Drift Velocity and origin of resistivity , Practice problems , FAQs

Your physics teacher gives you a task: take some connecting wires, connect them to a battery, and connect the other end of the wires to a bulb. You notice that the bulb glows. Your cell phone runs out of charge. You plugin the charger, and the battery starts charging. So what do you think made the bulb and the mobile phone work? The answer is electricity. One can imagine electricity, or current, to be charges flowing from one place to another. Current is not produced from anywhere; instead, when a metallic conductor is connected by a battery between its ends, current flows from the positive terminal to the negative terminal of the battery. A quantity named “emf” existing between the battery terminals pushes the charges from one place to another; this constitutes the flow of “conventional current”. The flow of electrons is, however; opposite to that of the conventional current. They move with a velocity called “drift velocity”; one can imagine a bunch of electrons “drifting” from one place to another. Let us learn about this drift velocity in detail.

Table of contents

• What is drift velocity?
• Current density
• Relaxation time
• Mobility
• Resistivity, conductivity, relaxation time
• Practice problems
• FAQs

What is drift velocity?

The velocity with which the negatively charged electrons drift towards the positive end of the conductor is called drift velocity. Whenever a voltage is applied between the ends of the conductor, an electric field is established between them. This exerts a force on the electrons; causing them to drift. The direction of drift velocity is opposite to that of the electric field.

Let be the current flowing in the conductor; let be the number of charges per unit volume and be the electronic charge. The conductor has a area of cross section and length Then,

; where is the charge flown in a time

Now is the total charge flowing in the conductor. Then, 

indicates the drift velocity of the electrons. 

The value of drift velocity is of the order of

Current density

A vector quantity whose magnitude is equal to the electric current flowing per unit area, a normal vector to the area of cross section (also called area vector) is known as current density. Let indicate the average current density where a current flows through an area vector  

Then,

If indicates the current density and indicates the area vector, then

Current  

Relaxation time

The electrons in a conductor are in a state of random motion colliding with each other frequently. The average time between two consecutive collisions when the electrons do not collide at all is called relaxation time(. 

Then the drift velocity , where is the acceleration. Let indicate the electric field that is established in the conductor; then 

Where indicates the mass of an electron. Now, 

sign indicates that the direction of the electric field and drift velocity are different.

Mobility

Mobility( refers to the ease with which the electrons can flow when a voltage is applied; it is defined as the ratio of the drift velocity to the electric field. 

The unit of mobility is

Resistivity, conductivity, relaxation time

We know that the current density . Substituting the value of in

where is called the conductivity of the material. 

Conductivity of a material is a measure of its ability to allow current to pass through it. 

Hence,

Resistivity , can be written as  

Resistivity of a material is a measure of its ability to stop current from flowing through it. 

Video explanation

https://www.youtube.com/watch?v=DHAHG_uDufM&t=5022s

Practice problems

Q 1.Calculate the current flowing through a copper wire whose length is area of cross section when a potential difference of is applied to it. Given ,

.

(a) (b) (c) (d)

A. a

Given,

Let be the electric field inside the conductor. 

Then 

Now mobility Drift velocity,

Current flowing in the conductor,

Q 2.Which of the following relations indicate the variation of drift velocity varying with the intensity of electric field ?

(a) (b) ( c ) constant (d)

A. a

Q 3. When a current of is flowing through a conductor, the drift velocity is recorded as When a current of is flowing through a conductor of radius the drift velocity will be 

(a) (b) ( c ) (d)

A. b 

The current is related to the drift velocity as 

Let indicate the new velocity. Then

Where is the new current. Dividing both equations, we get 

;

Q 4. The number density of electrons flowing in a conductor is given by How long does it take for an electron to reach from one end of the wire to another? Given that the length of the conductor is Given that the area of cross section of the conductor is and the current flowing in it is

(a) (b) ( c ) (d)

A. a

 Given ,

Drift velocity

Time taken to reach the other end of the wire,

FAQs

Q 1. Does drift velocity depend upon the applied voltage?
A. Yes,

  where is the applied voltage.

Q 2. Current density is a vector quantity. Why? 
A. Current density is defined as the current flowing per unit area vector, a normal vector to the area of cross section across which current flows, therefore direction matters. 

Q 3. Does temperature affect the drift velocity ?
A. Relaxation time, acceleration of electrons.

As temperature increases, the relaxation time decreases, leading to a decrease in drift velocity. 

Q 4. The direction of drift velocity is opposite to the direction of the electric field. Why?
A. Electrons travel from low potential to high potential. Therefore, the electric field is opposite to that of drift velocity.