# Relationship between current, drift velocity and thermal velocity

## Main Question or Discussion Point

for a normal solid cylindrical resistor, made of say copper, at room temperature, describe the relationshop between the current in the conductor, the drift velocity of conduction electrons in the conductor, and the thermal velocity of conduction electrons in the conductor.

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The drift velocity and current are proportional. The thermal speed depends on the temperature. Current is not much affected.

could u give a formula pls

The thermal energy is 3/2 kT, so equating that to kinetic energy, thermal velocity is sqrt(3kT/m), on the order of 10^5 m/s at room temperature.

The drift velocity is related to current like I = vnqA, where n is the concentration (per volume), of electrons, q is the charge. In terms of current density, J = vnq. Current density is charge per second per area, so dividing both sides by q relates a particle flux on the left hand side to a concentration times a velocity on the right. This is a general relationship in kinetics.