Capacitors And Capacitance (Copy)

What is Capacitance?

• Capacitance (C) is defined as the charge stored per unit potential difference between the plates (or terminals) of a capacitor.

  C = Q / V

  Where:
  C = capacitance (farads, F)
  Q = charge stored (coulombs, C)
  V = potential difference (volts, V)

• The unit farad (F) is large, so commonly used sub-units are:
  • microfarads (µF) = 10⁻⁶ F
  • nanofarads (nF) = 10⁻⁹ F
  • picofarads (pF) = 10⁻¹² F

Written and Compiled By Sir Hunain Zia, World Record Holder With 154 Total A Grades, 7 Distinctions and 11 World Records For Educate A Change A2 Level Physics Full Scale Course

Capacitance of Isolated Spherical Conductors

• An isolated spherical conductor of radius r has a capacitance given by:

  C = 4πε₀r

  • ε₀ = permittivity of free space = 8.85 × 10⁻¹² C² N⁻¹ m⁻²
  • Capacitance increases with radius
  • More charge can be stored at the same potential if the sphere is larger

Parallel Plate Capacitor

• For a parallel plate capacitor:

  C = ε₀A / d

  Where:
  A = area of one of the plates (m²)
  d = distance between plates (m)

• Capacitance increases with plate area and decreases with distance between the plates.
• Inserting a dielectric (an insulating material) increases capacitance:
  • New capacitance becomes: C = εA / d
    where ε = ε₀εᵣ and εᵣ is the relative permittivity of the dielectric

Written and Compiled By Sir Hunain Zia, World Record Holder With 154 Total A Grades, 7 Distinctions and 11 World Records For Educate A Change A2 Level Physics Full Scale Course

Capacitance in Series

• When capacitors are connected in series, the total capacitance C is given by:

  1/C = 1/C₁ + 1/C₂ + 1/C₃ + …

• This is similar to the formula for resistors in parallel.
• In a series connection:
  • Charge Q is the same on each capacitor
  • Potential differences add up

Capacitance in Parallel

• When capacitors are connected in parallel, the total capacitance C is:

  C = C₁ + C₂ + C₃ + …

• In a parallel connection:
  • Potential difference is the same across each capacitor
  • Charge adds up

Written and Compiled By Sir Hunain Zia, World Record Holder With 154 Total A Grades, 7 Distinctions and 11 World Records For Educate A Change A2 Level Physics Full Scale Course

Summary of Key Equations

Important Concepts

• Capacitors store electrical energy by holding separated charges on two plates.
• Capacitance is independent of the amount of charge—it depends only on geometry and material between plates.
• Capacitance is a scalar quantity.
• Dielectrics increase capacitance by reducing the electric field inside the capacitor.

Written and Compiled By Sir Hunain Zia, World Record Holder With 154 Total A Grades, 7 Distinctions and 11 World Records For Educate A Change A2 Level Physics Full Scale Course

Example Question

Q: Two capacitors of 4 µF and 6 µF are connected in series. Find the equivalent capacitance.

Solution:

1/C = 1/4 + 1/6 = (3 + 2)/12 = 5/12
C = 12/5 = 2.4 µF