Capacitance and Inductance as Inertia

Capacitance (C) and Inductance (L) as Inertia - against the change

Mass as related to 'inertia' of a body can be defined by the formula:

F = ma 

This can be rearranged as F/m = a. So m can be considered as against acceleration, which means against the change of velocity.

Capacitor analogy

This can be rearranged as i(t)/C = dv(t)/dt. So like m against F, C can be considered as against dv(t)/dt. Against dv(t)/dt means against the change of voltage.

CV = Q  (cv = q)
Q/C = V (q/v = v)

Quote from Physical Properties Chart - Tom Potter's World

"
Contrary to intuition, charge is stored by stressing the dielectric rather than in a pool of charges. When stressed by the application of a voltage, a good dielectric material remains in the stressed state longer than an ordinary insulator, and there is little charge movement (Leakage) across it. A dielectric can be compared to a spring. A dielectric stores an electrical stress (Voltage) whereas a spring stores mechanical stress (Force).
"

F = -kx

F: Restoring Force corresponding to the applied Force
k: spring constant
x: displacement

F can be considered as an applying Force, which is equal to -kx where <k> is Newton/meter. Then <kx> is Force (in Newton) and has the same magnitude as but is in the opposite direction of F.

When F is analogous to V , 1/C is analogous to <k> and <x> to Q (charge). Q/C = V

Inductor analogy

This can be rearranged as v(t)/L = di(t)/dt. So So like m against F, L can be considered as against di(t)/dt. Against di(t)/dt means against the change of current.

As the current is the time rate change of charge q or i(t) = dq(t)/dt. This is more like F/m = a as a (acceleration) is the time rate change of v (velocity) and v (velocity) is the time rate change of distance (more precisely displacement) d or  v (velocity) = dd(t)/dt. Charge q is not a distance (displacement) but a certain quantity, can be analogous to F/m = a and shows its dynamical nature (not static) - flow or motion of charge q, not static position or quantity like as in a capacitor.

Further analogy

From Wiki <Harmonic Oscillation> 09-Nov-2015

"

Translational Mechanical	Series RLC Circuit
Position	Charge
Velocity	Current
Mass	Inductance
Spring constant	Elastance
Damping	Resistance
Drive force	Voltage
Undamped resonant frequency
Differential equation:

"

The above are common analogies. I would say "beautiful analogy".

<x> is not just <position> but <displacement>. And <x> and <q> are not easy to be connected analogically.

Inductance is analogous to Mass (Inertial Mass). Very clear.

More precisely <->(minus sign) is required before <L>.

<Elastance> is a simply the reciprocal of Capacitance. Analogically <Elastance>, as the name suggests, is the unit showing <Elasticity> and roughly the reciprocal of <Stiffness>.

Let's review <displacement> to connect <charge> analogously.

The Penguin Dictionary of Physics says:

Displacement is

1. A vector representing in magnitude and direction the difference in position of two points. It is the basic vector used in physics. Velocity is defined as rate of change displacement, acceleration is rate change of velocity. Thus mechanical quantities such as MOMENTUM and force, and electrical quantities such as ELECTRICAL FIELD depend upon the concept of displacement.

2. The quantity of fluid displace by submerged or partly submerged body.

3. See ELECTRIC DISPLACEMENT

-----

ELECTRIC DISPLACEMENT is rather complicated to understand and to be convinced. The unit is coulomb / meter squared, which may be considered as a density on (though) the surface (surface density) of charge. Though <charge> is involved but difficult to relate with the mechanical displacement (the difference in position of two point) analogously.

The Penguin Dictionary of Physics says:

Electrical displacement is

---- the electric flux per unit area ( electric flux density) in the medium.




ACT