capacitors are generally described mathematically by those knowledgeable in the field . there are several systems of units and conversions which are commonly employed . it is not uncommon to jump back and forth among systems . the basic physical and mathematical definitions and relationships are as follows , using the passive sign circuit convention , where applicable : q = 8 . 9874 × 10 9 nm 2 c ou 2 ( unit of charge , the coulomb ) e0 = 8 . 854 × 10 12 c ou 2 / nm 2 ( permittivity of free space ) c = q / v v =( 1 / c ) σidt + vt 0 ( summation or integral from t 0 until t f ) i = c dv / dt p = vi = cv dv / dt w = cv 2 / 2 c = e 0 e r ( a / d ) ( parallel plate capacitor geometry ) capacitors are characterized by certain qualitative circuit actions and reactions . this circuit behavior is summarized by the following heuristics : i ) capacitors will permit an instantaneous change in terminal current , ii ) capacitors will oppose an instantaneous change in terminal voltage , and iii ) charged capacitors appear as an open circuit to constant ( dc ) voltages . fig3 illustrates a smooth two dimensional figure . the surface of the one or more conductive layers may be formed with a smooth surface . additionally , the dielectric layer may be formed in with a similar smooth surface . one mathematical model for a two dimensional , smooth figure is the sine wave . the smooth valleys 31 and peaks 33 can be physically extended into several smooth , three dimensional surfaces as further described below and show in fig4 . for example , the drawing can be considered a side view of a smooth , three dimensional , channel or hill and valley structure . fig4 illustrates a smooth three dimensional structure that may be utilized for the present invention . this structure can be considered a valley 31 and peaks 33 structure or a sine wave or similar undulation linearly extended in a planar surface . so long as the gradient variation is gradual the structure can be considered smooth . gradual changes in slope of the surface may be made . fig5 illustrates the concept of moiety between layers . the top and bottom structures are conformal . fig5 is shown emphasized with a distance separation between the top 41 and bottom 43 halves . as illustrated in the figure , the surfaces maintaining moiety with between the first surface 45 and the second surface 47 . in certain embodiments of the present invention , the conductive layer maintains moiety with dielectric layer . fig6 illustrates one of the many objects of the electrical charge storage device , one object to enhance power characteristics of electrical charge storage devices . fig6 is meant to be illustrative and not limiting . fig6 shows the relative relationship between the electrical energy storage characteristics and the power transfer aspects of the inventive electrical charge storage device . the figure illustrates energy 61 on the y - axis and power 62 on the x - axis . the box entitled “ area of interest ” shows generally where one implementation of the inventive technology lies in comparison to other presently available technology . the “ area of interest ” box 67 is believed to show the region of the energy to power graph where the inventive electrical charge storage device resides in comparison to other existing technology . as shown significant variation exists among each technology . for example lead calcium batteries 63 may be of the deep cycle type , having high energy storage design . an identical amp hour starting battery on the other hand will not store the total quantity of energy , but can provide significantly greater instantaneous power . similarly there are various symmetrical and asymmetrical super and ultra capacitor designs 64 which have widely divergent energy density and power density profiles . further , tantalum capacitors 65 have various power and energy characteristics . a non - polarized capacitor 66 may have good power characteristics , but low energy storage . the electrical charge storage device exhibits increases in power and energy over the existing technology . fig7 illustrates a construction method whereby the count of conductive layers is reduced in a parallel capacitor assembly . reducing conductor count is an object of this invention . fig8 illustrates a construction method whereby the count of conductive layers and interconnections is reduced in a series capacitor assembly . fig9 a and 9b illustrate a construction method whereby the count of conductive layers and interconnections is reduced in an anti - series capacitor assembly . this technique can be employed in the use of forwardly biased , polarized capacitors in continuous ac applications . fig1 illustrates an arbitrary scale capacitor design with increased surface area . this type gross structure serves to increase volume charge storage . fig1 exhibits some high angularities and can be considered a sharpy structure . fig1 illustrates a structure with high angularity : in certain embodiments the inventive electrical charge storage device utilizes a dendrite structure which tends to maximize the charge accumulation and energy storage . dendrite structures include tree and leaf , nerve and synapse , blood vessel and capillary . such sharpy structures are suitable for high energy density capacitors . fig1 illustrates an expanded surface area where z = a sin ( bx ) sin ( by ), a sinusoidal topology . in certain embodiments , the conductive and dielectric layers utilize curvilinear surfaces . for the case of a continuous simple mathematical surface such as z = a [ sin ( bx ) sin ( by )] the integral can be derived exactly . the surface area increase of the above surface is a function of the amplitude a and the period of bx and by . in this figure , the period of bx and by are identical . an object having a smooth curvilinear surface such as this , in which a conformal dielectric and second conformal conductive layer , can be shown to have great physical strength relative to the brittle structures present in electrolytic capacitors . the line integral ( length ) of a unit sinusoid over the period has a length of 2π . thus the surface integral for the sinusoidal unit structure is 4π 2 . the more general case of z as shown above includes the constants a and b . the surface area would increase in direct proportion with the magnitude of the constant a , and increase in inverse proportion to the constant b due to the mathematical properties of surface integrals . this surface area increase is physically analogous to the increase in energy with increases in wave magnitude and decreases in wavelength ( increasing frequency ). the z = a sin ( bx ) sin ( by ) a sinusoidal topology is smooth and can exhibit significant physical strength due to the conductors . a strongly bonded , physically strong , conformal dielectric will fill the separating space , providing significant mechanical support . a dielectric with good heat transfer characteristics and heat durability , such as the crystalline form of carbon ( diamond ) will allow a large displacement current . the conformal layer topology provides for the shortest distance for charge displacement within the dielectric to be an orthogonal path from conductor to conductor at each point of the curvilinear surfaces . thus material strength , topology , and thermodynamic properties combine with dielectric constant and dielectric strength to determine the allowable transient and steady state current densities for a capacitor . where structure dimensions are large relative to the atoms and molecules involved , a close approximation to uniform , conformal coating can be maintained . fig1 illustrates an expanded surface area region where the peaks and valleys are rectangular parallelelopiped in nature , exhibiting a unit saw tooth or pyramidal topology . in certain embodiments of the electrical charge storage device , conductive and dielectric surfaces have expanded surface regions . the line integral of a saw tooth 2d curve is 4 , while the surface area of the 3d surface is six ( 6 ): thus the 3d saw tooth topology exhibits six times the surface area of a flat surface but significantly less surface area than the sinusoidal topology . this shape can be described as tilted square box halves , slightly displaced . the topology structure of fig1 exhibits significant physical strength combined with an increase in surface area . as in the case of the sinusoidal topology above , the pyramidal structure will increase in surface area with increasing amplitude and frequency . also , the displacement current vector generally retains the orthogonal and shortest route characteristic of the sinusoidal structure above . the relatively straight realizable surfaces and edges are consistent with crystalline and polycrystalline growth structures . all patents and publications mentioned in the specification are indicative of the level of those skilled in the art to which the invention pertains . all patents and publications are herein incorporated by reference to the same extent as if each individual publication was specifically and individually indicated to be incorporated by reference . u . s . pat . no . 5 , 362 , 526 , entitled “ plasma - enhanced cvd process using teos for depositing silicon oxide ”, which is incorporated by reference herein . u . s . pat . no . 5 , 876 , 787 , entitled “ process of manufacturing a porous carbon material and capacitor having the same ”, avarbz et al , 1999 u . s . pat . no . 5 , 081 , 559 , entitled “ enclosed ferroelectric stacked capacitor ”, fazan et al , 1992 us pto 20020017893 w . b . duff , jr . published feb . 14 , 2002 method and circuit for using polarized device in ac applications us pto 20030006738 w . b . duff , jr . published jan . 9 , 2003 method and circuit for using polarized device in ac applications non - provisional u . s . application ser . no . 09 / 170 , 998 , entitled “ method and circuit for using polarized device in ac applications ,” filed nov . 9 , 2000 , which claims the benefit of provisional application ser . no . 60 / 174 , 433 , entitled “ method and circuit for using polarized device in ac applications ,” filed : jan . 4 , 2000 . uspto 20030010910 colbert , daniel t ., et al published jan . 9 , 2003 continuous fiber of single wall carbon nanotubes solid state electronic devices , 3 rd edition , ben g . streetman , prentice - hall , englewood cliffs , n . j ., 1990 . economic ac capacitors , w . b . duff , jr ., ieee power engineering review , volume 22 , number 1 , january 2002 , the institute of electrical and electronics engineers , ny n . y . although the present invention and its advantages have been described in detail , it should be understood that various changes , substitutions and alterations can be made herein without departing from the spirit and scope of the invention as defined by the appended claims . moreover , the scope of the present application is not intended to be limited to the particular embodiments of the process , machine , manufacture , composition of matter , means , methods and steps described in the specification . as one of ordinary skill in the art will readily appreciate from the disclosure of the present invention , processes , machines , manufacture , compositions of matter , means , methods , or steps , presently existing or later to be developed that perform substantially the same function or achieve substantially the same result as the corresponding embodiments described herein may be utilized according to the present invention . accordingly , the appended claims are intended to include within their scope such processes , machines , manufacture , compositions of matter , means , methods , or steps .