Lecture Notes: Electricity and Magnetism

Introduction

• Evening greetings.
• Booster energy: Flow of charges, flow of electrons.

Fundamental Concepts

Current (I)

• Symbol: I
• Formula: (I = \frac{Q}{T})
  • Q: Charge
  • T: Time
• Instantaneous current: ( \frac{dQ}{dT} )

Opposite Motion of Negative Charges

• Oppositional force to negative charge motion
• Potential difference directly proportional to current: Ohm's Law: (V = I \times R)

Resistance (R)

• Resistance opposes current flow.
• High resistance in conductors made of the same material.
• Key Formula: (R = \frac{\rho L}{A})
  • (\rho): Resistivity
  • L: Length of conductor
  • A: Cross-sectional area
• Unit of resistance depends on material.
• Relation between current and area: (J = \frac{I}{A})
• Equation: (V = IR)

Drift Velocity

• Definition: Average velocity of free electrons in a direction opposite to the applied electric field.
• Key Formulas:
  • (V_d = -\frac{eE\tau}{m})
  • (V_d = \frac{J}{nq})
  • e: Charge of electron
  • E: Electric field
  • \tau): Relaxation time
  • m: Mass of electron
  • n: Number of electrons
  • q: Charge
• Example: Calculate drift velocity.

Effect of Temperature on Resistance

• As temperature increases, resistance in conductors increases.
• Different effects on semiconductors and alloys like Nichrome and Manganin.
• Resistivity relation to collision time: (\rho = \frac{m}{ne^2\tau})

Cells and Batteries

• Electromotive Force (EMF): Voltage when no current flows.
• Internal resistance: Resistance inside the cell.
• Terminal voltage: Voltage across cell terminals.
• Key Formula: (V = E - Ir)
• Battery combinations:
  • Series: (E_{total} = E_1 + E_2 + ...)
  • Parallel: ( \frac{1}{R_{eff}} = \frac{1}{R_1} + \frac{1}{R_2} + ...)
  • Effective EMF: (E_{eff} = E_1 + E_2)
• Combination example._

Power

• Key Formula: (P = VI)
  • Alternate forms: (P = I^2R), (P = \frac{V^2}{R})
• Example: Calculate power dissipated.

Kirchhoff's Laws

Junction Rule

• Sum of currents entering a junction = Sum of currents leaving.
• Example problem using Kirchhoff's Junction Rule.

Loop Rule

• Sum of voltage drops in a closed loop = Sum of EMFs.
• Example problem using Kirchhoff's Loop Rule.

Wheatstone Bridge

• Used to find unknown resistance.
• Key concept: Null deflection of galvanometer.
• Balancing condition: ( \frac{R_1}{R_2} = \frac{R_3}{R_4} )
• Example problem using Wheatstone Bridge formula.

Summary and Conclusion

• Recap of key points.
• Note: Semiconductor's temperature response.
• Goodbye greetings and end of lecture.