Current is the flow of electrically charged particles. So we can say that current inside a conductor depends on number of charges present, speed at which they are moving and the charge they are carrying. Under the effect of electric field, charges inside a conductor move in random colliding with each other with random thermal velocities. When electric field is applied, the average speed of an electron with which it drifts towards the positive end of the conductor is called drift velocity. The current that flows inside the conductor due to the drift velocity is the drift current.
Any conductor will have some free electrons when the temperature around is above zero. So at room temperature, substances that are conductors are said to have free electrons inside them moving randomly, colliding with one another. This is what is happening inside a conductor before electric field is supplied. Good conductors (metals) have the most charge carriers while semi conductors have fewer charge conductors than the metals. Insulators do not have any free electron available for current conduction.
Copper wires are widely used at homes. Inside the copper wire, there are some trillions of electrons moving past any given point every second. If one electron is pushed, it causes many other electrons which in turn the movement of all the electrons.
Let’s see what happens when electric field is applied. The electrons start to move towards the positive terminal of the applied potential more randomly, colliding with each other, initially losing kinetic energy on collision and then re-acquiring some kinetic velocity due to the presence of electric field. Though the motion is random, there is a net resultant motion or we could say the electric field causes the electrons to drift towards the positive terminal.
The drift velocity of the electrons is actually very less which means electrons travel at incredibly slow velocities. So how does the bulb glow at the same instant when the switch is flipped ON? Hence when you switch ON a bulb, all that happens inside is that one electron starts moving instantly and this happens throughout the wire. We actually don’t have to “wait” for the electrons to move from the switch to the bulb.