The energy of a charged capacitor

[S.Roksund]

Hello all,

The folloving equation is used uncritical in most textbooks, technical reports - and also in this forum.
Energy of a charged capacitor = ½ CV^2  = wS (or Joules)

Further information on the exponential charge curve and time to full charge is only
mentioned in more complete documents, and one must most of the time read the complete document
to find this important information.

It is plainly not right to use the above equation in most applications, because  it is true ONLY for the
condition that the charge time is CR and which amount to a charge of a little less than 63 %.
Not a usable condition.

The charging of a capacitor has an exponential path and will at 4RC be charged to 98 %.
Usable for most applications.

In practice it is 5RC that is used for the capacitor voltage and charge to reach "fully charged".

Therefore a nearly correct equation is: Energy = CV^2 = wS (or Joules)

Find full information here:
http://www.rowan.edu/colleges/lasold/physicsandastronomy/LabManual/labs/Capacitor.pdf

Happy New Year!

Sigvald

[DrSimon]

Along the same line only looking at charge;

The energy of the electric field in a charged capacitor C with potential V would be U = VQ

If you start with the voltage difference between the plates of 0V then the 'Average' energy needed to establish the field would be Uav = 1/2 VQ

Simon.

[S.Roksund]

Agreed. Thanks for your comment.

And if one charge in steps the dissipated energy to fully charge a capacitor
will be much less. The discarging of the capacitor can also be done in steps and will deliver
most of the charge to the load.

The stepvice charge and discharge have been used in several successful designs to reduce
the power dissipation in c-mos uC chips.

Along this lines, one can work to try and make an OU circuit, as seen elswhere in the forum.

Regards
Sigvald

[Creativity]

It was quite time ago when i was studying it,but as i remember we used Fourier transformata(in english :transformates?) to describe  transient capacitor and coil states.By transient i mean charging,discharging of magnetic(coil) or electric field(cap).
Fourier was indeed exponential curve,but it requires to have some mathematical knowledge to use this "magic" . I guess everyday cap user stays cool with approximation given in most books.
Anyhow,here on this forum what u brought is very usefull.It is indeed of more importance for us if we want to make our research profi way.

[S.Roksund]

Hello all,

The folloving equation is used uncritical in most textbooks, technical reports - and also in this forum.
Energy of a charged capacitor = ½ CV^2  = wS (or Joules)

Further information on the exponential charge curve and time to full charge is only
mentioned in more complete documents, and one must most of the time read the complete document
to find this important information.

It is plainly not right to use the above equation in most applications, because  it is true ONLY for the
condition that the charge time is CR and which amount to a charge of a little less than 63 %.
Not a usable condition.

The charging of a capacitor has an exponential path and will at 4RC be charged to 98 %.
Usable for most applications.

In practice it is 5RC that is used for the capacitor voltage and charge to reach "fully charged".

Therefore a nearly correct equation is: Energy = CV^2 = wS (or Joules)

Find full information here:
http://www.rowan.edu/colleges/lasold/physicsandastronomy/LabManual/labs/Capacitor.pdf

Happy New Year!

Sigvald

Hello 

The link above is not working, and I have therefore found a website that have plenty of
information. One good starting point is:

http://hyperphysics.phy-astr.gsu.edu/hbase/electric/capeng2.html#c3

I am still studying the charging of capacitors and how much energy a fully charged
capacitor holds.
My background in mathematics is not good enough to discuss the integration of charge,
but with reference to the figure in the link above, I allow myself to comment as follows:
It seems to me that the area under the curve in the figure must contain much more energy
than stated. I believe that after 4 or 5 RC the capacitor must store almost the energy E=CV^2
If I am wrong, can someone explain this to me?

Best regards
S.Roksund