understanding
Two resistors, P (nichrome, length l, cross-sectional area A) and Q (copper, same length l, same cross-sectional area A), are connected in series across a battery. Even though the same current flows through both, the heat generated per second in P is much greater than in Q. (i) Name the physical property of the material responsible for this difference, and state how it differs between nichrome and copper. (ii) Using the expression for electrical power dissipated in a resistor, explain why P generates more heat per second than Q despite carrying the same current.
Generated by claude-sonnet-4-6 · 2026-06-26 01:12 · grounding rag
Model Answer
(i) The physical property responsible is electrical resistivity. Nichrome has a very high resistivity ($100 \times 10^{-6}$ Ω m), whereas copper has a very low resistivity ($1.62 \times 10^{-8}$ Ω m). Since both wires have the same length and cross-sectional area, nichrome has a much higher resistance than copper.
(ii) The power (heat per second) dissipated in a resistor is given by:
$$P = I^2R$$
Since both P and Q carry the same current $I$, the heat generated per second depends directly on resistance $R$. As nichrome has far greater resistance than copper, resistor P dissipates much more heat per second than Q.
Source: Chapter 11 — Sections 11.5 (Factors affecting resistance/resistivity) and 11.7 (Heating effect of electric current)
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Explanation
- Part (i) tests knowledge of resistivity as a material property. Examiners expect you to name "resistivity," state that nichrome's resistivity is much higher than copper's, and link this to higher resistance (same l and A).
- Part (ii) requires the formula $P = I^2R$ (from Joule's law). Since I is the same in series, more R → more heat/second. Always write the formula and then reason from it — that's what examiners award marks for.
- Do not confuse resistance (depends on dimensions too) with resistivity (material property only). Part (i) specifically asks for the material property, so "resistivity" is the key term.