Drift of Electrons and the Origin of Resistivity

What is resistance? The property of the material to oppose the electric current is known as resistivity. It is inversely proportional to the drift of electrons. To more about drift of electrons and resistivity, let’s explore the article further to know what is resistance, the drift of electrons and the origin of resistivity!

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Introduction

The net velocity of the circuit is zero when electrons move randomly in the circuit and electric field is not applied to the circuit. Drift force is the force driving the electrons through a conductor and the force opposing the drift force is resistivity.

What is Resistance or Resistivity?

The tendency of a material/device towards resistance is the resistivity of the device/circuit. The SI unit of resistivity is ohm-meter. The unit length across the cross-sectional area of the device is also resistivity. Therefore, the nature and temperature of the material also define resistivity (σ).

σ= \( \frac{RA}{ L} \)

The graph of resistivity as follows. The graphs depict current (I) to voltage (V) ratio, whereas, dotted line A, B, C shows the idealized graph. After a certain amount of current, the device starts resisting to the current flowing in the system and the resistivity becomes constant.

Drift of Electrons

The free electrons in a conductor have random velocities and move in random directions. When current is applied across the conductor the randomly moving electrons are subjected to electrical forces along the direction of the electric field.

Due to this electric field, free electrons still have their random moving nature, but they will move through the conductor with a certain along with force. The net velocity in a conductor due to the moving of electrons is referred to as the drift of electrons.

Drift Velocity = \( \frac {Current} {(no.of free Electrons )*(Area of conductor)*(Charge  of Eletrons)} \)

V_d=I/(A*n*e)

For example, let’s say you are crossing a river and moving from one bank to another bank along with the river flow, then you are the electron which is randomly moving and river water acts as the drift force. Then the force applied to the randomly moving electron will result in the change of course of the path of an electron.

Examples for You on What is Resistance!

Question 1: When a potential difference V is applied across a conductor at a temperature T, the drift velocity of electrons is proportional to

1. √V
2. V
3. √T
4. T

Solution: V. We know that Drift velocity v_d ∝ E ∝ (Vl) (∵E=Vl), so for a particular conductor of a particular length, the drift velocity will directly depend upon the voltage. Hence v_d∝V.

Question 2: A steady current flows in a metallic conductor of non-uniform cross-section. Which of the following quantities is constant along the conductor?

1. Drift speed
2. Current
3. Currently density
4. None of these

Solution: Current. When a steady current flows through a metallic conductor of non-uniform cross-section, then drift velocity
V_d=I/(Ane) or V_d∞(1/A). E∞(1/A). Both V_d and E change with A, only current I remain constant.

Question 3: Relation between drift velocity (v_d) of electron and thermal velocity (vt) of an electron at room temp is expressed as

1. v_d=v_t
2. v_d>v_t
3. as v_d<v_t
4. v_d=v_t=0

Solution: v_d<v_t. Electrons with the Fermi energy carry considerable kinetic energy. Their mean thermal velocity at temperature T should be v_t= √3kTm, which generally turns out to be quite large. The average velocity with which electrons must pass along a conductor to carry a current is called drift velocity is given by v_d=I/(Ane) which is much less than the thermal velocity. Hence v_d<v_t.