# How can DC current arise?

I'm curious to understand the properties behind direct current (DC) and alternating current (AC) which started when reading the definition and several articles online that, "AC periodically reverses direction and changes its magnitude continuously".

My understanding is that: current is the amount of charge per time, voltage is the potential of the electric field, and energy is an electromagnetic wave. So if the potential of an electric field is propagated by an electromagnetic wave, which is like $$\E = E_0e^{iwt}\$$ and therefore has some (maybe not uniform?) amplitude and phase which is related to the electric potential as the voltage, then shouldn't all currents also follow an oscillatory behaviour like $$\i(t) = I_mcos(\omega t+\phi_i)\$$ ?

Then I discovered the rectifier, which somehow filters out all of the phases which have the opposite sign:

Although, now this looks a little more like a pulsating "current"? Do more filters need to be added in order to make a direct current? I can sort of understand this if the system goes into a steady-state or something like it builds up a standing wave.

How can we get the direct current and alternating current to directly arise? Would it be dependent on the materials like metals / dielectrics? It makes sense to me that a galvanic cell gives rise to a direct current since the chemical potentials make it extremely unlikely for ions to flow in the opposite ways but this feels a little different to me.

Finally, does "alternating current changing directions" just mean the phase changes 180$$\^o\$$ in a given length of time? I'm not sure how to imagine this physically.

Thank you very much !

(1) graphs

(2) rectifier

• Would Electrical Engineering be a better home for this question? Commented Mar 10, 2023 at 7:37
• Hello ! Thank you for your suggestion, I was on the fence where to post this question haha and I will redirect my post over there. Commented Mar 10, 2023 at 7:43
• A DC electrical charge can move from one point to another (current flow) when charge carriers (electrons, ions, ...) physically move from point to point. For practical purposes, EM waves don't really feature there. Perhaps your misunderstanding is conflating "electric field" with "electromagnetic wave"...? Commented Mar 10, 2023 at 12:20
• You might get better "low level physics" answers back over at the physics SE. I think it's likely that you're going to get mostly "how do doides turn AC into DC" answers here :p Commented Mar 10, 2023 at 12:22

What you're looking for is a rectifier filter, usually with a capacitance (but not necessarily).

Semiconductor manufacturers had a few manuals on them in the past, as they affected the way you used their rectifier diodes. This has changed a bit over time, as simple diodes have become commodities, and big companies have steered to other fields.

Still, you can find a nice application note in the internet archive, the Motorola Rectifier Applications Handbook that from page 109 of the PDF explains a lot on why and how to employ a filter. Note that there are other sources for this handbook as well if you take a search on its original "HB214/D" reference code.

If you slap a capacitor across the load resistor (assuming the capacitor is appropriately sized) you'll get a similar waveform to the blue trace.

The capacitor gets charged by the transformer and then it supplies current when the diode is blocking.

simulate this circuit – Schematic created using CircuitLab

As you can see there are sharp peaks of current through the diode near the positive peaks of the input wavform, and nothing significant in between (the sign of the current is arbitrary here, the current in fact flows through the diode into the capacitor). At the beginning the simulator assumes the initial condition is that the capacitor voltage is zero, so the current follows the waveform all the way up to the peak, in this case it's limited mainly by the dv/dt of the sine wave since V1 is an ideal source. D1 also drops a bit more voltage at higher currents.

You can play with this simulation in Circuitlab or use something more sophisticated like LTspice (free) to get an idea of what is going on.

One fundamental difference between DC and AC lies in the expression: 'voltage is the potential of the electric field'

The circuit shown in the question has a transformer as a source of the emf. The relevant Maxwell equation is: $$-\frac{\partial \mathbf B}{\partial t} = \nabla \times \mathbf E$$ Note that, as the curl of the electric field is not zero, we can not find a scalar function V such that: $$\mathbf E = \nabla V$$ It is easy to proof it making the curl of the gradient of V, and verifying that it is identically zero.

So, the main difference between DC and AC is that only in the first case it is possible to say that voltage is the potential of the electric field.

In a solar cell for example, the current can vary all the time due to clouds, but it is a DC current anyway because there is no magnetic induction involved and the electric field is the gradient of a potential.

The pulsating current resulting from rectifying the original AC current, on the other hand, runs in a circuit where the (variable) electric field between the ends of the resistor is not the gradient of a potential.