# How fast is DC current/voltage?

The standard way to calculate the speed of information (current/voltage, EM wave) through a dielectric medium (like PTFE or fiber) is to determine the relative dielectric constant, and compute the velocity factor.

You could use this information, theoretically, to calculate the delay between a signal sent over CAT-7 from New York to London.

However, these properties are microwave/high-frequency properties. How is the propagation speed of information calculated for low-frequency EM waves? How long does it take my DC source to send information around my circuit? How long does it take a battery to turn on my device?

OP Edit When I asked this question, I wasn't careful to put my question into words. The real question is about what the frequency component at 0 Hertz even means. How long do I have to wait to measure it? What does it mean to use a DC meter to measure voltage and current? Why is DC special relative to all other components of a waveform. I ended up providing my own answer because I realize that the answers to my question (rightly) understood me to be asking a different question.

• DC sources can't send information. Commented Oct 5, 2020 at 1:23
• If I connect and disconnect a battery then I've sent information, right? Is that not "DC" because it changes state? If that's the case, then how can the "information speed" of a system be determined as a function of frequency? Commented Oct 5, 2020 at 1:26
• Correct. If you are switching the signal on and off, then it is no longer DC. Commented Oct 5, 2020 at 2:24
• Yes, if you turn it on and off it gets an AC component. Commented Oct 5, 2020 at 2:54
• The dielectric constant of a coaxial cable is a function of frequency. The rising edge when you turn on your switch contains a range of frequencies. The various frequencies travel through the cable at different speeds and become separated in transit through the cable. But probably you can just use the standard delay for the cable for a first approximation. I assume you are not going to actually do this, so I don't know how far you want to go down this path. Commented Oct 5, 2020 at 7:36

First, as stated, DC carries no information. Switching DC on or off creates a step function, i.e. a waveform with harmonics that may go into the RF. A "perfect" (theoretical) step waveform would have harmonics through radio frequencies (RF), infrared radiation (IR), visible light and all the way to gamma rays... but since decreasing the wavelength increases energy of the minimal photon, that is actually not possible. However, RF harmonics can be heard as a click on a nearby AM radio when opening or closing a DC circuit.

So your question should be how fast a specific frequency propagates in a specific medium, the velocity factor. For example, in RG-8/U cable, a common RF coaxial cable, the signal propagates about 3/4 the speed of light in vacuo. Or for light, the refractive index, n, expresses the ratio to speed in a medium vs. vacuum. In germanium, IR crawls at 1/4 the speed it would have in vacuo.

• Fair enough. And thanks for the explanation. But, imagine that at time t=0 I connect an ammeter to the ends of two very long copper wires. The other ends of each wire are connected to each of a battery's anode and cathode, respectively. How much time passes until current is measured through the ammeter? Or, what variables are at play? Commented Oct 5, 2020 at 4:12
• Related question: The Fourier transform of the step function will have a DC component. What is that component's speed? Commented Oct 5, 2020 at 4:19
• DC has a frequency of zero. How would that apply to a sinusoidal expansion?? See en.wikipedia.org/wiki/Fourier_series Commented Oct 5, 2020 at 18:21
• Good question. It applies to the 0 term in the sum under the Definition section of that page. It's often colloquially referred to as the "DC term" or " DC component" or "DC offset". Now, to be clear, I'm assuming an aperiodic waveform, so the limit of the period would be extended to infinity (one common approach to deriving the Fourier transform, which is what I was talking about before... not the series that you linked). Commented Oct 5, 2020 at 20:08
• A more interesting question would be: "what is the velocity factor in a circular (or square) circuit 1 m in diameter with battery and load diametrically opposed?" Commented Oct 8, 2020 at 17:49

How is the propagation speed of information calculated for low-frequency EM waves?

Same as for high frequencies, except the inductance is higher due to reduced skin effect. Inductance reduces the rate of current change in the wire, so higher inductance makes the signal travel slower.

For example the graph below (from here) shows resistance (red) and internal inductance (blue) of RG-58 coax from 1 kHz to 10 MHz. Below ~20 kHz the inductance is practically the same as its 'DC' value, so the propagation velocity in this region is constant. At higher frequencies (where skin effect kicks in) the inductance reduces, which makes higher frequency components of the signal propagate faster.

Here is the measured delay time of an 81 foot length of RG-58 cable from 10 kHz to 1 MHz, indicating ~10% increase in propagation velocity at 1 MHz.

How long does it take my DC source to send information around my circuit? How long does it take a battery to turn on my device?

That depends on the transmission line characteristics of the wiring. If your device was powered through the 81 foot length of RG-58 cable above, it would take ~134 ns for the 'DC' voltage to get to the device.

• Thanks @Bruce_Abbott. The details about the frequency-dependent properties of the cable is great to keep in mind. But, it seems to me that it takes ~134ns for the 10 kHz component to arrive at the end of an 81 foot length of RG-58. What about the 0 frequency component? It's missing in the travelling wave? Commented Oct 5, 2020 at 14:28
• Below 1 kHz the inductance is constant, so the propagation velocity is also constant - all the way down to 0 Hz. The DC component is present in the waveform. It adds the offset voltage that makes the AC waveform go from 0V to the PSU voltage, rather than swinging positive and negative with an average of 0V. Commented Oct 6, 2020 at 6:45

I'm electing to provide my own answer, since none of the other answers satisfies me completely. The following is a summary of this discussion from r/AskPhysics.

1. @DrMoishe Pippik's answer fails to address the original question which could be posed as "how is DC manifested in real life if DC can't be expressed as a non-zero sum of sinusoids" or "how is DC current/voltage measured if DC can't 'travel' around a circuit because it's not a wave"?
2. @Bruce Abbott's answer fails in a similar way, to couple the reported measurements of DC values to the propagation of waves down a transmission line.