Capacitance & Dielectrics AP E&M

Introduction What is a capacitor? What is a capacitance? Conductors of equal and opposite charge separated by an insulating material The ratio of the magnitude of the charge on either conductor to the magnitude of the potential difference between them.

Measured in [C/V] also known as [F] Farads Capacitance: Always positive A measure of how much electric potential energy or charge that a capacitor can store. Measured in [C/V] also known as [F] Farads 1 farad is very large. A 1 farad capacitor could store 1 coulomb of charge per unit of voltage.

Capacitance Parallel Plate: Cylindrical: Spherical:

Energy stored in a capacitor Suppose that the charge on a capacitor is q during an instant while charging. At this instant the potential difference is V=q/C. What is the work necessary to move charge dq from the –q plate to the q plate (which is at higher potential)?

Energy stored in a capacitor The work done in charging the capacitor can be considered as the potential energy U stored in the capacitor.

Energy stored in a parallel-plate capacitor We can consider the energy to be stored in the electric field of the capacitor.

Energy Density For a parallel-plate capacitor, the electric field occupies a space of volume Ad, so we will define the energy per unit volume, or Energy Density as: The energy density in any field is proportional to the square of the electric field in the unit volume.

Capacitors with dielectrics Dielectric: a nonconducting material such as rubber, glass, or waxed paper.

Capacitors with dielectrics If a dielectric fills the space between conductors in a capacitor, the capacitance increases by a factor of a dimensionless factor, called κ, the dielectric constant.

Capacitors with dielectrics The dielectric material is polarized. This reduces the effective electric field between plates, which also reduces the potential difference between plates. Lower potential difference results in higher capacitance.

Benefits of dielectrics in capacitors: The dielectric strength (maximum electric field that a material can be exposed to without breaking down and behaving as a conductor) of most materials is higher than air. Increases the capacitance of a capacitor. Increases the maximum operating voltage of a capacitor. My provide mechanical support between the conducting plates.