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Block 01 — Physical quantities and SI system

Learning objectives

90-minute plan

1. Warm-up (10 min):
   1. “What is the unit of conductivity? of energy?”
2. Quick prefix quiz; everyday magnitude estimates ($\rm mA$, $\rm k\Omega$, $\rm \mu F$).
3. Core concepts & derivations (60 min):
   1. SI base set → derived units; prefix rules;
4. quantity vs. normalized equations;
5. dimensional checks.
   1. Prefix ladder ($\rm E$…$\rm a$) and best-practice rounding/checks.
   2. Symbols & Greek letters in EEE1; time-varying vs constant symbols.
6. Practice (15 min): Fast conversions and unit checks (individual → pair).
7. Wrap-up (5 min): Summary table; common pitfalls checklist.

Conceptual overview

SI base quantities and units

• For practical applications of physical laws of nature, physical quantities are put into mathematical relationships.
• There are basic quantities based on the SI system of units (French for Système International d'Unités), see below.
• In order to determine the basic quantities quantitatively (quantum = Latin for how big), physical units are defined, e.g. ${\rm metre}$ for length.
• In electrical engineering, the first three basic quantities (cf. Tabelle 1 ) are particularly important.
  Mass is important for the representation of energy and power.

• Each physical quantity is indicated by a product of numerical value and unit:
  e.g. $I = 2~{\rm A}$
  • This is the short form of $I = 2\cdot 1~{\rm A}$
  • $I$ is the physical quantity, here: electric current strength
  • $\{I\} = 2 $ is the numerical value
  • $ [I] = 1~{\rm A}$ is the (measurement) unit, here: ${\rm Ampere}$

Common derived quantities

• Besides the basic quantities, there are also quantities derived from them, e.g. $[F] = [m]\cdot [a] \rightarrow 1~{\rm N} = 1 ~{\rm kg} \cdot {{1 ~{\rm m}}\over{1 ~{\rm s}^2}}$.
• SI units should be preferred for calculations. These can be derived from the basic quantities without a numerical factor.
  example:
  • The pressure unit bar (${\rm bar}$) is an SI unit.
  • BUT: The obsolete pressure unit „Standard atmosphere“ ($=1.013~{\rm bar}$) is not an SI unit.
• To prevent the numerical value from becoming too large or too small, it is possible to replace a decimal factor with a prefix. These are listed in Tabelle ##.

We will see, that a lot of electrical quantities are derived quantities.

Prefixes

• Use prefixes to keep magnitudes practical (see Tabelle 2 and Tabelle 3).
• Instead of writing zeroes for like in $0.000000004 ~\rm C $ is is easier to write $4 \rm ~nC $.
• For calculation it is often easier to write $4 ~\rm nC = 4 \cdot 10^{-9} ~C$ or the notation \rm 4e-9 C

Physical equations

• Physical equations allow a connection of physical quantities.
• There are two types of physical equations to distinguish:
  • Quantity equations (in German: Größengleichungen )
  • Normalized quantity equations (also called related quantity equations, in German normierte Größengleichungen)

Letters for physical quantities

Latin/Greek letters are reused across physics.

In physics and electrical engineering, the letters for physical quantities are often close to the English term.

Thus explains $C$ for Capacity, $Q$ for Quantity and $\varepsilon_0$ for the Electical Field Constant. But, maybe you already know that $C$ is used for the thermal capacity as well as for the electrical capacity. The Latin alphabet does not have enough letters to avoid conflicts for the scope of physics. For this reason, Greek letters are used for various physical quantities (see Tabelle 4).

Especially in electrical engineering, upper/lower case letters are used to distinguish between

• a constant (time-independent) quantity,
  e.g. the period $T$
• or a time-dependent quantity,
  e.g. the instantaneous voltage $u(t)$
• EE relies on case and context (e.g., $U$ vs. $u(t)$). Time-varying quantities often use lowercase, constants uppercase.

Common pitfalls & misconceptions

• Case matters: $\rm M$ (mega, $10^6$) vs. $\rm m$ (milli, $10^{-3}$);
• Micro symbol: use $\rm \mu$ (or u only when typing constraints exist);
• usage of prefixes never stack prefixes (no “$\rm mµF$”).
• Mixed units: keep SI consistently; avoid mixing $\rm hours$/$\rm Wh$ inside SI derivations.
• Units vs. variables: don’t confuse $W$ (work) with $\rm W$ (Watt = unit of power $\rm P$ = work per second).
  Don’t confuse $C$ (capacity = charge per voltage) with $\rm C$ (Coulomb = unit of charge $\rm Q$).
• Units vs. prefixes: don’t confuse $\rm mN$ (Millinewton) with $\rm Nm$ (Newton meter).
• Normalized vs. quantity equations: dimensionless ratios should cancel units; if not, something’s wrong.

Exercises

Worked example(s)

Quick checks

Embedded resources

Mini-assignment / homework (optional)

List 10 everyday EE-relevant quantities (e.g., USB current, phone battery energy, LED forward voltage). For each:

• write as value × unit with an appropriate prefix,
• convert to base SI units, and
• if a formula applies (e.g., $P=U\cdot I$), do a unit check.