The U.S. consumes about 100 EJ = 100 Exajoules = 100 x 1018 Joules of energy, annually. Americans, being Americans don’t often express energy in Joules. Rather, they prefer to use British Thermal Units (BTUs), where 1 BTU = 1055 J. Another way of expressing this is to say that Americans use about 100 quads of energy, where 1 quad = 1015 BTUs. If one is willing to accept a 5.5% error, one can say that 1 EJ is about equal to 1 quad.

Only about one third of energy consumed is used for productive work. The above Sankey diagram shows energy inputs and outputs, productive work is clumped together as energy services, in a dark gray box. The other 2/3 is wasted as heat, which in the above diagram is referred to as rejected energy, which is clumped together in a light gray box.

Renewable energy comes from solar (1.04 quads), hydro (2.5 quads), winds (2.75 quads) and geothermal (0.21 quads) sources, for a total of 6.5 quads. Thermal energy systems burn fuel or split atoms, and accounted for about 93.5% of American energy inputs in 2019. Most of this fuel come from fossil sources, that is responsible for most of the carbon emissions associated with climate change. Wasted/ rejected energy is a proxy/ surrogate/ substitute for the damage being done to the planet. The exception is the energy provided by nuclear power, although it also has issues of its own. In contrast, renewable energy (wind, solar, hydro, geothermal) capture energy, without creating heat. While there are some transmission loses, most of that energy provides energy services.

A modern electric vehicle (EV) with regenerative braking is about 95% energy effective. Even the most efficient internal combustion engine (ICE) vehicles, can only achieve about 30% energy efficiency. This means that an EV only needs about 1/3 of the energy inputs that an ICE vehicle needs.

The United States transportation sector uses 28% of the total energy. Of this, cars, light trucks, and motorcycles use about 58%, while 23% is used in heavy duty trucks, 8% is for aircraft, 4% is for boats and ships, 3% is for trains and buses, while the last 4% is for pipelines (according to 2013 figures). This means that road transportation accounts for over 80% of the total. From the Sankey diagram, one can see that the transportation sector has 28.2 quads of input of (mostly) fossil-fuel energy, which means that 22.5 quads are road related. This results in 5.93 quads of transportation services, of which 4.75 quads are road related. These figures show about a 21% efficiency, because transportation related engines are considerably less efficient than other engines, including those used for electrical power generation.

If one uses renewable energy for road transportation, 4.75 quads of transportation services could be produced from about 5.0 quads of renewable (wind/ solar/ hydro/ geothermal) energy. At the same time, 22.5 quads of oil production would be eliminated, without any negative energy-related consequences. In fact, there would be benefits in terms of improved health, and less pressure on the environment.

A shift to renewable sources in other sectors would also have benefits. Natural gas and coal currently make a large contribution to inputs for electricity generation used elsewhere, 11.7 and 10.2 quads each, respectively, for a total of 21.9 quads. However, using the 1/3 service, 2/3 rejected formula, this means that these fossil-fuel inputs only produce 7.3 quads of electrical services. This contribution could be replaced by 7.5 quads of renewable energy.

Gasoline has an energy density of about 45 MJ/kg, which can provide about 15 MJ/kg of energy services, and 30 MJ/kg of rejected energy, as discussed above. A litre of gasoline has a mass of 0.76 kg and produces 2.356 kg of CO2 and 11.4 MJ of energy.

For American readers: The United States Energy Information Administration (EIA) estimates that “About 19.64 pounds of carbon dioxide (CO2) are produced from burning a gallon of gasoline that does not contain ethanol. About 22.38 pounds of CO2 are produced by burning a gallon of diesel fuel. U.S. gasoline and diesel fuel consumption for transportation in 2013 resulted in the emission of about 1 095 and 427 million metric tons of CO2 respectively, for a total of 1 522 million metric tons of CO2. This total was equivalent to 83% of total CO2 emissions by the U.S. transportation sector and 28% of total U.S. energy-related CO2 emissions.Under international agreement, CO2 from the combustion of biomass or biofuels are not included in national greenhouse gas emissions inventories.”

Since 1 MJ = 0.2778 Kilowatt hours (kWh), 11.4 MJ is the equivalent of 3.17 kWh. According to Electric Choice, the average price a residential customer in the United States pays for electricity is 13.31 cents per kWh in December 2020. This means that gasoline would have to sell for 42.19 cents per litre to be cost effective. Since there are 3.785 litres per American gallon, a gallon would have to sell for about $1.60 to provide an equivalent price. According to Global Petrol Prices, the average price of mid-grade/ 95-octane gasoline was $2.752 per gallon, the equivalent of $0.727 per litre, as of 2021-02-01.

In Norway, the price is about NOK 1 per kWh for electricity, but with wide variations. The price of 95-octane gasoline is about NOK 16.33 per litre, once again according to Global Petrol Prices. This helps explain why EVs are so popular. To be price equivalent, gasoline would have to sell for about NOK 3.17 per litre. Currently, Stortinget, the Norwegian parliament, is debating increasing the CO2 tax by NOK 5 per litre, which would bring the price to over NOK 21 per litre. Not all political parties are in agreement, with this proposal.

There is a great deal of discussion about consumption figures for electric vehicles in Norway. In part, this is because the terrain varies greatly. Some people drive in urban landscapes, others out in the country. Some people are flatlanders, while others have more mountainous environments. However many consumers have experienced real-world energy consumption levels of about 15 kWh/100 km for vehicles such as a Hyundai Kona, Kia Soul and Tesla Model 3. This gives a fuel cost of about NOK 15/ 100 km. In American terms, this would be about 24 kWh/ 100 miles, or $3.20/ 100 miles, with the electrical costs noted above.

Seeds: Electric Power

In a quest to find inventor heros, Nicola Tesla (1856 – 1943) is frequently attributed as the inventor of alternating current (AC). Unfortunately, the world is a messy place, and a long list of contributors to the development of AC needs to be acknowledged. In 1831, Michael Faraday (1791 – 1867) devised a machine that generated electricity from rotary motion. This was made into a machine by Hippolyte Pixii (1808 – 1835) in 1832.

Pixii’s AC generator (Illustration: F. Niethammer 1906  Ein- und Mehrphasen-Wechselstrom-Erzeuger)

“ZBD” (Károly Zipernowsky, Ottó Bláthy and Miksa Déri) invented a highly efficient transformer in 1885. Transformers are important because they allow different voltages to co-exist on a network. High-voltages reduce transmission losses when transferring energy over long distances. Low-voltages offer safer environments in domestic, commercial and industrial settings.

Tesla did play a role in AC development, but is usually remembered for the invention of an AC motor, rather than anything to do with transformers or generators. The challenge at the end of the 19th century and the beginning of the 20th, was to develop a safe, convenient electrical system that could be commoditized.

Perhaps one should go further back in time, with William Gilbert’s experiments on the relationship between static electricity and magnetism, recorded in De Magnete (1600). Benjamin Franklin, is famous for his kite in lightning experiment of 1752. Alessandro Volta is credited as the inventor of the first electrical battery, the Voltaic pile in 1799.  Even if one regards Faraday’s thought experiment as the starting point,  it took almost 50 years for the technology to reach a commercially viable stage. In 1878 the time was ripe. Joseph Swan, Thomas Edison and perhaps as many as fourteen others developed domestic light bulbs. which led to the first commercial power plant in 1881.

As AC systems rapidly expanded in the United States, at the expense of DC systems, a media war of the currents emerged in the late 1880s and early 1890s. Many see it as a propaganda campaign by the (DC oriented) Edison Electric Light Company to stifle commercial competition by raising electrical safety issues that put its rival, (AC oriented) Westinghouse Electric Company, in a bad light.

Unfortunately, one of the main challenges with DC, is its inability to transform to lower or (especially) higher voltages, which was needed for the economic transmission of power over long distances. DC power conversion is not a hurdle today, and HVDC (high-voltage, direct current) systems always includes at least one  rectifier (converting AC to DC) and one inverter (converting DC to AC). HVDC systems can be less expensive to construct, and offer lower electrical losses compared to equivalent AC systems. HVDC is especially allows transmission between unsynchronized AC transmission systems. ABB entered into a contract in China in 2016 to construct an ultra-high-voltage direct-current (UHVDC) line featuring 1.1 MV voltage,  3,000 km transmission length and 12 GW of power, which, when completed, would set world records for highest voltage, longest distance and largest transmission capacity.

There is a lot of uncertainty about reason having any role in the selection of an AC frequency.  Since the main purpose of electricity was to provide lighting, the only consideration was to prevent flicker. Thus, a multitude of frequencies emerged, in the period 1880 through 1900. Single-phase AC was common and typical generators were 8-pole machines operating at 2000 RPM, a common frequency was 133 Hz.

At the other extreme 16.7 Hz is used in AC railway electrification system in Germany, Austria, Switzerland, Sweden and Norway. The low frequency was chosen to reduce energy losses from early 20th century traction motors. The  high voltage (15 kV) enables high power transmission. The preferred standard frequency for new railway electrifications is 50 Hz with an evening higher voltage (25 kV). Yet, extensions to existing networks, often use 15 kV, 16.7 Hz electrification. High conversion costs mean that older systems keep their voltage and frequency, despite potential on-board step-down transformer weight reductions to one third that used on the older system.

Preferred Numbers

In 1877, Charles Renard proposed a set of preferred numbers, later adopted  as international standard ISO 3 in 1952. This system divides the interval from 1 to 10 into 5, 10, 20, or 40 steps, leading to the R5, R10, R20 and R40 scales, respectively. For some, the R5 series provides a too fine graduation. Often a 1, 2, 5 series is used, a R3 series rounded to one significant digit, a pseudo preferred number.

Myth has it, that when AEG built their European generating facility, its engineers decided to fix the frequency at 50 Hz, because the number 60 wasn’t a “R3” preferred number. This standard spread to the rest of the continent, including Britain after World War II.

Lower frequencies have a number of negative characteristics. Not only is 50 Hz 20% less effective in generation, it is 10-15% less efficient in transmission, and requires up to 30% larger windings and magnetic core materials in transformer construction. Electric motors are much less efficient at the lower frequency, and must also be made more robust to handle the electrical losses and the extra heat generated. But there are advantages too, such as lower impedance losses.

Yet, there are enlightened countries with the insight to follow Tesla’s advice and use the 60 Hz frequency together with a voltage of 220-240 V: Antigua, Guyana, the Leeward Islands, Peru, the Philippines and South Korea.

Originally Europe was 110 V too, just like Japan and North America today. Voltages increased to get more power with less voltage drop (power loss) from the same copper wire diameter. At the time the US also wanted to change but because of the cost involved to replace all electric appliances, they decided not to. At the time (50s-60s) the average US household already had a fridge, a washing-machine, etc., but this was not the situation in Europe.

The end result is that now, the US seems static. It appears to be the same now as it was in the 1950s and 1960s. It still has to cope with transformer related problems, such as light bulbs that burn out rather quickly when they are close to the transformer (too high a voltage), or too far away, with insufficient voltage at the end of the line (105 to 127 volt spread !).

Most new North American buildings provides a 240 volt residential service in the form of two 120 volt conductors and a neutral conductor. When a load is applied from either 120 volt conductor to the neutral it uses 120 volts. When a load is applied from one 120 volt conductor to the other, without using the neutral, 240 volts is used, which is useful for air conditioners, clothes dryers, electric furnaces, stoves, water heaters and others high power appliances.

There is some confusion about North American voltages. It is 120 V, not 110 V. This was increased starting in the 1950s. The historic reason for 110 V was due to Thomas Edison’s DC power systems, which probably used 110 V because that was the optimal voltage for his light bulbs. These systems converted to AC, but the voltage wasn’t changed so existing lighting didn’t need to be replaced.

North Americans could get a better system than Europeans, with no infrastructure changes, except inside buildings. Since houses get 240 V delivered, wall outlets could be supplied this too, offering the lower current and higher power advantage of the European system.

In terms of safety, current (amperes) kills, not electrical potential (volts). Even so, 240 V is regarded as more dangerous than a 120 V system. To compensate Europeans use high quality insulation and wiring methods, that include Ground Fault Current Interruptor (GFCI) or Residual Current Device (RCD) in the breaker box to cut the supply instantaneously if any significant difference is detected between the currents flowing in the live (hot) and neutral wires. This saves lives.

Ethan & Ethel 03: Electrical Power

Some things in life are just so important that they just have to be learned. Memorization can be the right approach for some. For others, it might mean keeping a piece of paper handy, with formulas written out. Regardless, Ohm’s law and related formulas have to be learned.

Fortunately, a cool soldering iron will help explain Ohm’s law, and the related formulas. The soldering iron is a Miniware TS100.

A Miniware TS 100 Soldering iron shows a warning when it is too hot compared to a preset maximum temperature. (photo: Miniware)

Ethan has saved up his money to buy a TS 100 soldering iron. Unfortunately, he didn’t have enough money to buy a new power supply, so he wants to know if he can use this one, which he has lying around:

A power supply with 12 V and 2 A output values. Is it good enough to power a TS 100 soldering iron?

This gives him an opportunity to learn about electricity and how it works. A plumbing analogy is often used to explain electric power. Think of voltage, the pressure driving electricity through a wire, as water pressure forcing water through a pipe. The cross-section area of a pipe is like current, or amperage. The bigger the pipe, the more water that can be pressed through. The diameter of the electrical wires determines how much current is allowed through the system. If more current is pressed through than the wires are designed for, a device could fry.

The problem.

The TS 100 instruction sheet says that a maximum of 65 W can be obtained with a 24 V power supply. It also says that the minimum requirement is 17 W with a 12 V power supply. The power supply itself confirms that it provides 12 V output. But it doesn’t mention amperage, only wattage. The easiest way to find out if a correct amperage is being supplied is to use a power triangle. This is what it looks like, in three almost identical versions:

The power triangle allows Ethan to find an unknown value, when two values are known. In this thought experiment we know the power (P=17 W) and the voltage (V=12 V) but not the amperage (I). (illustration: http://www.electronics-tutorials.ws)

Ethan uses the middle power triangle, because he knows the power (17 watts) and the voltage (12 volts) but is missing the current or amperage, abbreviated as I. So he takes out his cell phone, uses the calculator app and inputs the necessary numbers, as shown here: I = 17 / 12 = 1.41 A. Since 1.41 A is less than 2 A, Ethan can use the power supply he already has.

A soldering iron works by using a resistor to heat up a metal tip. The relationship between the Voltage, Current and Resistance forms the basis of Ohm’s Law, which can be shown as another triangle, the Ohm’s Law triangle, also in three version, below:

The Ohm’s triangle shows relationships between I = current, measured in A = amperes or amps, V previously E = voltage, measured in volts. R = resistance, measured in Ω (ohms).

Using the third triangle, the resistance is found using the following formula: R = V /A = 12 / 1.41 = 8.5 Ω.

Starting off only knowing two values, Ethan ends up knowing four. These relationships are summarized in the Ohm’s law pie chart:

The Ohm’s law pie shows all of the twelve calculations that can be made. If you know two values, then you will only need to use two formulas to calculate the missing two values. The secret is knowing which two.

These relationships are explained even better in an Ohm’s law matrix. If any two values are know, the relevant row can be found by looking at the leftmost column. That row will show the two formulas that are needed to calculate the missing values.

ohm matrix

Electricity comes into houses in the form of alternating current (AC). This is because AC can be easily transformed into lower or higher voltages as required. Most workshop equipment uses standard household voltage. In North America, this is 120 V. In Europe, it is 220 (or 230 or 240) V. The other big difference is that North America supplies electricity at 60 Hz, while in Europe it is 50 Hz.

These differences used to create lots of problems, but if you look at the power supply shown above, you will see that it can use any input from 100 V to 240 V. There is also no problem using 50 Hz or 60 Hz. This means that the same power supply can be used anywhere in the world. The only thing needed is a plug adapter.

adapter US to EU
An adapter is useful when travelling from one part of the world to another. This adapter allows North American devices, for example a power supply, to be plugged into European wall sockets.

Not everything works this well. Clocks are notoriously bad, because many tell time based on the frequency of the network. A European clock brought to North America, may show 28.8 hours in the course of a day. A North American clock brought to Europe, may show only 20 hours in the course of the same day.

The biggest difference between North America and Europe is in the wiring that is required to run equipment. That is because current or amperage (and not power or wattage) determines the thickness of wires used. A 2 000 W mitre saw on a 120 V system needs a 20 A circuit breaker and #10 wire which is 5.26 mm² (in Europe, it has just exceeded the 16 A wiring limit, 2.5 mm²). On a 240 V system this same mitre saw only needs a 10 A circuit breaker and #14 wire which is 2.08 mm² ( In Europe, one could actually get away with 1.5 mm²).

Workshops need a lot of electrical power because they use machines that are transforming material into useful products. The work being done requires energy. That is not the only use of energy. Heating and dust extraction are also major energy consumers.

The Cost of Heating

Ethel and Ethan have a problem. They find the work space soooo cold that they have installed a 1500 W heater. The twins turn on the heat one hour before they begin working, and turn it off half an hour before they plan to stop. So far this month, they have had the heater on 46 hours.

A workshop needs energy to do work or create heat. Work is officially measured in joules ( J ). One joule is the same as one watt-second. If one knows how many watts one is using, and how many seconds it is being used, it is easy to calculate the number of joules.

Work = 1500 W · 46 hours · 60 min/hour · 60 sec/min = 248 400 000 J or 248.4 MJ (mega-joules). When calculating joules, it can be useful to know that there are 3 600 seconds in one hour, and 86 400 seconds in one day (24 hours).

When it comes to buying electricity, the kilowatt-hour is the standard units of energy recorded by the electricity meter. This can be a lot easier to calculate: 1 500 W, is the same as 1.5 kW; 46 hours is the same as, well, 46 hours. The heater’s electrical consumption is 1.5 kW · 46 h = 69 kWh. The price of 1 kWh varies, but in some places is about 15 cents.  So the cost of heating the work space for a month is 69 kWh · $0.15 = $10.35.

Bonus Questions. Since the twins live in Canada, they have 120 V electrical power in their workshop. Calculate: What is the Amperage required for a 1500 W heater? What is the resistance inside the heater? (answers: 12.5 A;  9.6 Ω)

Power Requirements

Here are the wattages I use in the Unit One workshop. If all of the machines and other equipment were all turned on, they would use over 19 kW. Fortunately, that has never happened.

Use Wattage

100 W


100 W


750 W

Workshop air cleaner

200 W

Dust extractor

1 100 W


 2 000 W

Stationary machines

1 250 W


1 500 W

Compound mitre saw

2 000 W

Table saw

1 400 W

Band saw

750 W

Drill press

500 W


500 W

Bench grinder

400 W

Portable tools
HVLP spray gun  600 W
Jig saw

800 W

Bayonet saw

1 000 W

Plunge (Track) saw

1 400 W


1 400 W

Power drill

500 W

Angle grinder

800 W



Because only one (perhaps two) power tools are being used at any one time, the workshop’s maximum load is 6 250 W. The worst tool to use is the compound mitre saw (2 000 W). In addition, there is a need for lighting (100 W), computing (100 W), workshop air cleaner (200 W), dust extractor (1 100 W). At times a compressor is in use (750 W), and in winter, a heater may be turned on (2 000 W).

Three-phase power is supplied to the workshop at 230 V and 16 A with three load lines (L1, L2 and L3) coming in. These load lines are paired up to make 3 single-phase circuits. The total power coming into the workshop is 6370 Watts.


Several illustrations for this blog post have been borrowed from: http://www.electronics-tutorials.ws, which is the place to go for electronics tutorials.

Electrical Installation: A prerequisite to Technical Innovation?

Norway has become a consumer society. In the first few decades after the second world war, house purchasers were encouraged to put physical labour into house construction. This reduced the total price of a house. Today, this is not happening. People are simply consumers of houses, and have little understanding of how they are actually made.

In this post, I want to look at the consequences of this consumerism, but focus on just one area, electrical installation.

Everywhere electrical material is sold in Norway, one is met with the following or similar warning, in Norwegian:

Although installation materials, such as heating cables, can be purchased by anyone, only registered companies can install the equipment. Stores are required to inform the buyer about this before the purchase is made. It is also not possible to install the equipment yourself, then ask an authorized installer to connect it to the facility in the house. That is a breach of regulations. In addition, there are no serious companies that will take responsibility for a work they do not control.” (from Jula.no)

For many people from other parts of the world, this warning is an affront. Where are the electrical inspectors? Registered electricians are given carte blanche to install electrical materials, but their work remains unsupervised by public officials representing other stakeholders, including house owners. Some electrical inspectors do exist, but they are not public employees. Frequently, they are employees of a major producer of electricity, and they only visit a house every twenty years or so, to ensure that it is in conformity with regulations. When they do come, they have a vested interest in finding mistakes, because they can require a house owner to hire a registered electrician to make changes.

Contrast this with the situation in Canada. Here is a typical sign at a store:

Sign at Home Hardware, Essex, Ontario (photo: Brock McLellan)

There is no discussion as to who is will do the work. In essence, anyone can do it. The requirement is that all work done, has to be inspected. This treats professional electricians and talented amateurs as equals, which in many cases they are. Without inspections, electricians can be tempted to take shortcuts or do shoddy work.

Inside the Home Hardware store, in Essex, Ontario, there is a display that shows precisely how to wire specific items in a house, including the breaker box:

Electrical wiring display, Home Hardware, Essex, Ontario (photo: Brock McLellan)

Amateurs in Canada are able to take night school courses in electricity. Here is a description of a night school course, open to anyone, at Saint Clair College, in Windsor, Ontario:

“Electricity 200 is for non-electrical tradespersons and related. Emphasis is placed on safety practices. Electrical protection of motors. Basic test equipment, purpose and testing of fuses, overloads and circuit breakers. Basic relationship of voltage, current and resistance. Basic relays and A.C. 3 phase motor control, interpreting basic motor nameplate information. Introductory residential wiring. Introductory diodes and rectifiers.”

The course lasts 12 weeks, one night a week, for three hours, from 19.00 to 22.00.

One of the resources used by many Canadian home owners is: Ray Mullin, Tony Branch, Sandy Gerolimon, Craig Trineer, Bill Todd and Phil Simmons  2015 Electrical Wiring Residential, 7th Canadian edition.


Electrical Wiring Residential E7 Can

Despite having an electrical code that requires the use of professional electricians, Norway has a much higher rate of house fires caused by a failure in the electrical system, than many other countries, including Canada. This is to be expected. Without training and experience, a house owner is unable to understand where electrical problems can arise. Because of the high cost of using professionals, potential problems may be ignored, which puts lives in danger.

As a former teacher of Entrepreneurship, there is one other reason to encourage people to do their own home wiring. Consumers are not good at understanding how products work. With a society of consumers, there will be nobody working in basements and garages to develop new products. Garage culture made America great. Amazon, Apple, Disney, Google, Harley Davidson, Hewlett-Packard, Lotus Cars, Maglite, Mattel and even Microsoft all started in garages. http://www.businesspundit.com/11-famous-garage-startups-that-rule-the-world/

Walt Disney was living at 4651 Kingswell Ave. in Los Angeles, California, when he started his company in a garage owned by his uncle, Robert Disney.

There is a trend in government to encourage coding, but most of the developments in the “Internet of Things” or robotics involve physical computing, a combination of electrical circuits, mechanical components including sensors and actuators as well as code.

It is possible for people to innovate without insight into residential wiring, but being able to wire will provide insights that will help a person to be more innovative.