Q4. Assertion: the resistivity of a metal rises with temperature. Reason: as the temperature rises the average time between collisions falls, while the number density of free electrons stays nearly the same. Are both true, and does the reason explain the assertion?
Both are true, and the reason explains the assertion: ρ = m/(neτ) with n nearly constant and τ falling (NCERT Eq. (3.27), page 91).
Q5. A nichrome heating element on a 230 V supply draws 3.2 A at first and 2.8 A once it is hot. The room is at 27.0 °C and α = 1.70 × 10−4 °C−1. Find the element’s steady temperature (NCERT Exercise 3.6).
Cold: R1 = 230/3.2 = 71.875 Ω; hot: R2 = 230/2.8 ≈ 82.14 Ω. Then T2 − T1 = (82.14 − 71.875)/
Q6. A copper wire and a piece of pure semiconductor are cooled. How does the resistance of each change?
The copper wire’s resistance falls; the semiconductor’s rises, since its resistivity falls with rising temperature and so rises as it cools (NCERT pages 90–91).