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For a metallic conductor obeying Ohm law, if temperature increases

A{'text': 'Resistivity ρ decreases with temperature', 'label': 'A'}
B{'text': 'Drift velocity increases with temperature at constant field', 'label': 'B'}
C{'text': 'Relaxation time τ decreases; therefore ρ increases', 'label': 'C'}
D{'text': 'Conductivity σ increases with temperature', 'label': 'D'}
Answer & Solution
Correct answer: C. {'text': 'Relaxation time τ decreases; therefore ρ increases', 'label': 'C'}
1. From v_d = -eEτ/m, drift velocity is directly proportional to relaxation time τ. 2. In metals, increased temperature makes lattice vibrations stronger, causing more electron-ion collisions. 3. Average time between collisions τ therefore decreases with temperature. 4. Since j = σE and σ = neτ e / m, decreasing τ decreases σ and increases ρ = 1/σ. _Source: NCERT Class 12 Physics, Ch 3 "Current Electricity", §3.5_
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