Is the energy flow due to a an alternating current constant or cyclic

Question

I understand that the Poynting vector shows us that energy flows in the region outside, or between, conductors, but the maths gets too deep for me to discover, when the current is alternating, whether the flow is constant, or varies cyclically with the varying electric and magnetic fields. Can anyone please resolve this for me?

Answer 1

Is the energy flow due to a an alternating current constant or cyclic

In the time domain, it is certainly not constant, it is cyclic and, if the load is reactive, alternating.

Consider the case of an AC current source driving a resistor. The power delivered to the resistor is:

$$p_R(t) = i^2(t)R = I^2_{max}\cos^2(\omega t) R = \dfrac{I^2_{max}R}{2}[1 + \cos(2\omega t)]$$

So, for a purely resistive load, the power cycles between

$$0 \leq p(t) \leq I^2_{max}R $$

Now, consider replacing the resistor with with a purely reactive load, e.g., an inductor. Then:

$$p_L(t) = v_L(t) i(t) = L \dfrac{di(t)}{dt}i(t) = -\omega L \sin(\omega t) cos (\omega t) = -\dfrac{\omega L I^2_{max}}{2}\sin(2 \omega t) $$

Note that the power associated with the inductor alternates between positive and negative, i.e., the inductor alternately absorbs and delivers power.

For a purely reactive load, energy "sloshes" back and forth between the source and load.

For a complex load, there is a combination of the above; a non-zero net power delivered to the resistive part and an alternating component associated with the reactive part.

The above can analyzed in the phasor domain too but, I think, it is especially transparent in the time domain.

Answer 2

Yes, the power in Single-phase AC systems is cyclic. For some values of the phase difference between current and voltage, it can even become negative (i.e. the flow goes in reverse) during a fraction of the whole period.

On the contrary, for three phases systems, with balanced loads, the power is constant. It can be seen of one of the main advantages of three-phase systems.

Answer 3

Electrical energy flows from energy source to load between the conductors via electromagnetic radiation, which has both wave-like and particle-like properties. Energy only flows in one direction - from energy source to energy sink. It isn't cyclic in the sense of moving back and forth between, say, a generator and a light bulb. It only flows from generator to light bulb. Whether the amount of energy being transmitted varies depends on the load.