The capacitance of a capacitor (or condenser) is characterized with the permittivity ε of the dielectric medium of thickness d which is between two electrodes of surface S.
Parallel connections for power applicationsThe resulting capacitance is the sum of the individual capacitances.
Series connections for high voltage applications
The resulting inverse capacitance is the sum of the individual inverse capacitances.
The force is oriented along the direction separating the two charges. The α factor depends on the unit system. In MKSA the charge is given in Coulomb [C], the distance in meter [m] and the force in Newton [N]. With Gauss law, it's given by
Electric fieldFinally the force is given by
Considering that the charge q2 is placed in the electric field created by q1, this field is given by
The vector electric field has its foot on q1 when this latter is positive.
The force on charge q2 is equal to:
The charge volumetric density is given the number of charge in an infinitesimal volume pondered by this volume:
It's more convenient to use the « polarization » P, instead of taking into account all the charges in a material. In the Maxwell macroscopic model only the free charges (those which are not involved in a dipole) are considered in the charge density. Historically Maxwell has written first his « microscopic » equations before the well-known « macroscopic » ones.
Electric voltage U:
Volt,[V]: is derived from the current definition in the MKSA system. (difference of potential in a conductor when the power losses of 1 A is equal to 1 W)
Electric field E:
Volt per meter, [V/m]: electric field intensity exerting a force of 1 newton on a charge of 1 coulomb.
Displacement electric field D:
Coulomb per square meter, [C/m2]
Technical capacitorsTechnical capacitors beside a capacitance Cp have a series resistance rs, a parallel resistance rp and a parasitic inductance L.
With the impedance given by:
Which may be separated in an imaginary and real part
Inductance influenceBoth the inductive and capacitive parts of the impedance are imaginary and can't be distinguished one from the other. For a given frequency, the parasitic inductance (often the inductance of the measurement circuit) is considered as a negative capacitance by the RLC meters. The distinction may be obtained with the frequency dependency of these two components which is completely different. If the parallel resistance Rp is very large, the impedance imaginary part is given by:
where fr is the resonance frequency.
RemarksAbove the resonance frequency, the capacitor behaves as a pure inductance.
For the following presentation we will consider that the frequency is much smaller than the resonance frequency. Clamp and snubber capacitors as electric shocks (BIL, interrupted BIL) don't fulfill this hypothesis, for them the full theory is necessary.