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