Why don’t charge carriers constantly accelerate in an electric circuit?

Question

With my current knowledge of electric circuits and electrostatic fields, I would expect that the electric field generated by the potential difference of, say, a cell should exert a constant force upon the charge carriers in the wire.

From Newton’s Second Law, which states $F = ma$, I would therefore expect the charge carriers to constantly accelerate.

However, from the equation $I = nAqv$, we can see that the drift velocity stays constant so long as the current and charge of the carriers does.

So my question is: how come the charge carriers don’t accelerate constantly? Is there some kind of balancing force that keeps them at a constant drift velocity?

Answer 1

So my question is: how come the charge carriers don’t accelerate constantly? Is there some kind of balancing force that keeps them at a constant drift velocity?

The charge carriers alternatively acquire kinetic energy from the electric field and give up kinetic energy due to collisions with atoms, other electrons, or impurities in the conductor that cause resistance.

Essentially, the positive work done by the electric field on the charge carriers equals the negative work done on the charge carriers by the resistance, for a net work of zero and no change in kinetic energy.

Hope this helps.