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)