Capacitors and Dielectrics Notes

Key Concepts about Capacitors

  • Definition of a Capacitor:

    • A device that stores electrical energy by accumulating electric charges on two insulated surfaces.

  • Capacitance (C):

    • The capacitance is the ability of a capacitor to store charge.

    • Formula:
      C = \frac{q}{V}
      where:

    • C = capacitance (Farads)

    • q = charge (Coulombs)

    • V = voltage (Volts)

  • Dielectric Materials:

    • Non-conductive materials that can be polarized by an electric field.

    • Common dielectrics include:

    • Solids: Ceramic, Plastic, Mica, Glass

    • Liquids: Distilled Water, Transformer Oil

    • Gases: Dry Air, Vacuum, Nitrogen, Helium

  • Electric Field and Potential Difference:

    • Electric field (E) relates to the potential difference (V) across the distance (d):
      E = \frac{V}{d}

Effects of Capacitors on Charge and Potential Difference

  • Charge Relationship:

    • The charge stored increases linearly with voltage applied, as described by the formula above.

  • Potential Energy:

    • Energy stored in a capacitor can be calculated using:
      U = \frac{1}{2} qV
      or
      U = \frac{1}{2} CV^2

Capacitors in Series and Parallel

  • Capacitance in Parallel:

    • Total capacitance for capacitors in parallel is the sum of individual capacitances:
      C{total} = C1 + C2 + C3 + …

  • Capacitance in Series:

    • Total capacitance for capacitors in series is calculated using:
      \frac{1}{C{total}} = \frac{1}{C1} + \frac{1}{C2} + \frac{1}{C3} + …

Dielectric Effects on Capacitance

  • cc

    • The presence of a dielectric increases the capacitance by a factor equal to the dielectric constant.

    • Formula:
      C = κε_o \frac{A}{d}
      where:

    • κ = dielectric constant

    • ε_o = permittivity of free space (8.85 × 10^-12 F/m)

    • A = area of plates

    • d = distance between plates

Practical Examples

  • Example Problem:

    • A keyboard uses variation in capacitance to detect keypresses. The distance between plates decreases when a key is pressed, thus increasing capacitance.

  • Capacitance Change Calculation:

    • Given:

    • Initial distance = 5.00 mm

    • Final distance = 0.150 mm

    • Dielectric constant = 3.50

    • Capacitor characteristics can be calculated to detect changes corresponding to key presses.

  • Energy Storage in Practical Applications:

    • Example: Defibrillator capacitors while storing energy can indicate the amount of energy via their capacitance and the resulting voltage.