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?
Is the energy flow due to a an alternating current constant or cyclic
energypower
Related Topic
- Energy absorbed by the condenser
- Electrical – Current Transfomer (CT) ratio setting on energy meter
- Electronic – the power / energy of a discrete time constant signal
- Electronic – How to calculate total current, power, energy consumption from device
- Electronic – How to know if a current source supplies or receive energy
Best Answer
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.