Notes from Toppers

Drift Velocity and Resistance

1. Drift Velocity:

  • Definition: Drift velocity is the average velocity of charge carriers (usually electrons) in a conductor under the influence of an electric field.
  • Formula:

$$v_d = \frac{eE}{m_e n},$$

where

  • $v_d$ is the drift velocity,

  • $e$ is the charge of an electron,

  • $E$ is the electric field strength,

  • $m_e$ is the mass of an electron, and

  • $n$ is the electron concentration.

  • Factors affecting drift velocity:

  • Electric field strength: Stronger electric fields result in higher drift velocities.

  • Temperature: Higher temperatures increase the thermal motion of electrons, reducing drift velocity.

  • Carrier concentration: Higher carrier concentration leads to more frequent collisions and lower drift velocity.

2. Resistance:

  • Definition: Resistance is the opposition offered by a material to the flow of electric current.
  • Formula:

$$R = \frac{\rho L}{A},$$

where

  • $R$ is the resistance,

  • $\rho$ is the resistivity of the material (a measure of how strongly it opposes the flow of current),

  • $L$ is the length of the conductor, and

  • $A$ is the cross-sectional area of the conductor.

  • Factors affecting resistance:

  • Resistivity of the material: Materials with higher resistivity offer more resistance to current flow.

  • Length of the conductor: Longer conductors have higher resistance.

  • Cross-sectional area of the conductor: Thinner conductors have higher resistance.

3. Mobility of Charge Carriers:

  • Definition: Mobility is a measure of how easily charge carriers (electrons or holes) move through a material under the influence of an electric field.
  • Formula:

$$\mu = \frac{v_d}{E},$$

where

  • $\mu$ is the mobility,

  • $v_d$ is the drift velocity, and

  • $E$ is the electric field strength.

  • Comparison of electron mobility and hole mobility:

  • Electrons generally have higher mobility than holes in most materials.

4. Ohm’s Law:

  • Statement: Ohm’s law states that the current (I) flowing through a conductor is directly proportional to the voltage (V) applied across it, provided the temperature and other physical conditions remain constant.
  • Formula:

$$V = IR,$$

where

  • $V$ is the voltage,

  • $I$ is the current,

  • $R$ is the resistance.

  • Graphical representation: Ohm’s law can be represented graphically as a straight line passing through the origin in a voltage (V) versus current (I) plot. The slope of this line represents the resistance.

5. Kirchhoff’s Laws:

  • Kirchhoff’s current law (KCL): The total current entering a node (junction) in a circuit must equal the total current leaving that node.
  • Kirchhoff’s voltage law (KVL): The algebraic sum of the voltages around any closed loop in a circuit must be equal to zero.

References:

  • NCERT Physics Class 12, Chapters 3 (Current Electricity) and 4 (Moving Charges and Magnetism)
  • NCERT Physics Class 11, Chapter 12 (Electricity)


Table of Contents