*In this study, we
revisit the concept of classical capacitor theory-and derive a possible new
explanation of the definition charge stored in a capacitor. We introduce a
‘capacity function’ with respect to time to describe the charge storage in a
classical capacitor and for a fractional capacitor. The observation regarding
capacitor breakdown is very interesting. This study practically described for
DC link capacitors (in power supply circuits), that the capacitor breaks down
even it were never exceeded its maximum voltage limit. Here we will describe
that the charge stored at any time in a capacitor as a ‘convolution integral’
of defined capacity function of a capacitor and voltage stress across it which
comes from the causality principle. This approach, however, is different from
the conventional method, where we multiply the capacity and the voltage
functions to obtain charge stored. This new concept is in line with the
observation of that charge stored as a step function and the relaxation current
in form of impulse function for ‘ideal geometrical capacitor’ of constant
capacity; when an uncharged capacitor is impressed with a constant voltage
stress. Also this new formulation is valid for a power-law decay current that
is given by ‘universal dielectric relaxation law’ called as ‘Curie
von-Schweidler law’, when an uncharged capacitor is impressed with a constant
voltage stress. This universal dielectric relaxation law gives rise to
fractional derivative relating voltage stress and relaxation current that is
formulation of ‘fractional capacitor’. A ‘fractional capacitor’ we will discuss
with this new concept of redefining the charge store definition i.e. via this
‘convolution integral’ approach, and obtain the loss tangent value. We will
also show how for a ‘fractional capacitor’ by use of ‘fractional integration’
we can convert the fractional capacity a constant that is in terms of
fractional units (Farads per sec to the power of fractional number); to normal
units of Farads. From the defined capacity function, we will also derive
integrated capacity of capacitor. We will also give a possible physical
explanation by taking example of porous and non-porous pitchers of constant
volume holding water and thus, explaining the various interesting aspects of a
classical capacitor and a fractional capacitor that we arrive with this new
formulation; and also relates to a capacitor breakdown theory-due to
electrostatic forces. Study investigates the charge stored in a capacitor, as a
function of time is not the usual multiplication operation of capacity and
voltage; instead, the charge is convolution integral of these two functions,
derived from causality principles. With this formulation, we showed for a
fractional capacitor, the charge goes to infinity for large times, when the
fractional capacitor is placed on a constant voltage; and is in line with
earlier fractional order models and observations. With this formulation of convolution
integral, this study also showed that the relaxation current is in the form of
impulse function for ideal geometrical capacitor of constant capacity, when
stressed by a constant voltage and for fractional capacitor with power-law
decay current that is given by universal dielectric relaxation law called as
Curie von-Schweidler law. Practically, this new ‘generalized- formulation’ has
use while getting the charge stored in a capacitor which is a function of time
with time-varying voltage stress across it, and to convert the fractional
capacity units to usual capacity units in Farads. *

## Biography of author(s)

**Shantanu Das**

Reactor Control System Design Section (E & I Group), BARC, Mumbai-400085,
India.

Department of Physics, Condensed Matter Physics Research Centre – CMPRC,
Jadavpur University, Kolkata-700032, West Bengal, India.

**Read full article: ***http://bp.bookpi.org/index.php/bpi/catalog/view/25/72/201-1***View Volume:*** **https://doi.org/10.9734/bpi/atpsr/v2*