The electrical field, its history, and units of measurement

A field that touches everything

Electrical engineers design the generators and lines of the power grid, the motors in factories and cars, the radios and fibre links of communication networks, the sensors and control loops of robots, and the integrated circuits inside every computer. The quantities span an astonishing range: a medical sensor may pass a few nanoamperes, while a transmission line carries over a thousand amperes at hundreds of thousands of volts. Working across that range needs shared units, compact notation for very large and very small numbers, and honest rounding.

From amber to the battery

Ancient Greeks noticed that rubbed amber attracts light objects; their word for amber, elektron, gives us "electricity". In 1600 the English physician William Gilbert published De Magnete, separating electric attraction from magnetism and coining the Latin word electricus. Benjamin Franklin's kite experiment of about 1752 linked lightning to electricity. In the 1780s Charles-Augustin de Coulomb measured the force between charges with a torsion balance. Luigi Galvani's experiments with frog legs, published in 1791, prompted Alessandro Volta to build the voltaic pile in about 1800, the first source of steady current.

Electricity meets magnetism

In 1820 the Danish physicist Hans Christian Ørsted saw a current deflect a compass needle, and André-Marie Ampère soon described the forces between currents. Georg Ohm published his law relating voltage and current in 1827. In 1831 Michael Faraday showed that a changing magnetic field induces a voltage, the principle behind every generator and transformer; Joseph Henry found the same effect independently at about the same time. James Clerk Maxwell unified these results in equations published in the 1860s and 1870s, predicting electromagnetic waves, and Heinrich Hertz produced and detected radio waves in the late 1880s.

Power, electronics and computing

Thomas Edison's Pearl Street station in New York began supplying dc power in 1882. Alternating current, championed by Nikola Tesla and George Westinghouse, won out for long-distance supply because transformers can step its voltage up and down; the Niagara Falls plant of the mid-1890s was a landmark. Electronics began with John Ambrose Fleming's vacuum diode in 1904 and Lee de Forest's triode in about 1906. At Bell Labs in 1947, John Bardeen and Walter Brattain, working in William Shockley's group, built the first transistor. Jack Kilby (1958) and Robert Noyce (1959) independently created the integrated circuit, and Intel's 4004 microprocessor followed in 1971.

Systems of units

The English (US customary) system measures length in feet and power in horsepower; the older metric MKS and CGS systems were built on the metre, kilogram and second or the centimetre, gram and second. The International System, SI, is now the engineering standard and is used throughout this course. Its base units include the metre (m), kilogram (kg), second (s), ampere (A) and kelvin (K). Since 2019 SI has been defined by fixing exact values of natural constants; the elementary charge, for example, is exactly \(1.602176634 \times 10^{-19}\) C. Derived units are built from base units: the coulomb is an ampere-second and the volt is a joule per coulomb.

Powers of ten and prefixes

Scientific notation writes a number as a value between 1 and 10 times a power of ten: 47,000 is \(4.7 \times 10^{4}\). Engineering notation instead keeps the exponent a multiple of 3, so the same number is \(47 \times 10^{3}\), which matches an SI prefix:

So 47,000 Ω is 47 kΩ. The rules for arithmetic are short: multiplying powers of ten adds the exponents, dividing subtracts them, and adding or subtracting requires the same exponent first.

Worked example: engineering notation

Write each value with a suitable prefix, then evaluate a product and a quotient. 1. A sensor current of 0.00068 A: move the decimal point to get \(680 \times 10^{-6}\) A, so 680 µA. 2. A resistance of 2,200,000 Ω is \(2.2 \times 10^{6}\) Ω, so 2.2 MΩ. 3. A time of 0.015 s is \(15 \times 10^{-3}\) s, so 15 ms. 4. Product: \((4 \times 10^{3})(5 \times 10^{-6}) = 20 \times 10^{-3} = 0.02\), adding the exponents 3 and \(-6\). 5. Quotient: \(\frac{8 \times 10^{-3}}{4 \times 10^{-7}} = 2 \times 10^{4}\), because \(-3 - (-7) = 4\). Check each answer by size: 680 µA is a little under 1 mA, as 0.00068 A should be.

Significant figures and rounding

A calculated answer cannot be more precise than its data. When multiplying or dividing, keep as many significant figures as the least precise factor: \(4.7 \times 2.15 = 10.105\), which rounds to 10 because 4.7 has only two. When adding or subtracting, keep the decimal place of the least precise term: \(12.6 + 0.25 = 12.85\), reported as 12.9. Round up when the first dropped digit is 5 or more, and round only at the end. This course reports three significant figures unless more matter. Accuracy, closeness to the true value, differs from precision, how finely a value is stated.

Worked example: converting between systems

A motor nameplate reads 0.75 hp, its cable run is 250 ft, and the room is at 77 °F. Express all three in SI. 1. Power: 1 hp is about 745.7 W, so \(0.75 \times 745.7 = 559\) W, or about 560 W to the two figures of 0.75. 2. Length: 1 ft is exactly 0.3048 m, so \(250 \times 0.3048 = 76.2\) m. 3. Temperature in Celsius: \(T_C = \frac{5}{9}(T_F - 32) = \frac{5}{9}(45) = 25\) °C. 4. Temperature in kelvin: \(25 + 273.15 = 298.15\) K. 5. Check: each factor is written so the old unit cancels, as in \(250\,\text{ft} \times \frac{0.3048\,\text{m}}{1\,\text{ft}}\), and 76.2 m is roughly a third of 250.

Symbols, calculators and software

A quantity symbol is written in italics and a unit in upright type: \(V = 12\,\text{V}\) means the voltage \(V\) is 12 volts. Symbols such as \(\approx\) (approximately equal) and \(\propto\) (proportional to) appear constantly. On a calculator, enter powers of ten with the EXP or EE key, so \(6.8 \times 10^{3}\) is typed as 6.8 EE 3, and use brackets to force the order of operations; an engineering display mode shows exponents in multiples of 3. Circuit simulators of the SPICE family, such as the free, open-source ngspice, and languages such as Python are useful for checking hand calculations.

Common mistakes to avoid

First, confusing m (milli, \(10^{-3}\)) with M (mega, \(10^{6}\)): a 1 mΩ resistance and a 1 MΩ resistance differ by a factor of a billion. Second, adding values with different powers of ten without first matching the exponents. Third, keeping every calculator digit: an answer of 10.105 from data with two significant figures claims a precision you do not have. Fourth, rounding at each intermediate step, which lets errors build up. Fifth, writing a conversion factor upside down; always check that the unwanted unit cancels. Sixth, quoting a temperature in °C where an absolute temperature in kelvin is needed.

Key takeaways

The field grew through Volta's pile (about 1800), Ørsted (1820), Ohm (1827), Faraday (1831) and Maxwell to dc and ac power in the 1880s and 1890s, then the vacuum tube (1904), transistor (1947), integrated circuit (1958-1959) and microprocessor (1971). SI, defined since 2019 by fixed constants, is the standard. Engineering notation keeps exponents in multiples of 3, matching the prefixes p, n, µ, m, k, M and G. Multiply powers of ten by adding exponents. Round to the least precise data, only at the end, and make every unwanted unit cancel.

Question 1 of 5

Which value is equal to 0.0039 A?

Question 2 of 5

What is (6 × 10⁴)(3 × 10⁻⁶)?

Question 3 of 5

A length is measured as 4.7 m and a factor as 2.15. How should their product, 10.105, be reported?

Question 4 of 5

Who first showed, in 1820, that an electric current deflects a compass needle?

Question 5 of 5

A pump motor is rated 1.5 hp. Using 1 hp ≈ 745.7 W, what is its rating in SI units?