Overview: Capacitors and Dielectrics

The capacitance of a conductor is defined as the ratio of the charge given to the rise in the potential of the conductor.

Mathematical definition: C = \[\frac {Q}{V}\]

A capacitor is a pair of two conductors of any shape which are close to each other and have equal and opposite charges. These conductors are called the 'plates' of the capacitor.

OR

A system of two conductors separated by an insulator, is called a capacitor.

The capacitance of a capacitor is defined as the ratio of the charge given to a plate of the capacitor to the potential difference produced between the plates.

“The total amount of work in charging the capacitor is stored up in the capacitor in the form of electric potential energy.”

The dielectric constant (or specific inductive capacity) of a material is the ratio of the capacitance of a given capacitor completely filled with that material to the capacitance of the same capacitor in vacuum.

OR

A non-conducting substance that has no (or negligible) free charge carriers and can be polarised in an external electric field, is called a dielectric.

A ‘polar' molecule is one in which the centre of gravity of the positive charges (protons) is separated from the centre of gravity of the negative charges (electrons) by a finite distance.

OR

A molecule in which the centres of positive and negative charges are separated, giving it a permanent dipole moment, is called a polar molecule.

The Molecules in which the centres of positive and negative charges coincide and so the molecules have zero electric dipole moment. Such molecules are called ‘non-polar' molecules.

OR

A molecule in which the centres of positive and negative charges coincide and has no permanent dipole moment, is called a non-polar molecule.

To sum up, an electric field produces in a dielectric (non-polar or polar) a net dipole moment in the direction of the field. This phenomenon is known as 'dielectric polarisation' or 'electric polarisation of matter'.

Dielectric strength is defined as the maximum value of the electric field that it can tolerate without its electric breakdown.

C = 4 π ε_0​ a farad

U = \[\frac {1}{2}\] C V²

C = \[\frac{K\varepsilon_0A}{d}\] farad

If there is vacuum (or air) between the plates, then K = 1

C₀ = \[\frac {ε_0 A}{d}\] farad

\[U=\frac{1}{2}\frac{Q^{2}}{C}=\frac{1}{2}CV^{2}joule.\]

• In metals, electric current is due to the drift of free electrons; positive ions remain fixed in the lattice and do not move.
• Valence electrons in the outermost orbit are loosely bound and can become free (conduction) electrons, especially at room temperature.
• When an external electric field is applied to a conductor, free electrons acquire a drift velocity opposite to the field, producing current.
• The electrical conductivity of a solid depends on the number of free electrons available for conduction.
• In dielectrics, an applied electric field causes electric polarisation; charges appear on the surface, but no charge flows through the material.

• Capacitance is directly proportional to the area of the plates
  C ∝ A
  Increasing the effective overlapping area increases capacitance.
• Capacitance is inversely proportional to the distance between the plates
  C ∝ \[\frac {1}{d}\]​
  Reducing the separation between plates increases capacitance.
• Capacitance depends on the medium between the plates
  It increases when a dielectric is introduced and is directly proportional to the dielectric constant K:
  C ∝ K

• Series combination: All capacitors connected in series carry the same charge Q, while the total potential difference is the sum of individual potential differences.
• Equivalent capacitance in series is given by​
  \[\begin{aligned}
  \frac{1}{C}=\frac{1}{C_1}+\frac{1}{C_2}+\frac{1}{C_3}
  \end{aligned}\]
  and is less than the smallest individual capacitance.
• In a series combination, the potential difference across each capacitor is inversely proportional to its capacitance, and the capacitor with the least capacitance has the highest voltage.
• Parallel combination: All capacitors connected in parallel have the same potential difference, while the charge distributes according to capacitance.
• Equivalent capacitance in parallel is given by​
  C = C₁ ​+ C₂​ + C₃​
  and is greater than any individual capacitance.

• An electric field produces dipoles in non-polar dielectrics and aligns them in polar dielectrics, resulting in a net dipole moment along the field.
• Polarisation causes bound charges to appear only on the surfaces of the dielectric slab; the interior remains electrically neutral.
• The polarisation charges create an electric field opposite to the applied field, reducing the field inside the dielectric.
• When a dielectric is inserted in an isolated capacitor, the electric field and potential difference decrease, while capacitance increases.
• A dielectric can withstand the electric field only up to a certain limit, beyond which electrical breakdown occurs.

A capacitor consisting of two large parallel conducting plates separated by a small distance is called a parallel plate capacitor.