Energy in AC Circuits: No Frequency Involved

[p75213]

Given that:

E = hν where

E = energy of a photon
h = Planck's constant = 6.626 x 10-34 J·s
ν = frequency

Why is it that the energy (electromagnetic waves) in AC electrical circuits does not include frequency as part of the formula? eg.
$$\begin{array}{l} P = \frac{1}{2}{V_m}{I_m}\varphi \to \omega = \int_0^t {P\,dt} \\ {\rm{Where: }} \\ {\rm{P = average power, }} \\ {V_m} = {\rm{voltage magnitude, }} \\ {I_m}{\rm{ = current magnitude, }} \\ \omega = {\rm{energy, }} \\ \varphi {\rm{ = power factor(}}\cos ({\theta _v} - {\theta _i})) \\ \end{array}$$

The same thing applies to the formula for the energy contained in an inductor:
$$\begin{array}{l} \omega = \frac{1}{2}L{i^2} \\ {\rm{Where:}} \\ L{\rm{ = inductance}} \\ i{\rm{ = current}} \\ \end{array}$$

 

[Bobbywhy]

Electromagnetic waves do not propagate in an AC electrical circuit. Alternating Current flows in an electrical circuit. They are not the same, so they are not described by the same formulas.

 

[p75213]

That's what I thought until I read this: http://amasci.com/miscon/whatis2.html#2
The guy says he is an electrical engineer so I figured he must know what he is talking about.
Seems to make sense as the electrons in AC electricity are simply vibrating inplace. As I understand it a vibrating electron will set up an electromagnetic wave.

 

[Bob S]

Energy (Joules) can be stored in electrical circuits only in capacitors (½CV²) and inductors (½LI²). Power (watts) in electrical circuits is given by V·I (real and reactive). Power (watts per m²) in an electromagnetic wave (including waveguides) is given by the Poynting vector $\overrightarrow{S} = \overrightarrow{E}\times \overrightarrow{H}$ (vector cross product).

 

[truesearch]

p75213...I think your reference is referring to electromagnetic radiation (radio waves usually) from the wires of the circuit.
Whenever AC flows through a wire there is electromagnetic radiation from the wire. It is this radiation that can cause 'interference' in radio reception etc.
This is an energy loss from the circuit and shows that energy must be continuously supplied to maintain oscillation.