You’re right that electrons, which carry electric current, have mass and are influenced by gravity. However, the gravitational force on an electron is minuscule compared to the electromagnetic forces driving the electrons through a circuit or a conductor.

To give you some perspective:

1. Gravitational Force: The force due to gravity on an electron is given by ( F_g = m \times g ) where ( m ) is the mass of an electron (~9.11 × 10^-31 kg) and ( g ) is the acceleration due to gravity (~9.81 m/s^2). The resulting force is extremely small.

2. Electromagnetic Force: When an electric potential (voltage) is applied across a conductor, it exerts an electromagnetic force on the electrons. This force is many orders of magnitude larger than the gravitational force on the electrons.

Due to the vast difference in magnitude between these forces, the gravitational force on electrons in a circuit is effectively negligible. Electrons “move” because of the electric field (from the applied voltage) pushing/pulling them, not because of gravity.

That said, in the absence of any other forces, electrons would indeed fall due to gravity, just as anything else would. However, in the context of electrical circuits and currents, gravity’s influence on individual electrons is overshadowed by the much stronger electromagnetic forces.