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
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$v_d$ is the drift velocity,
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$e$ is the charge of an electron,
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$E$ is the electric field strength,
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$m_e$ is the mass of an electron, and
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$n$ is the electron concentration.
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Factors affecting drift velocity:
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Electric field strength: Stronger electric fields result in higher drift velocities.
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Temperature: Higher temperatures increase the thermal motion of electrons, reducing drift velocity.
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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
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$R$ is the resistance,
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$\rho$ is the resistivity of the material (a measure of how strongly it opposes the flow of current),
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$L$ is the length of the conductor, and
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$A$ is the cross-sectional area of the conductor.
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Factors affecting resistance:
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Resistivity of the material: Materials with higher resistivity offer more resistance to current flow.
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Length of the conductor: Longer conductors have higher resistance.
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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
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$\mu$ is the mobility,
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$v_d$ is the drift velocity, and
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$E$ is the electric field strength.
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Comparison of electron mobility and hole mobility:
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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
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$V$ is the voltage,
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$I$ is the current,
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$R$ is the resistance.
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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)