Capacitor

Focuses dielectric-field lines, dielectric storage.

Flow

1. Magnetic effect is applied on the circuit
2. Magnetic field builds up almost immediately
3. Capacitor issues a resisting dielectric-effect
4. Dielectric field grows gradually until it reaches its max-applicable value

Details

Like in the previous circuit, the generator applies a magnetic effect on the circuit, which builds up a magnetic field. Here we don’t have a magnetic-storage element in our circuit, except for the small ones namely the conductors. So, the magnetic field is build up almost immediately (ie. the less magnetic-storage, the faster it builds up, the shorter the transient).

The permanent condition after the transient will not be the same as with the inductor circuit. When the capacitor is charged, there is no magnetic constructor, it behaves like an open circuit. The capacitor will charge up to the voltage given by the generator. Well, almost.

Calculations

The generator issues a magnetic effect in volts (also called EMF).
The capacitor has a dielectric-storage coefficient (also called capacitance).
The circuit has a certain magnetic loss (also called resistance of the conductor).
The circuit has a certain dielectric constructor (also called electro-static potential).

Formulae

Dielectric effect, I.
Dielectric constructor, e.
Dielectric storage, C.
Dielectric loss, G.
Dielectric field, Psi.

This defines our relation between the dielectric field and the capacitor: e * C = Psi

e = Phi / t
Which is the same formula as for a magnetic effect.
Our magnetic effect from our generator becomes a dielectric constructor.

Transient

Phi is unknown, so we can’t use it to calculate the dielectric constructor during the transient, we will have to find another way to calculate this. We can do this by using Ohm’s law again, but this time in slightly different form.

Calculation:

1. Take the dielectric effect from across the capacitor: I = Psi / t
2. Calculate the magnetic effect from across the capacitor: E_cap = I * R
3. Figure out the dielectric constructor after the transient: e_max = E_generator
4. e = e_max - E_cap

Time constant

To calculate the time constant of the transient: T = C * R
With this we can calculate the approximate duration of the transient: 5 * T

We can also calculate an approximation of e at a given point during the transient:

-- Javascript
-- :: Eg = supply voltage

let
    dielectricConstructor = Eg
    timeDerivative = Basics.e ^ (-t / T)
in
    -- e =
    dielectricConstructor * (1 - timeDerivative)