Chapter 3: Current Electricity

Overview

• One-shot detailed explanation of Chapter 3
• Covers all concepts, derivations, and numericals
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Current Electricity

Introduction to Current Electricity

• Previous topics: Electrostatics (charges at rest)
• Chapter focus: Charges in motion
• Current electricity is different from electrostatics

Electric Current

• Definition: Rate of flow of charge (i = q/t)
• Area should be perpendicular to the direction of charge flow
• Types: Instantaneous current (dQ/dt)
• SI Unit: Ampere (1A = 1 Coulomb/1 Second)
• Conventional current: Flow of positive charge
• Electronic current: Flow of electrons
• Direction of current: Opposite to the direction of electron flow
• Electric current is a scalar quantity despite having magnitude and direction

Ohm's Law

• V ∝ I (provided temperature and other physical conditions remain constant)
• V = IR (introducing proportionality constant R – resistance)
• Resistance definition and its unit: Ohm (Ω)
• Symbols for fixed and variable resistances (Resistor, Rheostat)
• Factors affecting resistance: Length, cross-sectional area, nature of material
• Formula: R = ρL/A (ρ = resistivity)
• Resistivity depends on nature of material and temperature

Current Density

• Definition: Current per unit area (J = I/A)
• SI Unit: A/m²
• Current density is a vector quantity
• J = σE (Ohm's Law in vector form)

Conductance and Conductivity

• Conductance (G): Reciprocal of resistance (G = 1/R)
• Unit: Siemens (S)
• Conductivity (σ): Reciprocal of resistivity (σ = 1/ρ)
• Unit: S/m or Ω⁻¹m⁻¹

Drift Velocity

• Definition: Average velocity gained by free electrons in the conductor
• Formula: v_d = (eEτ)/m
• τ = relaxation time (average time between two successive collisions)
• Drift velocity is much less than the thermal velocity of electrons

Derivations

• Ohm’s Law from drift velocity
• Relationship between current and drift velocity (I = neAv_d)
• Resistivity formula: ρ = (m/e²nτ)

Numerical Problems

• Example problem calculating drift speed and current

Additional Topics

Mobility of Charge Carriers

• Definition: Drift velocity per unit electric field (µ = v_d/E)
• Unit: m²/V/s

Temperature Dependence of Resistivity

• Metals: Resistivity increases with temperature
• Semiconductors: Resistivity decreases with temperature r
• Electrolytes: Depend on concentration and viscosity
• Formula: ρ_t = ρ_0 [1 + α(T - T₀)]
• α: Temperature coefficient of resistivity

Heating Effects of Current

• Joule's Law: Heat produced (H = I²Rt)
• Electrical power (P = IV)
• Household heating appliances, electric bulbs, electric fuses
• Efficiency: η = (Useful power output / Total power input)

Combination of Resistors

• Series: R_eq = R₁ + R₂ + R₃...
• Parallel: 1/R_eq = 1/R₁ + 1/R₂ + 1/R₃...

EMF and Internal Resistance

• EMF (E): Work done per unit positive charge in a complete circuit
• Terminal voltage (V): Potential difference across terminals when current flows
• V = E - Ir (discharging), V = E + Ir (charging)
• Internal resistance (r): Resistance within the cell
• Factors affecting internal resistance:
  • Nature and concentration of electrolyte, distance between electrodes, temperature

Kirchhoff's Laws

• Junction Rule: Sum of currents entering a junction = sum of currents leaving
• Loop Rule: Sum of potential differences around a closed loop = 0
• Applications in series-parallel networks

Wheatstone Bridge

• Used to measure unknown resistance accurately
• Balance condition: P/Q = R/S
• Sensitivity: Maximum when resistors are of the same order
• Advantages: Accurate, does not depend on the resistance of the meter or EMF of the cell
• Problem-solving using Wheatstone Bridge

Problem Solving

• Application of concepts in numerical problems
• Detailed solutions with explanations

Further Learning

• Students interested in joining the Drona batch for detailed study and doubt clearing
• Arvind Academy app: Free PDFs, courses, and live classes available
• Importance of regular study and concept clarity for achieving high marks

Conclusion

• Comprehensive coverage of Chapter 3: Current Electricity
• Encouragement to review notes, solve numerical problems, and clarify doubts
• Availability of additional resources and live classes for further assistance

Special Notes & Tips

• Utilize all provided materials and apps for a complete understanding of the topic
• Regular practice and revision are crucial for mastery
• Stay curious and keep questioning to ensure deep learning