5.3 Dielectrics and their effect on capacitance

Dielectrics are insulating materials that can be polarized by electric fields. They're crucial in capacitors, increasing their ability to store charge. Understanding dielectrics helps us grasp how capacitors work and why they're so important in electronic devices.

Dielectric materials affect capacitance by increasing it. When placed between capacitor plates, they reduce the effective electric field, allowing more charge storage. This property makes dielectrics essential in designing efficient capacitors for various applications.

Dielectric Materials

Properties and Characteristics of Dielectrics

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• Dielectric refers to an insulating material that can be polarized by an applied electric field
• Dielectric constant ($\kappa$) represents the ratio of the permittivity of a substance to the permittivity of free space ($\kappa = \frac{\epsilon}{\epsilon_0}$)
  • Dielectric constant is a measure of how easily a material can be polarized in response to an electric field
  • Materials with high dielectric constants (water, ceramic) are more polarizable than those with low dielectric constants (air, vacuum)
• Polarization occurs when an external electric field causes the charges within a dielectric material to shift, creating electric dipoles
  • Polarization can be caused by the alignment of permanent dipoles or the induction of dipoles in atoms or molecules

Induced Dipoles and Electric Susceptibility

• Induced dipole moment ($\vec{p}$) is the dipole moment that is induced in an atom or molecule by an external electric field ($\vec{E}$)
  • Induced dipole moment is proportional to the electric field strength and the polarizability ($\alpha$) of the atom or molecule: $\vec{p} = \alpha \vec{E}$
  • Polarizability is a measure of how easily an atom or molecule can be polarized by an electric field
• Electric susceptibility ($\chi_e$) is a dimensionless quantity that describes the degree to which a dielectric material can be polarized in response to an applied electric field
  • Electric susceptibility is related to the dielectric constant by: $\chi_e = \kappa - 1$
  • Materials with high electric susceptibility (water, barium titanate) are more easily polarized than those with low electric susceptibility (air, teflon)

Dielectric Breakdown

Dielectric Strength and Breakdown Voltage

• Dielectric strength is the maximum electric field that a dielectric material can withstand before it undergoes dielectric breakdown
  • Dielectric strength is typically measured in volts per meter (V/m) or kilovolts per millimeter (kV/mm)
  • Materials with high dielectric strength (mica, glass) can withstand stronger electric fields than those with low dielectric strength (air, paper)
• Breakdown voltage is the minimum voltage that causes a portion of an insulator to become electrically conductive
  • When the applied voltage exceeds the breakdown voltage, the dielectric material experiences a rapid increase in electrical conductivity, leading to failure
  • Breakdown voltage depends on factors such as the dielectric material, its thickness, and the presence of impurities or defects

Capacitance

Effect of Dielectrics on Capacitance

• Capacitance with dielectrics is the ability of a capacitor to store electric charge when a dielectric material is inserted between its plates
  • The presence of a dielectric material increases the capacitance compared to a capacitor with vacuum between its plates
  • The capacitance of a parallel-plate capacitor with a dielectric is given by: $C = \kappa \frac{\epsilon_0 A}{d}$, where $\kappa$ is the dielectric constant, $\epsilon_0$ is the permittivity of free space, $A$ is the area of the plates, and $d$ is the distance between the plates
• The increase in capacitance due to a dielectric is caused by the polarization of the dielectric material in response to the electric field between the capacitor plates
  • Polarization of the dielectric reduces the effective electric field between the plates, allowing more charge to be stored for a given voltage
  • The dielectric constant of the material determines the extent to which the capacitance is increased (higher $\kappa$ leads to greater capacitance)