Capacitance

Below is a discussion about what is a capacitor, the physical rules it follows and how this directly relates to the track we use.  Capacitors have electrical properties that "Come Alive" in an electrical circuit when there is a changing voltage or some form of AC present.   In other words, capacitors conduct current like resistor between it two terminals when presented with AC voltages regardless of how they are created. 

1) WHAT IS A CAPACITOR?
2) WHY WIRES AND RAILS ARE CAPACITORS
3) CAPACITOR POLARITY
4) CAPACITORS PASS CURRENT
5) CAPACITORS HAVE AN AC RESISTANCE (IMPEDANCE)


1) WHAT IS A CAPACITOR?

A Capacitor is very simple electrical device.   It stores and releases energy (Charge) a lot like a battery in the form of current flow going into or out of the capacitor respectively.  The capacitor can convert current into voltage (Charge) or voltage back into current (Discharge) not unlike a battery.  The capacitance value is a reflection of the amount of energy the capacitor can store for a given voltage.  Capacitors use this ability to store or discharge energy to OPPOSE any change in voltage across it.  From an electrical circuit point of view, capacitors can look like heavy load (Short Circuit) when the voltage increases across it OR a power source when the voltage falls across it.  When there is no voltage changing across the capacitor, the capacitor literally disappears from the electrical circuit.

Capacitor Basics:

It is a very simple device that consist of two metal conductors separated by an electrical insulator (Dielectric) of a given thickness.    The insulator is any material that does not conduct electricity.  A common insulating material is plastic not unlike what is found on insulated wires.  But it can also be simply air! 

Anyone remember any discussion of the Leyden Jar "capacitor" from science or physics class?   http://en.wikipedia.org/wiki/Leyden_jar
This was the very first capacitor.

Look at the picture on the left.  This is a mechanically adjustable capacitor which means you can precisely adjust for the amount of capacitance you want over a wide range.

One conductor is on the left and the other conductor is on the right with each connected to a round flat plate.  You can see there is only air between the two round plates. 

This device allows you to adjust the spacing between the round plates which in turn adjust the amount of capacitance.  






The electrical symbol for a capacitor is:



Notice is looks like two plates facing each other just like the picture above.  Each plate has a wire connected to it.  The symbol rotated 90 degrees is the same symbol and has the same meaning.






A physical diagram of a capacitor rotated 90 degrees is shown below.

The equation the describes the capacitance value is:
C= \frac{\varepsilon A}{d}

C = Capacitance value
A = Surface Area of the conductive plates
d = Distance between the conductive plates that is filled with an insulator.
e = Dielectric Constant or insulator.  Accounts for the type of insulator material being used such as plastic versus air.


The two most important laws to remember from this equation are:

1) Surface Area: For a given spacing distance between the two metal conductive plates, capacitance will:
    a) increases if the surface area between the two plates goes up.
    b) decrease if the surface area between the two plates goes down.  

2) Spacing Distance: For a given surface area of the two metal conductive plates, capacitance will: 
    a) increases if the spacing distance between the two plates goes down. 
    b) decrease if the spacing distance between the two plates goes up.


2) WHY WIRES AND RAILS ARE CAPACITORS

In the above section, we show how a capacitor is composes to two metal plates.    Now imagine if you could magically start stretching and molding each surface plate of a given capacitor into long thin wire or rail but still have the same exact spacing and plate thickness as before.  Given the laws above, the capacitance would remain the same despite the dramatic shape change.

Hence the shape of the plates make no difference for a given value of the capacitance.  It is all about maintaining the exact same amount of surface area and distance between the two conductive plates.

No if we increase the spacing between the rail to accommodate a given track gauge , the capacitance value will change but never go away.  Bottom line is capacitance is found everywhere when you have wiring or track.  Only the amount will vary.


3) CAPACITOR POLARITY

Normally a capacitor does not have any polarity or no "+" or "-" terminals.  It turns out it depends on the type of Dielectric being used.  Hence capacitor fall into classes depending on the material used for the Dielectric.   Bulk energy storage or large value capacitors starting around 1uF (1 microfarad) on up start to use special Dielectrics which allow the capacitor to greatly increase the the capacitance value per unit volume at the expense of requiring polarization or having "+" and "-" terminals.  For example: "Ceramic" capacitors have no polarity but "Aluminum Electrolytic" capacitors do.


4) CAPACITORS PASS CURRENT

The capacitor's job is to oppose changes in voltage across it's terminals and it does so by accepting current (charging up) or supplying current (discharging).  Literally the capacitor passing current THROUGH itself.  There is an equation that describes the actual current flow value based on how fast (time/frequency) the applied voltage is changing.  The equation is:

I = C*dv/dt

where:
I = Capacitor Current in Amps
C = Capacitance Value in Farads.
dv = "Change in Voltage" across the capacitor in volts
dt = "Change in Time" the voltage changes over in seconds.

which is calculated by:

dv =  |V(initial) - V(final)|  (Absolute Value of calculation)
dt =   |T(initial) - T(final)|  (Absolute Value of calculation)

Time (T) and Frequency (F) are directly tied to each other.   Time period is the reciprocal of frequency. T = 1 / F.  So when we say "change in time" or "dt", we are also describing the Frequency.

Note: The dv/dt term also goes by the technical name of "Slew rate"


5) CAPACITORS HAVE AN AC RESISTANCE (IMPEDANCE)

We know that the lower the resistance gets, the more current can flow.  The same is true with capacitors.   The lower the reactance (AC resistance) gets, the more current can FLOW THROUGH the capacitor.   Stated another simplistic way, a capacitor is a resistor who's ohm value changes with applied frequency.  The higher the frequency, the lower the resistance and visa versa. The equation showing capacitor reactance is:

Xc = 2*π*f*C

Where:
Xc  = (Ohms) is the reactance value of the capacitor
π   = 3.141 (Pi) is a mathematical constant.
f    = (Hertz) is the AC frequency of the applied voltage.
C   = (Farads) is the capacitance value of the capacitor.

If you explore this equation, you will find that the reactance (ohms) gets LOWER when:

1) you increase the capacitance (size of the capacitor capacitance value).
2) you increase the frequency of the applied AC voltage.

or any combination of the above two. 

The term "Impedance" for the capacitor (Zc) consist of two parts, the capacitors parasitic series resistance (R) + reactance (Xc), combined into a calculated single value. 

Zc = Xc + R

However for our purposes to keep things simple, lets just assume Reactance and Impedance are the same thing since they both use the same units of "Ohms". 

Zc = Xc

In other words, we are not going to worry about the (R) value.  Why?  It is to small to worry about in this specific application.

Last Update: 5/21/15