Re: There's work, and then there's work

[David Rutherford <drutherford@SOFTCOM.NET>]

Bob LaMontagne wrote:
> David Rutherford wrote:
>
> > Could someone please refer me to experimental evidence that the total
> > energy stored by a capacitor is 1/2 CV^2. Thanks.
>
> That's an easy one. In General Physics II the students charge a capacitor to
> an arbitrary voltage, V. They then discharege it through a large resistor,
> measuring the current as a function of time. They then graphically integrate
> i*dt to get the total charge,Q. They calculate the value of 1/2 Q*V, which is
> found to be identical to 1/2 C*V^2. Not as direct as a calorimeter experiment,
> but the point is that the value 1/2 C*V^2 is not only well know, it has been
> verified often - even by introductory students.

It seems to me that you could have, just as easily, started with QV and
ended up with CV^2, since according to the conventional definition, Q =
CV, you can say that

QV = (CV)V = CV^2

or you could have said that

1/4 QV = 1/4 CV^2

How does the way you did it prove that the correct value for the energy
stored in a capacitor is 1/2 CV^2?

--
Dave Rutherford
"New Transformation Equations and the Electric Field Four-vector"
http://www.softcom.net/users/der555/newtransform.pdf

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