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# Ohm’s Law

#### Issue 154

In Issue 151 (“Shop Class”), I made a note to remember Ohm’s law and that we would come back to it later. There’s been so much national press coverage on this issue in the last few weeks that I thought maybe we might discuss it sooner rather than later, as the amount of disinformation warrants some attention.

And now, back to the Ohm’s law equation, which defines the relationship between voltage, amperage, resistance, and power. We’ll also tie this piece to that first article in the series. As the old advertising slogan said, here’s “Something to think about from the folks at Getty.”

Ohm's law wheel with interntational notation. Courtesy of Wikimedia Commons/Per Mejdal Rasmussen.

The first Law of thermodynamics says energy can neither be created nor destroyed. If you put electricity into a powerline and not all of it comes out the other end, it went somewhere. Our Ohm’s law equation’s little secret allows you to calculate the power loss in a wire. That power loss is converted to heat. Of course, we don’t know the largest parameter of powerline loss under normal operating circumstances, the resistance, although the utilities do. To be sure, there are other losses, such as leakage due to humidity, but let’s look at the bigger picture. To keep the conversation simpler, we’ll assume we’re all residential customers and ignore the power factor, which is how utilities surcharge industrial customers.

If you convert the energy of automotive fuels into watts, you quickly observe that making a move to all-electric vehicles is an intractable solution under today’s conditions as it would yield a frightening increase in the electric grid’s load. Even Elon Musk has commented on this. One thing you can be sure of is if Elon Musk is interested in something, he smells money. Lots of money, and he makes it off of battery sales, among other things. And remember two things here: one, we’re not even talking about eliminating fossil fuels for heating. Further, mining and processing lithium creates large quantities of very hazardous waste. Do we really want that on our shores? After all, the sun is shining and the wind is blowing somewhere. Surely we can just move power around the country. Oh wait, that requires an already overloaded grid…

Remember twinkle twinkle little star, power equals A2R? You can see from Ohm’s law that the power loss increases with the square of the amperage. Thus, if you increase the current in the grid by a factor of 3, the loss increases by a factor of 9. Typical losses in the transmission lines of the grid are 1 to 4 percent per hundred miles. You must generate that much more electricity just to cover the loss. Charging your car will generate local load relative to population density. Additionally, you must charge batteries with more energy than you will get out. The actual loss depends on the charge rate, discharge rate and battery chemistry, but can be as high as 40 percent.

Ohm's law expressed as an electrical diagram showing V, I and R.

Old-technology coal-fired power plants have efficiencies in the twenty-something percent range. New-technology coal-fired plants have efficiencies in the range of 35 to 38 percent. It’s not unusual for two-thirds of the energy in coal to be lost before the electricity gets to the consumer. It’s no wonder these power plants have an impact on the environment. But they tend to be located close to sources of fuel, so we can assume the transmission losses were negligible compared to the cost of transporting the fuel closer to the load (the load is anything that consumes power, such as your lights, toaster, or high-end audio system).

The days of facilities such as the Jim Bridger Plant are over, due to the inefficiencies involved. For sure, the utility companies will attempt to backfill the grid with power from photovoltaic cells or windmills, but the coal leases at Bridger are nearly expired or mined out and losing a plant of this magnitude, as an example, will leave a 2-gigawatt loss of generating capacity.  There are many more examples where the generated power is shipped off to remote states rather than used locally. But, read on.

Increasing the wire diameter of the powerlines to handle more current would be problematic. Since this is alternating current, the skin effect applies. Electrons have such an intense dislike for each other that they only flow on the outer edge of the AC conductor. They try to put as much real estate between themselves and others of their kind as they can. In other words, the core of an AC wire is relatively unused, with electron flow on the circumference

Good electrical conductors are generally highly ductile but don’t exhibit great tensile strength. Suspended exterior powerline wires not only need to handle their own weight, but also what nature throws at them, including wind, the accumulation of snow or even several inches of ice, and the span between support insulators. Some of the diameter of the wire you see on a powerline is a steel core that’s there for strength. The conductor, often high-purity aluminum, is wound around the steel core. They are referred to as aluminum-conductor steel-reinforced (ACSR) wires, and they are expensive. The cost of replacing the wire to handle more amperage across the nation would be prohibitive.

Back in the 1970s, when we had all those blackouts, some of the transmission lines became so overheated from the loads that they drooped dangerously low to the ground. Think of the wires in your toaster. If you came close to hitting them with 380,000 volts, more would happen than just having the hair stand up on your head, although maybe not as much fun as being on what is now known as the Continental Divide Trail leading North from Rollins Pass in a thunderstorm. I’ve hiked it in a storm and it ranks as one of the scariest and dumbest things I’ve ever done. It was literally a hair-raising experience. I was never so happy to get off that ridge. Fortunately, I did not become a study in conductivity, but I digress.

Lightning rod buddies 45 years later. All present and accounted for: Paul Kellogg (L), Steve "Hoss" Foss (R). Not one of us was struck by lightning that day.

The traditional solution to our power delivery dilemma has been to increase the voltage, so the equation becomes power equals V2/R, where V is electromotive force (in volts). Sounds easy, and it has been the time-honored solution to accommodating increased energy consumption.

However, this would require a total rebuilding of the grid infrastructure. All of the insulators and transformers would need to be replaced. And let’s not forget, we need to get those wires higher off the ground to protect anything below them from man-made lightning. A good discussion of this can be found in a German study, although it’s getting a little long in the tooth, that says converting the grid to a capacity of handling 1,000,000 volts would not be profitable. Another European study shows transmission losses approaching 10 percent in highly-developed nations.

Of course, the further electricity travels from the source, the higher the resistance it encounters (which is a relatively linear phenomenon), and the greater the power loss. What this all boils down to is that the future sources of electrical generation will need to be very close to the consumer as demand surges. And yes, you will see wires, and windmills, and solar cells, maybe even a new nuclear facility, and they will be in your backyard, or visible from your backyard, or maybe even on your roof. Don’t laugh. Bill Gates and Warren Buffett are funding breeder reactor research for this very reason.

Utilities are already planning for distributed generation. Note how one utility in Colorado is adding capacity nominally equivalent to one half of a coal-fired generator, but spread throughout multiple communities. Minigrids and microgrids, with their own generating capacities, are most likely the future for the modernization of the electrical grid, as they can be detached when bad things happen to the grid at large, such as the recent Texas outage, and still maintain service to their customers. A good place to start your research is with looking at the PEER rating system.

An easy alternative would be to build additional transmission lines for the grid. Good luck getting this past concerned citizens and many legislators. You would need to acquire new rights of way, conduct environmental studies, get construction permits, deal with all the protests, and finally build the facilities. It would take decades, certainly not within the eight-to-15-year period many states are mandating to become carbon-free. Of course, it can all be brought to fruition much more quickly by uttering the two magic words that cause property owners everywhere to absolutely lock up: eminent domain.

As for alternative power generation, there are two classes of solar farm as defined in current regulations: utility-scale and community-scale. The thinking is that lots of mom-and-pop farming operations will want to lease their land out to a commercial developer. The developers can then get Federal assistance for these community-scale projects. The landowners would receive maybe \$1,000 per acre per year for land that is covered with cells, (and much less for land without cells over it). Most developers will try not to have cost of living increases included in the lease, but will want to lock you down for 25 to 50 years.

Here’s the kicker. A community-scale site can only be 80 acres or less. With today’s technology, it takes 40 acres to generate five megawatts of electricity. And, your site must be within five miles of an access point to the grid, such as a substation or switch yard. The expected lifespan of the equipment is less than 25 years, and its efficiency degrades over time.

If the developer declares bankruptcy before the end of the lease, you’d then have acres of hazardous electronic waste to deal with. It would be an ecological trainwreck for the landowner. Clearly, this isn’t an easy solution. We know this, as my family has been approached about leasing land to a solar developer. We chose to stay friends with the animals and not have our forested property clear-cut and bulldozed.

Penn State University has a program that’s set up to study the industry. This podcast from the university is a good primer.

So, if we’re to solve the Earth’s woes, I’m praying for superconductors. That may seem overly optimistic, and I’m not holding my breath, but it seems more palatable than, say, a mass extinction event. I have faith in science and technology.

In the meantime, the concerned citizens of New York City have just enacted a law that states that, starting in 2023, new construction and gut-out remodels of seven stories or less must be 100 percent fueled by electricity. No more natural gas heat, hot water, or gas ranges. Their intent is to be carbon-neutral by 2050. The cost of rent is going up and the restaurant industry will be unhappy as gas delivers instantaneous heat, which chefs everywhere prefer.

There you have it.” I’ve been an engineer and nerd my whole life. I continue to live by the three laws of gas entropy:

1. You can’t win.
2. You can’t break even.
3. You can’t get out of the game.

Oh my, what a twisted fate those electrons hath wrought for me. I encourage you to, as Matt Damon repeatedly said in The Martian, “do the math,” and do your own research. The math doesn’t lie. J.J. Cale said the same of “Cocaine.” He was wrong. There are a lot of dead rock stars out there. Science and mathematics are the truth. Art (music) isn’t necessarily the truth, but it makes us whole. Consider your priorities and choose wisely.

After surviving a misguided youth, the author briefly dabbled in civil engineering and professional photography. Facing bankruptcy, he found his true calling as a software engineer. He spent the last 25 years of his career writing device drivers, firmware, protocol stacks, engineering specifications and documentation. After watching the evening news, he undergoes mandatory sensory deprivation therapy by going under the headphones for several albums.

Header image courtesy of Pixabay.com/analogicus.

### 8 comments on “Ohm’s Law”

1. Bob says:

Well, a very interesting article in a Hi Fi magazine. I joined Westinghouse Electric Corporation in 1975 and started my long career in Electric Power at the East Pittsburgh works (a gigantic factory that made large electrical generators, among other things), a facility that opened in the late 1800s. Tesla's ghost was most definitely present. Westinghouse was a leader in Nuclear Power and was promoting the breeder reactor, a concept where the spent fuel from a light water reactor (the type of plants we currently have in the US) is taken out and put back into the breeder, which "re-enriches" it so it can be used to produce more heat (steam). As the articles in your links discuss, the problem with this concept is that involves the transportation of bomb grade fuel. During the Carter administration, Jimmy basically killed a breeder economy due to concerns about this. Although a breeder cycle would solve much of the waste issue and open the door for a great source of carbon free electricity, he probably was right.

I think the game changer will be a major breakthrough in battery technology, which inevitably will come. This will allow utilities to store renewable energy on a large scale (it's already getting big) and will also make feasible on site photovoltaic generation and storage, like the battery in your car. Think of the day when you can park your car under a car port with solar panels in the roof and never visit a gas station again. This is why the oil companies are so against regulations against plastic bags...

1. lrj says:

Major breakthrough will come from nuclear fusion reactors. There’s been recent progress actually.
It will make battery powered EVs completely ridiculous. They are certainly not “green” today, and this will become obvious once we have other viable options.

1. Bob says:

I hope you're right about Fusion - it's been 30 years away my whole file (I'm 69) - however I don't get your comment about battery powered EVs. the Fusion power plant will generate electricity which will charge the EV batteries....unless the fusion power plant makes Hydrogen

Wind and solar are VERY inexpensive and low tech - they have a lot going for them

1. lrj says:

When we get to the point of commercializing fusion reactors, we won't be using them to generate electricity to then charge a battery. There is no point to a battery if you have essentially an infinite supply of energy in a compact form. Even if the reactor is not compact, I highly doubt we will be using it to charge today's batteries.

BTW, if anyone still thinks EVs are "green" - read this. You have to drive more than 100,000 km just to BREAK-EVEN with CO2 emissions from a gas car! And by that point, the battery will need to be replaced, restarting the process.
https://www.weforum.org/agenda/2017/11/battery-batteries-electric-cars-carbon-sustainable-power-energy/

2. JamesColthorp says:

I have a class D Amplifier with a 21 volt battery. The rail voltage after Diodes, two Transistors, Efficiency, and a DC safety circuit is about 17.6 volts. When I run my Amp and bump up the gain to this maximum peake-to-peake sign wave on the oscilloscope. The RMS Voltage out is this divided by the square root of two. 17.6÷1.414 = 12.44 volts RMS. Power out is (12.5×12.5)/4Ohm's, 35 Watts RMS. Now, when I increase the gain I begin to see Clipping on the top of sign wave. I continue increasing the gain and even see clipping on the input, until I reach saturation of the Transistors. This sign wave is now a little broader on the side's and flattened on the top. Because this is no longer a true sign wave, my RMS voltage is now about 14 volts. 14 Squared divided by 4 Ohms is 50 Watts RMS. Which is the rated power of the Amplifier with the now increase in distortion.

3. OldHardwareTech says:

I did a google search and couldn't find the disinformation alluded to under the 1st pic. Could you provide a link or two to point me in the right direction?

Thank You for an enjoyable and very relatable series of articles.

OHT

1. Jack Flory says:

Hi OHT,

Near the end of the year, there was a lot of press coverage of concerned citizens pushing back on grid modernization and alternative energy. Here are just a few of the many articles I saw. Some folks just don't like change, but the world is changing, and it will continue to do so.

I can see your wires now and I don't like it:

https://www.timescall.com/2021/11/24/xcel-may-have-to-redo-boulder-county-project-after-appeal/

I don't own the land, but you can't take away my view: