A bit about capacitors




I recently (June 2008) received email from a visitor to this site asking if I might post something on capacitors. 

Rather than regurgitate the standard fodder which can be found on innumerable other sites I shall try initially to use the water analogy which has often been of help in d.c. circuits.




In this simple closed circuit, which is full of water, it doesn't matter which way the pump works, forward, backward or alternating back and forth between the two, the water will flow equally well in whatever direction the pump is working at any moment. 

The circuit is similar to a resistive one - the "resistance" to current flow being proportional to the pipe diameter and the pressure difference across the pump. 

If the pump is working one way we have one 'polarity' of current flow.  If the pump is working the other way we have the opposite 'polarity' of current flow, and if the pump's direction alternates from one way to the other we have alternating current flow. 




We will now introduce a modification to the circuit.  A flexible membrane is inserted across the pipe as indicated.  It could be a piece of rubber from a party balloon or a bit of a condom. 

This tries to illustrate something of the nature of a capacitor.  




If the pump operates in a "clockwise" direction, it tries to force the water in the direction of the red arrow as seen below.

The membrane, or diaphragm, is distended by the pressure and then stops where it is.  Apart from the initial small surge there is no current flow.  We are applying direct pressure, our equivalent here of d.c. 




If the pump is switched on in the "anticlockwise" direction, it tries to force the water in the direction of the blue arrow, below:

Similarly to the previous case, the membrane is initially distended and stops where it is, being held there by the pressure. 




Both these cases can be thought of, very loosely, as being similar to a capacitor being charged.  There is an intial brief current which ceases as soon as the membrane has been forced to some state governed by the water pressure.  However, we can disconnect a charged capacitor from the voltage source which charged it - the pump in this analogy - and it will retain its charge.  But the water/hydraulic analogy breaks down here.  If we disconnected the section of the pipe containing the membrane (without taking very elaborate precautions), the membrane would simply return to its unpressurised state. 



Now let's change the pump's direction on a regular and repetitive basis. 

The membrane will first be distended one way and then the other.  We are applying a.c.

A suitable flow indicator connected in series with the previous two examples would show a brief initial flow as the membrane was moved.  Now, however, we have a continuously changing flow- alternating from one direction to the other. The membrane is distended first one way then the other, alternately.  It's an alternating current, albeit of water but an alternating current nevertheless.



A capacitor doesn't pass direct current.  But an alternating current does flow through a capacitor. 



Let's connect some of our "hydraulic capacitors" in parallel.  Here there are four of them.

The pressure across parallel connected items is common to all of them, so all four membranes will be subject to the same pressure, and, if they are similarly constructed, will move by the same amount.  The initial brief surge of current as the membranes are forced into their distended positions will be equal in each of the four branches of our plumbing system.  Their sum, therefore, will be four times the value of one of them.  The result is as if we have one capacitor whose membrane is more compliant - a capacitor with a value four times higher than one of them. 

The values of capacitors in parallel are added together. 



We might as well look at a series combination too.

The pressure difference across the series combination is now shared between them.  If the membranes are of similar construction (or the capacitors are of the same value) the pressure across each one will be the total pressure divided by the number of capacitors.  It follows that each membrane will be distended less now.  I won't take a guess at, or research, what happens to the value of the initial brief 'charging current' in a hydraulic system.  Suffice it to say that the total value of four equal-value series connected capacitors is one quarter of the value of one of them. 

I'm sure you have seen, or will see, the formulae for calculating series connected capacitors elsewhere. 



What do we use capacitors for? 

Coupling, decoupling (filtering), making circuits which have a 'resonant' frequency (for tuning) - it's a special case of filtering.


An example of COUPLING

A capacitor is often used in series with the input to an amplifier, particularly audio ones.  It protects the first amplifier stage from any d.c. which could be present on the signal input cable (from another item of equipment) (it doesn't pass d.c.) but allows the signal, which is a.c., to pass to the first stage. 

There may be a capacitor which pass the signal from the output of one amplifier stage to the input of another for the same reason. 



How do we make a filter with capacitors? 

We had first better define what a filter is.  A filter is something which either permits the passage of something/s while inhibiting that of others, or vice versa, inhibiting the passage of something/s while permitting that of others. 

If you have a swimming pool you will also have a filter for the water.  It permits the water to pass but inhibits solids from passing.

If you have a motor car it will have an oil filter.  It permits the oil to pass but inhibits the passage of solids (very small bits of metal which have been worn away from the moving parts of the engine.) 


We have seen how a capacitor doesn't pass d.c. but it does pass a.c. 

A resistor passes both d.c. and a.c., resisting or impeding the flow of either by a degree proportional to its resistance value.  The value of a resistance being expressed in ohms (with a lower case 'o'), abbreviated to the upper-case Greek letter Ω, pronounced omega, not omeega. 

A capacitor also impedes the flow of a.c.  It does so by a degree which is (inversely) proportional to not only its value but to the frequency of the current too.

In the case of a capacitor, the resistance or impedance to current flow is also expressed in ohms, but is called reactance, capacitive reactance, abbreviated to Xc.

The value of a capacitor's reactance can be calculated by:   Xc =      1    
                                                                                                                 2π f C

f being in Hz and C in farads.   You will sometimes see  2π f  abbreviated to the lower-case Greek omega, ω, which is sometimes referred to as 'pulsatance'. 



So, the current flow through a capacitor will be opposed less as the frequency of the current increases, and vice versa.


Look at this.


The same thing drawn two ways.  A signal of some sort is applied across a C and an R in series, the output being taken from across the R.

The reactance of the C and the resistance of the R form a voltage divider across the signal.  If the frequency of the applied signal is such that Xc = R then the voltage across R will be half the input voltage. 

If the signal frequency is increased, Xc decreases, and more of the signal appears across R.  And vice versa. 

It's a basic high-pass filter.



The converse is a low-pass filter. 

Similarly, if the signal frequency is such that R = Xc then the voltage across C will be half the input voltage.

As the frequency is lowered, Xc increases, and more of the signal appears across C.  And vice versa.


The study of filters is, itself, a very complex one but these two simple examples serve as an introduction.



The 'hydraulic' analogy used at he start of this essay falls down in so many ways but I hope that it has helped some beginner somewhere to start to get a feel for capacitors.

One extremely important property of capacitors to which I have not referred is the phase relationship between the voltage across them and the current through them. 

If we apply a.c. across a resistor the current through it will be in phase with the applied voltage,  i.e. the peaks of the current will be in phase with the voltage peaks, and the zero crossings will coincide.

This is not true in a capacitor.  Applying a.c. across a capacitor, the current through it will lag the applied voltage by 90 degrees. 


If you read about inductors you will find the opposite true.  The current through an inductor will lead the applied voltage by 90 degrees. 

These two facts lead to some interesting results when considering series and parallel resonant circuits.