2.2 SI units and unit conversions

SI Units and Base/Derived Units

SI units are the standardized measurement system used across all of science and engineering. Every calculation you do in electrical engineering depends on these units being consistent, so getting comfortable with them now saves you a lot of headaches later.

International System of Units and Base Units

The SI system is built on seven base units. These are considered fundamental because they can't be broken down into simpler units:

For electrical engineering, the ones you'll use constantly are the meter, kilogram, second, and ampere. Every other unit in the SI system is built from combinations of these seven through multiplication or division.

Derived Units and Scientific Notation

Derived units are what you get when you combine base units to describe more complex quantities. In EE, these four show up everywhere:

• Volt (V) — electric potential difference: $1 \text{ V} = 1 \text{ kg} \cdot \text{m}^2 \cdot \text{s}^{-3} \cdot \text{A}^{-1}$
• Watt (W) — power: $1 \text{ W} = 1 \text{ kg} \cdot \text{m}^2 \cdot \text{s}^{-3}$
• Ohm (Ω) — resistance: $1 \text{ Ω} = 1 \text{ V/A}$
• Joule (J) — energy: $1 \text{ J} = 1 \text{ kg} \cdot \text{m}^2 \cdot \text{s}^{-2}$

These all have special names so you don't have to write out the full base-unit expression every time.

Scientific notation expresses numbers as a value between 1 and 10 multiplied by a power of 10. For example, the charge of an electron is $1.6 \times 10^{-19}$ coulombs. Writing that out as 0.00000000000000000016 C would be impractical, so scientific notation keeps things readable and reduces errors.

Unit Prefixes and Conversions

Prefixes for Multiples and Submultiples

SI prefixes let you scale units up or down so you're working with manageable numbers. In electrical engineering, you'll encounter a wide range of magnitudes, from gigahertz frequencies down to picofarad capacitances.

Here are the prefixes you need to know:

Unit Conversion Factors and Dimensional Analysis

A conversion factor is a ratio that equals 1, expressed in two different units. For example, $\frac{1000 \text{ m}}{1 \text{ km}} = 1$. You can multiply any quantity by a conversion factor without changing its value, only its units.

Dimensional analysis is the method of chaining conversion factors together to get from one unit to another. Here's the process:

1. Write down the quantity you're starting with, including its units.
2. Identify the conversion factor(s) you need. Arrange each one so the unit you want to cancel is in the denominator.
3. Multiply through, canceling units as you go.
4. Check that your final answer has the correct units.

Example: Convert 4.7 kΩ to ohms.

$4.7 \text{ k}\Omega \times \frac{1000 \text{ }\Omega}{1 \text{ k}\Omega} = 4700 \text{ }\Omega$

Example: Convert 250 μA to milliamps.

$250 \text{ }\mu\text{A} \times \frac{1 \text{ mA}}{1000 \text{ }\mu\text{A}} = 0.25 \text{ mA}$

A quick shortcut for prefix-to-prefix conversions: count the difference in powers of ten between the two prefixes. Going from micro ($10^{-6}$) to milli ($10^{-3}$) is a difference of $10^3$, so you divide by 1000. This becomes second nature with practice, but dimensional analysis is always there as a safety net to verify your answer.