A metallic resistor is connected across a battery. If the number of collisions of the free electrons with the lattice is somehow decreased in the resistor (such as cooling it), the current will
Answer & explanation
Correct answer: option 2
The correct answer is Option (2) → increase
Between collisions the free electrons are accelerated by the field, so the drift speed depends on the average time between collisions \( \tau \). Fewer collisions mean a longer \( \tau \).
\( \displaystyle v_d = \frac{eE\tau}{m} \)
\( \displaystyle \rho = \frac{m}{ne^{2}\tau} \)
A longer \( \tau \) gives a larger drift speed and a smaller resistivity, so the resistance of the resistor falls. The battery keeps the same voltage across it, so by \( I = V/R \) the current increases.
Note: A similar question was also asked in CUET (UG) 2026 on 29-05-2026 (Slot 1).
NCERT (2026-27):
Temperature Dependence of Resistivity – “… From this equation, resistivity of a material is given by
\( \displaystyle \rho = \frac{1}{\sigma} = \frac{m}{n e^2 \tau} \qquad (3.27) \)
\( \rho \) thus depends inversely both on the number \( n \) of free electrons per unit volume and on the average time \( \tau \) between collisions.”