Question

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 (for example, by cooling it), the current will
(a) increase
(b) decrease
(c) remain constant
(d) become zero

Answer 1

(a) increase

If the number of collisions of the free electrons with the lattice is decreased, then the drift velocity of the electrons increases.
Current i is directly proportional to the drift velocity 'V_d' and is given by the following relation:
i = neAV_{d ,} where 'n' is the number density of electrons and 'A' is the area of the cross-section of the conductor.
So, we can easily see that current increases with increase in drift velocity.