# Capacitors & Capacitance

Discussion in 'Electronic Basics' started by Richard Harris, Jan 24, 2005.

1. ### Richard HarrisGuest

Hi,
capacitance. The problem is I don't see how this property is of use, many
circuits use capacitors but I don't understand what there role is.

I know capacitors don't allow current to flow through them and that they can
be charged and discharged and that the time taken to charge and dischage can
be calculated. But how are these devices off any real use?

Thanks for ya time guys.

2. ### John PopelishGuest

Capacitors are a class of devices that have time dependent response.
The mathematical description of the relation between the current
through a capacitor and the voltage across it is
I=C*(dv/dt)

With I an amperes, C in farads and dv/dt, the time rate of change of
voltage, in volts per second.

Since pure DC has no rate of change, it produces no current through a
capacitor. but any other voltage waveform from varying DC to
sinusoidal AC or any other variation in voltage over time causes
current to pass through capacitors.

There is also energy stored in any capacitor that does not have zero
volta across it. The energy is

E=(1/2)*C*V^2
With E being the energy in joules or watt seconds, C in farads and V
in volts.

The voltage cross a capacitor is also related to the total charge that
has passed through it since its had zero volts across it.
Q=C*V
Where Q is charge in coulombs, C is farads and V is volts across the
capacitor.

Capacitors are used for energy storage, filtering (frequency dependent
response) including resonance with inductors, DC blocking (while
passing AC riding on the DC bias), and timing circuits the measure the
time it takes for a specific voltage change caused by a charging
current. They can also be used to add up the total (integral) of a
signal over a period of time as a voltage change across the capacitor,
if the signal can be converted to a proportional current that charges
the capacitor.

3. ### Richard HarrisGuest

current through a capacitor never happens.
AC will charge and discharge a capacitor, reversr polarity of charge will
occur based on the frequency of the AC but no current will pass through a
capacitor.
Agin if current can't flow through a capacitor how can voltage or a charge?

4. ### Tom BiasiGuest

Hi Richard,
John has given you a technical and eloquent (as usual) explanation.
Your response indicated that you may not have comprehended the explanation.
You say "I know capacitors don't allow current to flow through them ".
Well if you look at DC you could be considered somewhat correct.
If you understand the capacitors mechanisms you may see that AC will 'Pass'.
You also say, "they can be charged and discharged and that the time taken to
charge and discharge can
be calculated. ".
After saying those things you still can not think of any uses for
capacitors?
Think some more,
Regards,
Tom

5. ### GarethGuest

Well, that is true sort of true. I expect that is why John used the
quotes. If a capacitor is charging or discharging then it appears that
current is flowing though it.

You know that capacitors can be charged and discharged, well the charge,
Q, stored in a capacitor is:

Q = C*V 

Where V is voltage and C is capacitance. Now, if you change the voltage
you must also change the charge on the capacitor. This charge has to
come from somewhere in the circuit, so charge must be moving. Moving
charge is current, so we have some current, but only while the voltage
is changing. If the voltage is constant then no current flows.

Current is actually the rate of flow of charge. So if we increase the
charge on a capacitor by dQ (where dQ means a small amount of charge) in
a time dt (where dt means a short time) then the current which appears
to flow through the capacitor during the time, dt, is dQ/dt

so I = dQ/dt 

For example if the charge increased by 1 C (Coulomb) in 1 second, the
average current flowing though the capacitor in that time would be 1 Amp

According to  a change in charge would also mean a change in voltage,
dV. Using equations 1 & 2 we can eliminate Q from the equation. This
gives, as John said:

I = C*(dV/dt)

If you use the water flow analogy and think of wires as pipes full of
water and voltage as pressure, then a capacitor would be a stretchy
rubber sheet blocking a pipe.

Now, if you increase the pressure (voltage) the rubber sheet will
stretch and some water (current) will flow in the pipe. Note that as
the rubber sheet stretches the water on the other side of the sheet will
be pushed down the pipe. No water actually crosses the rubber sheet but
as you increase the pressure water flows into one end of the pipe and
water flows out the other end. It is different water, but we don't care
about that, as far as we are concerned we force water in one end, by
increasing the pressure, and water comes out the other end.

If the pressure is constant no water will flow. If you reduce the
pressure the rubber will contract and push water back down the pipe.

If you constantly increase and decrease the water pressure water will
flow up and down the pipe. No water will actually cross the rubber
sheet but water is flowing up and down the pipe.

A capacitor will do a similar thing.

Gareth

--

6. ### John PopelishGuest

People who run motor windings with capacitors in series would be
amazed to hear that. While it is true that no particular electron
that goes in one side ever makes it out the other side, if you push an
electron in one side, a different one comes out the other side. And
that is still current.
Charge flows into one sire and out of the other, even though no charge
makes it through the insulation between the plates. An electron
arriving onto the surface of one plate creates an electric field that
repels an electron on the other side of the insulation to leave the
other plate and leave the capacitor. Since there are electrons moving
through both leads, there is effectively current passing through the
capacitor. All that is required to make this current is to force a
change in the voltage applied to the capacitor. Once the voltage
stops changing, the current stops.

7. ### Andrew HolmeGuest

Current *can* flow through a capacitor - but not forever, in the same
direction. As it flows, charge is taken from one plate and piled up on the
other. The greater the current, and the longer it flows, the more charge is
moved, and the greater the potential difference between the plates. If this
goes on for too long, the dialetric breaks down.

8. ### Andrew HolmeGuest

That should be "dielectric" of course.

9. ### Richard HarrisGuest

Thanks guys

My documentation must be inaccurate as it states that AC can not pass.

10. ### Richard HarrisGuest

I have two statements I would like to know if they are correct and that my
interpretation of them is good.

1.) Capacitance is the property that opposes changes in voltage in a
circuit.
There fore a capacitor can be used to steady voltage and keep it constant.

2.)Inductance is the property that opposes changes in current in a circuit.
There fore a coil can be used to steady current and keep it constant.

Thanks

11. ### John PopelishGuest

If it does then it is.

12. ### John PopelishGuest

A bit overstated, I think. I would say that a capacitor is a device
that must pass current in order for the voltage across it to change.
There are other devices that oppose voltage change by other means than
capacitance.

Capacitors are often connected across DC supply rails for the effect
you describe. If only small and brief currents are involved, then
small capacitors may do (e.g. .1 uf across the power pins of a logic
chip). If larger and longer lasting currents are involved, then quite
large capacitors ar used (following rectifiers in power supplies, for
instance). In both cases, the voltage is certainly more steady with
the cap in place than it is without it. This is using caps as
something like small rechargeable batteries, except that chemical
batteries can supply current with almost no change in their output
voltage, while capacitors must always have some voltage change if they
are going to pass current.
Again, a bit overstated, but not wrong. Change "the property" to "a
property".
There are other things that oppose current change that do not involve
inductance.

13. ### bxbxb3Guest

Hi,
Its been a bit late, but I hope someone will read this. Could anyone tell
me, if a capacitor is compared to a rubber sheet connected to a water
pump, what could be the possible analogy for an inductor. That example was
pretty good to compare and imagine. Thanks

14. ### GarethGuest

An inductor is a bit like a heavy object on wheels. The current in the
inductor is analogous to the speed of the object. The force applied to
the object is analogous to the voltage applied to the inductor.

If you apply a force to the heavy object on wheels it will slowly
accelerate. Similarly, if you apply a voltage to an inductor the
current in the inductor will ramp up smoothly.

If you stop pushing the heavy object it will slow down due to friction.
Similarly if you remove the voltage from an inductor current will
continue to flow through it but the current will decrease due to
resistance in the circuit (for a perfect frictionless object or a
perfect inductor with no resistance the motion or current will continue).

If you try to stop your heavy object quickly when it is moving fast the
inertia of the object resists this change. Similarly if you try to stop
the current in an inductor quickly the inductance opposes this change.
This is why you need to be careful when you switch inductive loads like
relays and motors.

The equations for a heavy object are:

F = ma

Where F = Force, m = mass, a = acceleration (rate of change of speed)

E = 1/2*m*(v^2)

Where E = Kinetic Energy, m = mass, v = velocity

The equations for an inductor are:

V = L*dI/dt

Where V = Voltage, L = inductance, dI/dt = rate of change of current

E = 1/2*L*(I^2)

Where E = Energy stored in the inductor, L = Inductance, I = current

If you think of inductance as mass, voltage as force and current as
velocity the equations are the same.

Gareth.

--

15. ### John PopelishGuest

If you imagine that voltage is torque and rotational speed is current,
then inductance is something like the inertia of a flywheel. Apply
torque and the flywheel steadily increases its rate of rotation (apply
voltage across an inductance, and current ramps up). It takes a large
spike of torque the other way to bring the rotation to a halt (it
takes a large applied reverse voltage to bring an inductive current to
zero, quickly).

while current goes around the magnetic field of an inductance.

16. ### Roger JohanssonGuest

An inductor is like a water pump without a motor, it is driven by the
water that is pushed through it.

It needs a pressure and a current to get going, and then it keeps on
running, pumping water, until the resistance slows down the current.

This is used in cars for creating a spark, or to create the starting
spark in a flouroscent tube.

Voltage is used to get the current running in a coil, and then suddenly
the connection is cut off, the current still pumps through the coil and
where is that current going to go? It has nowhere to go so the voltage
increases until a spark jumps over to ground, and that spark starts the
car or the fluoroscent tube.

Inductors have a resistance against quick changes in the current,
capacitors have a resistance against quick changes in the voltage.

The resistance changes with frequency, so inductors have little
resistance at low frequencies and high resistance at high frequencies.

There is a diagram over these factors which I think is very useful but I
can only find it in a pdf file from a swedish company.
http://www.elfa.se/se/fakta.pdf

This pdf is written in swedish but that doesn't matter because it is
only the diagram we need. In the index find the word " Induktanser" and
click on it, then scroll down one page, there is the diagram. Zoom in to
see the details. It is on page 33 in the pdf file.

You can see how the horizontal scale is the frequency scale, the vertical
scale is resistance, diagonally you see inductance and capacitance.

This diagram tells you what resistance a certain inductance or
capacitance has at a certain frequency.

For example, we want to know what inductor is needed for a loudspeaker
filter, it should have a resistance of 10 Ohms at 200Hz.

We go into the diagram from the horisontal 10 Ohm line, follow it to the
(vertical) 200Hz line, there is our working point. From there, follow the
diagonal line down left towards the border of the diagram and you see the
value 10uH.

So, we need a 10uH coil for this purpose.

I wish there was a better way to find such a diagram, better than to have
to download a pdf file in swedish and find the diagram. If anybody knows
about such diagrams in other places on the web, tell us about it.

These diagrams are useful because you only need your eyes to focus and
follow lines, there is no need to do calculations or touch anything, I
have this diagram in front of me all the time at the work bench, and use
it very often.

17. ### PeteSGuest

Although I agree with that desccription, it might not go far enough, in
a way. (IMO)

Strictly speaking (and you have to, quite often), capacitance is
exhibited between any two points where there is a difference in
potential.
This leads to the interesting observation that a resistor with current
flowing through it is, in fact, a parallel RC network (the amount of
capacitance is roughly proportional to the resistance but
obviously depends on the physical dimensions of the resistor). This,
incidentally, is one of the reasons to avoid large resistor values in
the feedback loop of an opamp (it makes an integrator out of it).

It also means that there is capacitance between virtually any two
points on the
average PCB. That is a point of major importance to practising
designers. Thousands more examples may be found of where capacitance
exists (static discharge testing uses, amongst other things, the 'human
body model').

When designing filters or PCBs that are low frequency, you usually
don't have to worry about those effects but as soon as things get above
a few 10s of MHz or so, (and don't forget transients), they can become
of overriding importance. Note that in a switching power supply with an
oscillator of 100kHz (quite low by current standards), board layout
capacitive effects are of major significance (the transients are in the
order of 10s of MHz, typically).

Note my first statement - it is what led to the development of a slick
little arrangement called 'guarded leakage' used quite a bit in the
input to sample and hold circuits. You can find that in Horowitz & Hill
(don't ask for the page, it's been over 20 years since I read it) As with many things electrical and electronic, the model one uses
depends on the circumstances.

So the answer to "what is capacitance" is long, and you have to decide
which parameters are of importance at a given time PeteS

18. ### Rodney KelpGuest

It's used in filtering power to smooth it out.

19. ### Rodney KelpGuest

You should read up on ELI the ICE man.

20. ### Richard HarrisGuest

What is ELI and ICE ?  