Special Consideration of Capacitors and Coils
When Subjected to
Controlled Current Sources
04/06/2009, revised 06/01/2021
Key words
Rate of Flow & Container Volume (Capacity)
Rate of Change of Voltage vs Amount of Current Flow
Rate of Change of Current vs CEMF
Review of some definitions
1 Amp is a flow of 1 Coulomb per second
1 Coulomb (besides being a quantity) is 6.24 x 1018 electrons (i.e. a "bucket-full")
1 Farad will hold 1 Coulomb at 1 Volt
1 Henry will develop 1 Volt CEMF against a change of 1 ampere per second, as a Rate of Change
A Constant-Voltage Source requires a low internal resistance, and supplies whatever current is needed,
while a Constant-Current Source has a high internal resistance and supplies whatever voltage is needed.
New Considerations
Capacitors depend on a Dialectric between the Conductive Elements to increase the Charge Amount.
The property of this Dialectric, depending on the substance or material, varies as its Permittivity (not to be confused with Permeability), also known as its Dielectric Index, which determines its ability to hold a charge.
Things to look for
We are going to discover a case where a constant Voltage causes a rate change, and we are going to discover another case where a rate change causes a constant Voltage.
Remember that Capacitors react to voltage changes by drawing or discharging current, and that Inductors react to changes in current by opposing the voltages by CEMF, but...
- what happens to a Capacitor if we deliberately control the current being fed to a capacitor?
- what happens to the CEMF of an Inductor if we don't change the current?
- what determines the CEMF of an Inductor if we increase or decrease the rate of change?
Now, where are we going with this?
How about an ultra-simple example for a start:
Example:
Imagine a container for compressed dry air, with a pump supplying a flow of air at a consistent rate.
The container not only consists of volume, but also pressure builds at a predictable value.
Feeding a Capacitor with a Constant Current
Now, if we take a capacitor with a known "Capacity", totally discharged, and feed this capacitor with a Constant Current, it will charge at a determined linear Rate of Change of its Voltage.
Note that here a constant current will cause a "Rate of Change of the Voltage" of the Capacitor.
(As there is a collection of electrons on one side and displacement of electrons on the other side)
If we alter the value of the Constant Current, we will find that the Rate of Change of the charging voltage (i.e. The slope) will change accordingly.
Click for Circuit Illustration #1: Feeding a Capacitor with a Changeable, but Otherwise Constant Current
Note particularly that the "Rate of Change" (i.e. Rate of Charge) will be altered to be less (lower slope) or more (higher slope), depending on the actual value of current.
Final Note: With the Capacitor, the "Rate of Change" (of the Capacitor's Voltage) depends on the value of the charging current.
Feeding an Inductor with a Constant Current
Click for Circuit Illustration #2: Feeding an Inductor with a Constant Current
Once a current value is established, and stays constant, there will be no CEMF created.
As the Inductor is not a storage unit, there is no "Collective Value" to consider, except with the energy stored in the magnetic field.
Feeding an Inductor with an Increasing Current "Rate of Change"
However, if current is being increased at a linear rate, the CEMF with be a constant value, based on the "Rate of Change" and the "Inductive Value".
If the "Rate of Change" is doubled, the amount of CEMF will also double.
Note particularly that the "Rate of Change" (i.e. Rate of Current Change, as a higher or lower slope) will cause a "Constant CEMF" of the Inductor.
Final Note: With the Inductor, the "Rate of Change" (of the increase or decrease of current) will determine the "Constant Value of the CEMF".
