Summary of CUET Physics: Current Electricity in One Shot | CUET 2024 Preparation

Summary of "CUET Physics: Current Electricity in One Shot | CUET 2024 Preparation"

This comprehensive lecture covers the entire chapter of Current Electricity for CUET 2024 and Class 12 board preparation in a single session. The instructor explains fundamental concepts, formulas, laws, and practical applications, often including examples, derivations, and problem-solving techniques. The lecture also touches on related topics like resistivity, conductivity, circuit analysis, and measuring instruments.

Main Ideas, Concepts, and Lessons

1. Electric Current: Definition and Basics

Electric current is the rate of flow of charge through a conductor’s cross-sectional area.
Formula: \( I = \frac{Q}{t} \), where \( I \) is current, \( Q \) is charge, and \( t \) is time.
Unit of current: Ampere (A), where 1 Ampere = 1 Coulomb/second.
Direction of current is taken as the direction of positive charge flow.
If negative charges move, current direction is opposite to their movement.

2. Current as a Scalar Quantity

Current has magnitude and direction but is not a vector because it doesn’t follow vector addition rules.
When currents combine, they add algebraically (scalar addition).

3. Average and Instantaneous Current

Average current: \( I_{avg} = \frac{\Delta Q}{\Delta t} \).
Instantaneous current: \( I = \frac{dQ}{dt} \), derived using calculus.
Example problems demonstrate calculating average and instantaneous current using charge-time functions.

4. Current in Different Materials

Conductors: Have free electrons that move easily.
Electrolytes: Ions carry current through liquid medium.
Semiconductors: Both electrons and holes act as charge carriers.
Insulators: Very few free charge carriers; high resistivity.

5. Ohm’s Law

Relationship between voltage \( V \), current \( I \), and resistance \( R \): \( V = IR \).
Resistance is proportional to length \( L \) and inversely proportional to cross-sectional area \( A \): \( R \propto \frac{L}{A} \).
Resistance depends on material (resistivity \( \rho \)) and temperature.
Ohmic conductors follow Ohm’s Law; non-ohmic conductors do not.

6. Resistivity and Temperature Dependence

Resistivity \( \rho \) is a material property with units ohm-meter.
Resistance formula: \( R = \rho \frac{L}{A} \).
Resistivity increases with temperature for conductors (positive temperature coefficient \( \alpha \)).
Resistivity decreases with temperature for semiconductors (negative \( \alpha \)).
Formula for resistance at temperature \( T \): \( R_T = R_0 (1 + \alpha \Delta T) \).

7. Alloys and Temperature Coefficient

Alloys like Nichrome, Manganin, and Constantan have very low temperature coefficients, making their resistance almost independent of temperature.

8. Conductance, Conductivity, and Mobility

Conductance \( G = \frac{1}{R} \).
Conductivity \( \sigma = \frac{1}{\rho} \).
Mobility \( \mu = \frac{v_d}{E} \) where \( v_d \) is drift velocity and \( E \) is electric field.

9. Current Density

Current density \( J = \frac{I}{A} \) (vector quantity).
Relationship: \( \mathbf{J} = \sigma \mathbf{E} \).

10. Microscopic Model of Current

Electrons exhibit random thermal motion with zero net current.
When electric field is applied (battery connected), electrons drift with a small average velocity (drift velocity).
Relaxation time: average time between collisions.
Derivation of current in terms of number density \( n \), charge \( e \), drift velocity \( v_d \), and area \( A \):
\( I = n e A v_d \)

11. Kirchhoff’s Laws

Junction rule (Kirchhoff’s First Law): Sum of currents entering a junction equals sum leaving.
Loop rule (Kirchhoff’s Second Law): Sum of potential differences around any closed loop is zero.

12. Series and Parallel Circuits

Series: Resistances add \( R_{eq} = R_1 + R_2 + \ldots \).
Parallel: Reciprocal of resistances add \( \frac{1}{R_{eq}} = \frac{1}{R_1} + \frac{1}{R_2} + \ldots \).