Question

In: Physics

Describe the relationship between current and the speed of electron flow

Describe the relationship between current and the speed of electron flow

Solutions

Expert Solution


The volume of the conductor = Al

If n is the number of free electrons per unit volume of the conductor, then the total number of free electrons in the conductor=A/n.

If e is the charge on each electron then total charge on all the free electrons in the conductor

Q=A/ne (1)

Let a constant potential differences V is applied across the ends of the conductor with the help of a battery

The electric field set up across the conductor is given by

E=V/l

Due to this field, the free electrons present in the conductor will begin to move with a drift velocity vd towards the left hand side of the conductor.

Thus the time taken by the free electrons to cross the conductor is

t=l/vd (2)

As current i=q/t (3)

By substituting equation (1) and (2) in equation (3),

We get

i=Alne/l/vd

Or i=Anevd (4)

Since A,n and e are constant

i∞(vd)

Hence the current flowing through a conductor is directly proportional to the drift velocity.


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