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Capacitors – Some more specifics.

Capacitor in a Switched DC circuit.

In the post “Energy Storage – Capacitors – Equalization of Pressure“, my main interest was presenting some analogies.  In this post we will start talking some specifics.  In that post I embedded the video incorrectly you may find it here:  you tube capacitance video

A capacitor can be constructed almost exactly as the one drawn schematically in the video.  I have seen articles talking about high voltage projects and a capacitor was build by using a piece of window pane glass and placing a metal sheet on either side.   Although the physical size of this is large, the electrical size of the capacitor is very small.  The things that determine the electrical size of a capacitor are:

  • The surface area of the plates facing plates of opposite polarity.  The bigger the better and both sides of each plate are usable for the purpose.
  • The spacing between the plates.  The smaller the better.
  • The type of insulator between the plates and the dielectric constant we talked about in the previous post.

When capacitors are sold the main description is usually the type of insulation used. Often the capacitor is built up by using two strips each of insulation and metal foil and winding these together to form a cylinder. Another way to get lots of capacitance in a small area is to fold the strips in a Z fold manner.  The way to get the most capacitance in a small container is to used anodized aluminium and a conductive liquid.  Anodized aluminium forms an oxidized layer on it and that layer is not conductive.  The conductive liquid keeps the oxidized layer oxidized.  This type of capacitor is called an electrolytic capacitor.  However, it is polarized and if it receives an inverse voltage, it shorts out, and “lets the smoke out.”  The oxidized film is very thin making lots of capacitance in a small container.

The other thing to be aware of is some materials are good insulators at some frequencies, but are not good at higher frequencies.  Before choosing a capacitor do some research to make sure the type you are choosing is good for the application.

In addition to fixed capacitors there are some adjustable capacitors.  One type used in many radios is an set of fixed blades with a set of movable blades meshed between the fixed ones.   The movable blades gradually increase in radius as they are turned changing the surface area exposed to the fixed blades.  Another type of adjustable capacitor uses a screw to squeeze leafs closer together.  This type is used for a calibration type of adjustment where it is set once and then not adjusted again for a long time and is referred to as a trimmer capacitor.

Semiconductor devices, transistors, diodes, & I.C.’s, also form capacitors.  This is done two ways. First by charges within the device forming a “boundary layer”.  This will have to wait until a future post(s) to explain.  The second method is by very thin glass and aluminium deposits formed in the device as it is built.

In the video I stated that a capacitor would ideally hold the charge forever.  As usual, real life is not ideal. The insulator conducts a small amount of current forming a very high value resistor in parallel to the capacitor.  This current is called “leakage current” because it allows the charge to leak out of the capacitor.  If the insulating ability of a material is affected by frequency this means means this effective resistance in parallel to the capacitor is becoming less.  Also, the leads to the capacitor and the foil within it are not perfect conductors effectively acting as if a very small resistor is in series with the cap.

If capacitors are connected in parallel the amount of capacitance is the sum of the individual capacitors.   This makes sense if you think about it,  because the surface area is being increased.   If capacitors are connected in series the total capacitance uses the same rule as resistors connected in parallel, the reciprocal of the some of the reciprocals.    Ctotal = 1/(1/C1 + 1/C2 + 1/C3…).  Again this makes sense if you think about it.  You are increasing the spacing between the plates by doing this.

The circuit shown in the first picture is essentially the same as shown in the video.  The graph to the right shows the charging of the capacitor in that circuit.   The time constant, tc,  can be determined in seconds by multiplying the resistance by the capacitance value.  In the circuit one time constant is R (1000) X C (0.001) or 1 second. At one tc the capacitor will have charged to a value = 63% of the voltage source, or in the case of the circuit in the diagram 6.3 Volts.

Current through the circuit.

The current through the circuit is shown in the graph to the left.   Again the time constant is calculated the same as before.  Since Ohms Law still applies the voltage across the resistor will follow the current.  The maximum current is at the moment the switch is closed.  At this moment the capacitor acts as if it is shorted and the resistor is limiting the current.  That means that in our circuit the 100% value is 10/1000 or 0.01 A.

The equations for those two curves are:

where Vc is the voltage across the capacitor and Vr is the voltage across the resistor and tc is the time constant calculated by R X C.

Whole number multiples of the tc value give the values show in the table to the right.   The only ones I commit to memory is a t=0 (100%), t=1 (63%), and t=5 (very near 0%).

It was my intention to talk about what happens to AC with capacitors, but this post has already grown fairly long so I will put that off until a future post.  I promise it will be very soon but we probably need to learn a new type of math first.

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