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:
    $C<em>{total} = C</em>1 + C<em>2 + C</em>3 + …$

• Capacitance in Series:

  • Total capacitance for capacitors in series is calculated using:
    $\frac{1}{C<em>{total}} = \frac{1}{C</em>1} + \frac{1}{C<em>2} + \frac{1}{C</em>3} + …$

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.