Lecture on Capacitors

Introduction to Capacitors

• A capacitor is a device that stores electrical charge.
• Composed of two metal plates separated by an insulator (air, paper, water, etc.).
• Stores charge by moving electrons from one plate to another.

Key Equations

• Q = CV
  • Q = Charge (Coulombs)
  • C = Capacitance (Farads)
  • V = Voltage (Volts)
• Q = IT
  • I = Electric Current (Amps)
  • T = Time (Seconds)

Understanding Capacitance

• Capacitance as charge efficiency: the ability to store charge per volt.
• Example: Capacitor A (10 Farads) vs Capacitor B (2 Farads)
  • Capacitor A can store more charge per volt than Capacitor B.
• Capacitance does not change with voltage; it depends on the construction of the capacitor.

Voltage and Electric Charge

• Electric charge is the quantity of charged particles (electrons in metals).
• Electrons have a charge of -1.6 x 10⁻¹⁹ Coulombs.
• Voltage is the ratio of electric potential energy to charge.
• Voltage is the difference in electric potentials between two points.

Units and Measurements

• Farad: Unit of capacitance, very large; commonly measured in microfarads (10⁻⁶ F), nanofarads (10⁻⁹ F), picofarads (10⁻¹² F).
• C = ε₀ × A / D
  • ε₀: Permittivity of free space
  • A: Area of plates
  • D: Distance between plates

Effect of Dielectrics

• C = k × ε × A / D
  • k: Dielectric constant
  • Different materials have different k values (e.g., air ≈ 1, water ≈ 80).
• Adding a dielectric increases capacitance.
• When a dielectric is added, capacitance increases, and voltage decreases if not connected to a battery.

Electric Field and Charge

• Electric field (E) between plates is V/D.
• Charge on plates can be calculated as surface charge density (σ) times area.

How Capacitors Work

• Capacitors charge by transferring electrons from one plate to another through a battery.
• Discharge occurs when electrons flow back, equalizing charge.

Energy Stored in Capacitors

• Potential Energy Equations
  • U = 0.5 QV
  • U = 0.5 CV²
  • U = Q² / 2C
• Energy is based on charge and voltage.

Practical Insights

• Capacitors store energy quickly but discharge completely when equilibrium is reached.
• Used in various applications for energy storage and release.