Question

The figure shows two connected wires that are made of the same material. The current entering the wire on the left is 2.0 A and in that wire the electron drift speed is vd. What is the electron drift speed in the wire on the right side?

Answer 1

Concepts and reason

The concept required to solve the problem is the drift speed.

Write the relationship between the current, the drift velocity, number of electrons per atom, electronic charge and cross-sectional area of the wire. Derive the proportionality of the drift velocity with the area of cross section of the wire. Compare the areas to calculate the drift velocity.

Fundamentals

The drift velocity of the electron through the wire is,

Here, is the current, is the number of electrons per atom, is the electronic charge and is the area of cross section.

Area of cross section of wire is,

Here, is the diameter of the wire.

Area of cross section of left wire is,

Here, is the diameter of the left wire.

Substitute for and for . The area of cross section of left wire is,

Area of cross section of right wire is,

Here, is the diameter of the right wire.

Substitute for and for . The area of cross section of right wire is,

The ratio of cross sectional areas, , is.

The drift velocity of the electron through the left wire is,

Here, is the current through the left wire, is the number of electrons per atom, is the electronic charge.

The current through both the wires is same since the wires are connected in series. The number of electrons per atom is same for both the wires since the wires are made of same material. The electronic charge is a unique value.

The drift velocity of the electron through the left wire is,

The ratio of drift velocities, , is,

Substitute for . The ratio of drift velocity,

The drift velocity of electron in right wire is,

Ans:

The drift velocity of electron in right wire is .