6.1 Capacitors and capacitance

Capacitors are essential components in electrical circuits, storing energy in electric fields. They consist of two conductors separated by an insulating material called a dielectric. Understanding capacitors is crucial for grasping how energy is stored and released in various electronic devices.

Capacitance, measured in farads, determines a capacitor's ability to store charge. The amount of charge stored depends on the capacitor's physical properties and applied voltage. This topic explores capacitor construction, specifications, and the fundamental equations governing their behavior.

Capacitor Fundamentals

Definition and Concepts

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• Capacitor stores electrical energy in an electric field between two conductors (plates) separated by an insulating material called a dielectric
• Capacitance measures a capacitor's ability to store electric charge
  • Depends on the size of the plates, distance between them, and properties of the dielectric material
• Farad (F) is the unit of capacitance
  • One farad equals one coulomb of charge stored per volt applied ($1 F = 1 C/V$)
  • Common capacitor values range from picofarads (pF) to microfarads (μF)

Charge Storage and Energy

• Capacitors store charge when a voltage is applied across their terminals
  • Positive charges accumulate on one plate while negative charges accumulate on the other
• The amount of charge ($Q$) stored in a capacitor is directly proportional to the applied voltage ($V$) and the capacitance ($C$)
  • Relationship expressed by the equation: [Q = CV](https://www.fiveableKeyTerm:q_=_cv)
• Energy stored in a capacitor depends on its capacitance and the voltage across it
  • Calculated using the formula: $E = \frac{1}{2}CV^2$, where $E$ is the stored energy in joules (J)

Capacitor Construction

Parallel Plate Capacitor

• Consists of two parallel conductive plates separated by a dielectric material
• Capacitance of a parallel plate capacitor depends on the area of the plates ($A$), the distance between them ($d$), and the permittivity of the dielectric ($ε$)
  • Calculated using the formula: $C = \frac{εA}{d}$
• Increasing plate area or decreasing distance between plates increases capacitance

Dielectric Materials

• Dielectric is an insulating material that separates the conductive plates in a capacitor
  • Examples include air, paper, plastic, ceramic, and various oxides
• Permittivity ($ε$) is a measure of how easily a dielectric material can be polarized by an electric field
  • Higher permittivity results in higher capacitance for a given plate area and separation
  • Permittivity of a material is often expressed relative to the permittivity of free space ($ε_0$) as relative permittivity or dielectric constant ($ε_r$)
• Dielectric strength is the maximum electric field a dielectric can withstand before breakdown occurs
  • Breakdown leads to conduction through the dielectric and capacitor failure
  • Dielectric strength is an important factor in determining a capacitor's voltage rating

Capacitor Specifications

Voltage Rating and Breakdown

• Voltage rating specifies the maximum voltage that can be safely applied to a capacitor without causing dielectric breakdown
  • Exceeding the voltage rating can lead to permanent damage and failure
• The maximum voltage is determined by the dielectric strength and the thickness of the dielectric material
  • A thicker dielectric or one with a higher dielectric strength allows for a higher voltage rating

Electric Field Considerations

• Electric field strength within a capacitor is determined by the applied voltage and the distance between the plates
  • Calculated using the formula: $E = \frac{V}{d}$, where $E$ is the electric field strength in volts per meter (V/m)
• The electric field must be kept below the dielectric strength to prevent breakdown
  • Capacitor design must balance the desired capacitance with the need to maintain a safe electric field strength
• Non-uniform electric fields can lead to localized regions of high field strength, increasing the risk of dielectric breakdown
  • Capacitor construction and geometry should aim to minimize field non-uniformities