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Capacitors, previously called condensers, are one of 2 types of reactive device, inductors being the other one. Reactance is negative, proportional to the inverse of frequency. With a sine wave Voltage applied, current is said to lead by 90 degrees. This is a cause of perplexity among many electrical engineering students, since it implies that the component can predict a Voltage's arrival.
As with many things, the reality is both simpler & more complex than this. One solution is that the current wafeform is traced by the cosine, not the sine. In this animated plot, comparing the yellow cosine with the green sine clearly shows this. Move the mouse cursor near the image to start it. This fact is arithmetically convenient but resolves nothing.
Assume the sine wave Voltage is switched on at the monent of zero crossing. The current trace will be exactly as in the image, with the current starting at the maximum point. Not what would happen if it was due to a phase lead.
This drawing shows the result if current is 90 degrees in advance of Voltage, as taught. The phase relationship is the same, but in this case the Voltage starts at maximum. Current starts, at maximum, a quarter cycle earlier. The capacitor anticipates the application of Voltage, obvious nonsense.
A capacitor draws current only when the Voltage across it changes. This current is in phase with and proportional to such changes. A sine wave has the maximum rate of change at the moment of zero crossing. At that instant the current is at its maximum, in the direction of change. At the instant when the Voltage is at maximum, it is not changing, so the current is zero.
A sine wave Voltage has a constantly changing slope, causing a constantly changing current. When the Voltage slope is in a positive direction the current is positive. For a negative slope the current is negative. Therefore it is in phase. A 90 degree phase shift is real, but only because maximum change occurs 90 degrees before maximum value. The same applies to zero change & value.
Other waveforms show the capacitor's performance in a different light.
Here a capacitor has a triangle Voltage applied, white trace. The resultant current is shown in purple. The signal is switched on at zero crossing but continues beyond the right end. Very different result to a sine wave & seldom shown in books on the subject.
As can be seen, with suitable circuitry, a condenser can be used as a triangle to square wave converter. I have never seen this property used, although it is inherently more stable than the usual electronic comparator type. When the Voltage is changing to a more positive value the current is positive. As the rate of change is constant the current is constant,
At the peak of the triangle the slope reverses direction sharply, causing an abrubt reversal of current.
Application of a square wave Voltage shows another characteristic of capacitors.
The Voltage waveform is again shown switched on at the point of zero crossing. In this case both traces are in white & are separated. The second, current, trace is at 50% vertical scale.
Current only flows during the change of Voltage, very brief with a good square wave. The trailing curve shown is due to resistance in a practical circuit. The capacitor has a reactance at the frequency concerned. If this is high compared to resistance, a small time constant, the curvature will be slight.
This is called differentiation, the current is the differential of Voltage. There are many practical circuit applications for this function.
In basic form a capacitor is 2 conductive plates spaced apart.. Effectively a break in a circuit, yet an alternating or changing Voltage causes current to apparently 'flow'. Early on it was realised that no current actually flows across the gap. Yet the connecting leads do carry current.
With DC applied, an electrical charge is said to accumulate on one plate, fed by current in the connecting wire, An equal opposite charge builds up on the other plate. This continues until equilibrium is reached, when the potential difference across the plates equals the source P.D. At this point the capacitor is 'charged'.
Changing or reversing the Voltage causes further current to flow. Until a new equilibrium is acheived. A sinusoidal alternating Voltage will thus cause a matching current to flow.
The sticking point was the magnetic field caused by or causing any current flow. This field 'rotates' around the current. Since no current actually flows across the gap it was thought that the capacitor could not have a magnetic field. In the steady DC case this was obviously so. When AC was considered, Ampere's law no longer produced correct results.
Maxwell's Equations
At the time of the American civil war James Maxwell solved a great many problems, including this one, by inspired theoretical thinking. He produced a set of equations still in use today. These were later rationalised by Oliver Heaviside, making them simpler & more useful.
To correct errors he introduced the concept of 'Displacement Current'. This explained why introducing insulating (dielectric) material between the plates increases capacitance. Adding terms to take account of this current gives correct results with Andre Ampere's & Michael Faraday's equations in the AC case.
Many University & college sites etc. go into the mathematics in depth. There seems little point in duplicating such work here.
Displacement current is explained as the minute movement of charge in the molecules of insulators, when subjected to an electric field. In a capacitor, negative charge moves towards the positive plate. This leaves the side of molecules facing towards the negative plate with a net positive charge.
Including this displacement current solves problems in calculating the performance of capacitors. The concept is obviously right, the work done by this current even precisely explaining capacitive dielectric loss & heating.
Even as he was working on this theory Mr. Maxwell was the first to realsise it had an obvious large hole. One not yet plugged, even today. A capacitor still works with a vacuum between the plates.
The displacement current is still required to balance the equations, but in what is it now flowing? James Maxwell's solution was 'the aether' sometimes spelt without the 'A'. This indetectable substance was said to pervade all of space & fill any vacuum. Electromagnetic waves, which he prophesied must exist, propogate through it.
The atoms of this ethereal matter supply the displacement current in this case. We all now know that the aether does not exist, yet its postulation still holds the theory together. There is worse to come, for example: with Transverse ElectroMagnetic (TEM) waves. **
Many years ago, when I was a teenage apprentice, I was given the task of designing a transistor VHF receiver. I used a new device, the tunnel diode, as a local oscillator. Transistors of the time were usually not up to the job. Initially an arrangement called a Lecher Line was used as the resonant circuit. Basically an unterminated transmission line, with length chosen to suit the frequency required.
Anomalies with accuracy & operation of this gave cause for some pondering. Because the job had to be done I finished up using a coil & capacitor like everyone else. I did not pursue the reason for deviations from the theoretical model. If I had, avenues to a new understanding may have opened up much sooner.
The nature of capacitors.
** There is a surprising concorde between my thinking on this subject & that of Ivor Catt. My viewpoint originated from a study of VHF sine waves along a Lecher Line, essentially a transmission line. Due to this similarity, the following example is a hybrid of text from his book & my thinking. I apologise to Ivor for this, hopefully it gives the general idea.
Ivor Catt. Electromagnetism & The Catt Anomaly. 
For infomation on the Catt Anomaly & electromagnetism Ivor Catt's books on the subject are essential reading. A visit to his web site is well worth while. You will find a man, underestimated by the establishment, who may yet bring our discipline out of the dark ages.
This subject may not, initially, seem to be associated with capacitors, but patience. A capacitor is, usually, 2 parallel plates or strips.
< Start with 2 parallel wires of length L in a vacuum, a transmission line. One end connected, via a switch, to a source of Voltage, the other to a resistor.
Shut the switch, a TEM wave, with its front perpendicular to the wires, will travel at the speed of light, (c). After a time L/c, it will arrive at the resistor & current will start to flow. Where does this current come from? The first thought is usually that the electrons flowing through the wire are the current.
Electrons however, have mass & cannot travel at the speed of light. If they did, their mass would become infinite, requiring infinite energy to move them. A second possibility is that the wave provides the current. There are however several problems with this.
The wave is travelling along the space between the wires at speed c. If displacement current between the wires is a component of this wave it will involve a rotating magnetic field. In the forward direction this will be moving in excess of c, a theoretical impossibility. >
If the resistor matches the characteristic impedance of the line there will be no reflection. The wave will be absorbed and dissipated as heat. Current through the resistor will then cease, until current from the wires catches up. There is no practical evidence of this two step start of current, in any case the wave is transverse to the resistor and cannot cause current in it.
If the wave causes no current then flow will not start until electrons arrive. In this case why is the wave dissipated? If it causes no current, how does it know the resistor is there? Let alone that it is the right value.
A further problem is that current flows from the source at a speed below c. Ahead of it no current flows, In the return wire current flows to the source at a similiar speed. Behind it no current flows. Where is it coming from? We have already ruled out displacement current crossing the gap.
Add these anomalies together, with others to be found later. Then realise that two parallel wires are no different, in principle, to two parallel strips, an unwound capacitor.
When I was a teenager these anomalies led me to believe that the Physics & Electrical Engineering courses I was taking were wrong. I knew noone I could discuss this with, lecturers said, in essence, 'this is what the course says, these people have a century of experience behind them'.
I was effectively told that disagreeing with those who knew more was foolish. Certainly using the theory as it has always stood has rarely caused problems with my work. On the other hand, occasionally doing something that 'cannot work' has made me a minor mark in history.
The fact that Very High Frequencies caused so many unexplained oddities probably helped my decision to stick with frequencies I can hear. This has worked for me, audio & music was always a passion. I have always had this feeling however, that we know so much less than we think.
A huge number of questions remain unanswered. For example:
it is obvious that electrons are busy, active dynamic little things. Whirling in constant motion, with associated waveform & frequencies. Also a clear mutual repulsion, yet frequently working together. Rather like the Chipmunks in their cage in our workshop.
How can they sit still, in a pile at the end of a wire, waiting patiently, for a chance to jump the gap to another empty wire? Energy & matter are interchangable, one can become the other. How can particles of matter come to a halt without ceasing to exist? Unlike our Chipmunks they surely do not hibernate?
A thought experiment to check for particles: Take a 1 Farad capacitor & charge it to 1 Volt. This requires 1 Coulomb, 6.24 X 10^{18} electrons, a mass of 5.685 nanograms. Dismantle the capacitor & weigh its plates. Assuming they had the same mass uncharged, the negative plate should now weigh 11.37 nanograms more than the positive plate. Has this been tried?
Now I find, via the Web, that I am not the only one. Another fledgling branch of science is around, studiously ignored by the mainstream, but increasingly answering questions that established theory skates round. If I can make formal contact, I will keep everyone informed of progress.
It will be good to help formulate, to a reasonable level of certainty, what I have always instinctively known. It is time for younger people to escape from the trap built by physicists, electricians & experimenters of yesteryear. They did their best, without the facilities available today, but much of their theory is inspired supposition, adapted to fit measured phenomena.
If we are ever to leave the confines of our past & our planet we must learn something of the universe's true nature. Everything is not built out of blocks, like the bricks in a child's play box.
A Form of Words
On various pages of this site, including this one, we refer to current flow, capacitors being charged etc. This is merely a convenient form of words, based on habits spanning 4 centuries. It does not mean we accede to the dualist or particle theories. Nor do we accept quantum mechanics, the uncertainty principle & all their ramifications.
Until we get our house in order, a new form of language, in keeping with reality, will not fully evolve. So, for the present, we are stuck with the arcane way of describing things.
The Origin of Capacitors
In 1746 physicist Pieter van Musschenbroek, of Leiden University in the Nederlands, tried pumping electricity from an electrostatic generator into a bottle of water. There's no accounting for some people. Nothing seemed to happen but, when he picked up the jar to disconnect it, he got an almighty wallop. The Leyden Jar was born, called a condenser, because it held 'condensed' electricity!
