Block 01 — Physical Quantities and SI System

1.0 Intro

1.0.1 Learning Objectives

After this 90-minute block, you can

Use the SI base quantities, units, and symbols correctly; convert between units with prefixes.
Distinguish base vs. derived quantities; express key EE units (e.g. $\rm V$, $\rm \Omega$) in SI base units.
Apply quantity equations and perform unit (dimensional) checks; contrast with normalized (dimensionless) equations.
Read and use common Latin/Greek letter symbols; distinguish uppercase/lowercase and instantaneous vs. constant quantities.

1.0.2 90-minute plan

Warm-up (10 min):
1. “What is the unit of conductivity? of energy?”
Quick prefix quiz; everyday magnitude estimates ($\rm mA$, $\rm k\Omega$, $\rm \mu F$).
Core concepts & derivations (60 min):
1. SI base set → derived units; prefix rules;
quantity vs. normalized equations;
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.
Practice (15 min): Fast conversions and unit checks (individual → pair).
Wrap-up (5 min): Summary table; common pitfalls checklist.

1.0.3 Conceptual overview

Units are the grammar of engineering and physics.
The SI defines seven base quantities and units; all other (derived) units are built from these without extra numerical factors. The SI defines seven base quantities and units.
In EEE1 we work strictly in the SI system, combining numerical value × unit and tracking dimensions at every step (e.g., $I=2~\rm A$ means “two times one ampere”).
Derived units (e.g., $\rm V$, $\rm \Omega$, $\rm S$) must reduce to base units without hidden factors.
Prefixes scale units by powers of ten to keep numbers readable. Prefixes compress very large and very small numbers so we can compute and compare safely.
Quantity equations keep units; normalized equations cancel units to yield dimensionless ratios (e.g., efficiency).
In EE, symbol choices and letter case matter: $U$ vs. $u(t)$, $\rm M$ (mega) vs. $\rm m$ (milli). We adopt a consistent symbol set (Latin + Greek), and distinguish constants (capital letters) from time functions (lowercase, e.g., $u(t)$).
Finally, we preview the three anchor quantities for the next blocks: charge (what moves), current (how fast charge moves), and voltage (energy per charge). Physics describes quantities with a numerical value × unit (e.g., $I=2~\rm{A}$).

1.1 Core Content

1.1.1 SI Base Quantities and Units

Base quantity	Name	Unit	Definition
Time	Second	${\rm s}$	Oscillation of $Cs$-Atom
Length	Meter	${\rm m}$	by s und speed of light
el. Current	Ampere	${\rm A}$	by s and elementary charge
Mass	Kilogram	${\rm kg}$	still by kg prototype
Temperature	Kelvin	${\rm K}$	by triple point of water
amount of substance	Mol	${\rm mol}$	via number of $^{12}C$ nuclides
luminous intensity	Candela	${\rm cd}$	via given radiant intensity

Tab. 1: SI base quantities (SI)

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. table 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: ${\rm Ampere}$

1.1.2 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.

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

1.1.3 Prefixes

prefix	prefix symbol	meaning
Yotta	${\rm Y}$	$10^{24}$
Zetta	${\rm Z}$	$10^{21}$
Exa	${\rm E}$	$10^{18}$
Peta	${\rm P}$	$10^{15}$
Tera	${\rm T}$	$10^{12}$
Giga	${\rm G}$	$10^{9}$
Mega	${\rm M}$	$10^{6}$
Kilo	${\rm k}$	$10^{3}$
Hecto	${\rm h}$	$10^{2}$
Deka	${\rm de}$	$10^{1}$

Tab. 2: Prefixes I

prefix	prefix symbol	meaning
Deci	${\rm d}$	$10^{-1}$
Centi	${\rm c}$	$10^{-2}$
Milli	${\rm m}$	$10^{-3}$
Micro	${\rm u}$, $µ$	$10^{-6}$
Nano	${\rm n}$	$10^{-9}$
Piko	${\rm p}$	$10^{-12}$
Femto	${\rm f}$	$10^{-15}$
Atto	${\rm a}$	$10^{-18}$
Zeppto	${\rm z}$	$10^{-21}$
Yocto	${\rm y}$	$10^{-24}$

Tab. 3: Prefixes II

Use prefixes to keep magnitudes practical (see table 2 and table 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 $\rm 4e-9 ~C$

1.1.4 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)

1.1.5 Quantity Equations

The vast majority of physical equations result in a physical unit that does not equal $1$.

Example: Force $F = m \cdot a$ with $[{\rm F}] = 1~\rm kg \cdot {{{\rm m}}\over{{\rm s}^2}}$

A unit check should always be performed for quantity equations
Quantity equations should generally be preferred

1.1.6 Normalized Quantity Equations

In normalized quantity equations, the measured value or calculated value of a quantity equation is divided by a reference value. This results in a dimensionless quantity relative to the reference value.

Example: The efficiency $\eta = {{P_{\rm O}}\over{P_{\rm I}}}$ is given as quotient between the outgoing power $P_{\rm O}$ and the incoming power $P_{\rm I}$.

As a reference the following values are often used:

Nominal values (maximum permissible value in continuous operation) or
Maximum values (maximum value achievable in the short term)

For normalized quantity equations, the units should always cancel out.

Example for a quantity equation

Let a body with the mass $m = 100~{\rm kg}$ be given. The body is lifted by the height $s=2~{\rm m}$.
What is the value of the needed work?

physical equation:

Work = Force $\cdot$ displacement
$W = F \cdot s \quad\quad\quad\;$ where $F=m \cdot g$
$W = m \cdot g \cdot s \quad\quad$ where $m=100~{\rm kg}$, $s=2~m$ and $g=9.81~{{{\rm m}}\over{{\rm s}^2}}$
$W = 100~kg \cdot 9.81 ~{{{\rm m}}\over{{\rm s}^2}} \cdot 2~{\rm m} $
$W = 100 \cdot 9.81 \cdot 2 \;\; \cdot \;\; {\rm kg} \cdot {{{\rm m}}\over{{\rm s}^2}} \cdot {\rm m}$
$W = 1962 \quad\quad \cdot \quad\quad\; \left( {\rm kg} \cdot {{{\rm m}}\over{{\rm s}^2}} \right) \cdot {\rm m} $
$W = 1962~{\rm Nm} = 1962~{\rm J} $

1.1.7 Letters for physical Quantities

Uppercase letters	Lowercase letters	Name	Application
$A$	$\alpha$	Alpha	angles, linear temperature coefficient
$B$	$\beta$	Beta	angles, quadratic temperature coefficient, current gain
$\Gamma$	$\gamma$	Gamma	angles
$\Delta$	$\delta$	Delta	small deviation, length of a air gap
$E$	$\epsilon$, $\varepsilon$	Epsilon	electrical field constant, permittivity
$Z$	$\zeta$	Zeta	- (math function)
$H$	$\eta$	Eta	efficiency
$\Theta$	$\theta$, $\vartheta$	Theta	temperature in Kelvin
$I$	$\iota$	Iota	-
$K$	$\kappa$	Kappa	specific conductivity
$\Lambda$	$\lambda$	Lambda	- (wavelength)
$M$	$\mu$	Mu	magnetic field constant, permeability
$N$	$\nu$	Nu	-
$\Xi$	$\xi$	Xi	-
$O$	$\omicron$	Omicron	-
$\Pi$	$\pi$	Pi	math. product operator, math. constant
$R$	$\rho$, $\varrho$	Rho	specific resistivity
$\Sigma$	$\sigma$	Sigma	math. sum operator, alternatively for specific conductivity
$T$	$\tau$	Tau	time constant
$\Upsilon$	$\upsilon$	Upsilon	-
$\Phi$	$\phi$, $\varphi$	Phi	magnetic flux, angle, potential
$X$	$\chi$	Chi	-
$\Psi$	$\psi$	Psi	linked magnetic flux
$\Omega$	$\omega$	Omega	unit of resistance, angular frequency

Tab. 4: greek letters

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 table 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.

1.1.8 Notation & Units

The course consistently uses the following symbols, units, and typical values:

Symbol	Quantity	SI unit	name of the unit	Typical values
$q$	Electric charge	$\rm C$	Coulomb	$10^{-19} ~\rm C$ (electron) to $\rm mC$
$I$	Electric current	$\rm A$	Ampere	$\rm \mu A$ (sensors) to $\rm kA$ (lightning)
$U$	Voltage (potential difference)	$\rm V$	Volt	$\rm \mu V$ (noise) to $\rm MV$ (transmission lines)
$\varphi$	Electric potential	$\rm V$	Volt	—
$P$	Power	$\rm W$	Watt	$\rm mW$ (electronics) to $\rm MW$ (machines)
$W$	Energy	$\rm J$	Joule	$\rm µJ$ (capacitors) to $\rm MJ$ (batteries)
$R$	Resistance	$\rm \Omega$	Ohm	$\rm mΩ$ to $\rm MΩ$
$G$	Conductance	$\rm S$	Siemens	$\rm µS$ to $\rm S$
$\rho$	Resistivity	$\rm \Omega \cdot m$	—	$1.7 \cdot 10^{-8} ~\rm \Omega m$ (Cu)
$\sigma$	Conductivity	$\rm S/m$	—	$5.8 \cdot 10^{7} ~\rm S/m$ (Cu)
$C$	Capacitance	$\rm F$	Farad	$\rm pF$ (ceramic) to $\rm F$ (supercaps)
$L$	Inductance	$\rm H$	Henry	$\rm \mu H$ to $\rm H$
$E$	Electric field strength	$\rm V/m$	—	$\rm 1 ~\rm V/m$ to $\rm MV/m$ (breakdown)
$D$	Electric flux density	$\rm C/m²$	—	—
$B$	Magnetic flux density	$\rm T$	Tesla	$\rm \mu T$ (Earth) to several $\rm T$ (MRI)
$H$	Magnetic field strength	$\rm A/m$	—	—
$\Phi$	Magnetic flux	$\rm Wb$	Weber	$\rm \mu Wb$ to $\rm mWb$
$\theta$	magnetic voltage (Magnetomotive force)	$\rm A \cdot turn$	—	—
$R$	Reluctance	$\rm A/Wb$	—	—

Tab. 5: Course-wide notation and units

1.2 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.

1.3 Exercises

Quick checks

1.1 Unit check (quantity equation)

Show that $P=U\cdot I$ has unit watt. (Better to be calulcated after reading Block02)

Result

$[U]=\rm{V}=\rm{kg}\,\rm{m}^2\,\rm{s}^{-3}\,\rm{A}^{-1}$, $[I]=\rm{A}$.
$[P]=[U][I]=\rm{kg}\,\rm{m}^2\,\rm{s}^{-3}=\rm{W}$.

2.2 Work from lifting (quantity equation)

How much energy is needed to lift 100 kg for 2 meters?

Result

$W=mgs$ with $m=100~\rm{kg},\,g=9.81~\rm{m/s^2},\,s=2~\rm{m}$
$W=100\cdot9.81\cdot2~\rm{Nm}=1962~\rm{J}$

3.1 Conversion

Convert $47~\rm{k\Omega}$ to $\rm{M\Omega}$ and $\Omega$.

Result

$47~\rm{k\Omega}=0.047~\rm{M\Omega}=47{,}000~\Omega$.

4.2 Dimension

Is $\eta=\dfrac{P_\rm{O}}{P_\rm{I}}$ dimensionless?

Result

Yes. Units cancel ($\rm W/W$); normalized equation.

5.3 Conversion

Which is larger: $5~\rm{mA}$ or $4500~\rm{\mu A}$?

Result

$5~\rm{mA}=5000~\rm{\mu A}$, so $5~\rm{mA}$ is larger.

6.4 Conversion

True/False: $1~\rm{V}=1~\rm{Nm/As}$.

Result

True (from $W=U \cdot Q$).

Longer exercises

1 Conversions: Battery

1. How many minutes could a consumer with $3~{\rm W}$ get supplied by an ideal battery with $10~{\rm kWh}$ ?

Solution steps

\begin{align*} W &= 10~{\rm kWh} &&= 10'000~{\rm Wh}\\ \\ t &= {{W }\over{P }} &&= {{10'000~{\rm Wh}}\over{3~{\rm W}}} \\ &&&= 3'333~{\rm h}= 200'000~{\rm min} \quad (= 139~{\rm days}) \end{align*}

Result

\begin{align*} t = 200'000~{\rm min} \end{align*}

2. Hard: Why is a real Lithium-ion battery with $10~{\rm kWh}$ unable to provide the given power for the calculated time?

Result

There are additional losses:

The battery has an internal resistance. Depending on the current the battery provides, this leads to internal losses.
The internal resistance of the battery depends on the state of charge (SoC) of the battery.
The wires also add additional losses to the system.

1 Conversions: Speed, Energy, and Power

Convert the following values step by step:

1. A vehicle speed of $80.00~{\rm {km}\over{h}}$ in ${\rm {m}\over{s}}$

Fast Solution

\begin{align*} v = 80.00~{\rm {km}\over{h}} \qquad \rightarrow \qquad {{\rm {numerical~value}}\over{3.6}} \qquad \rightarrow \qquad v = 22.22~{\rm { m}\over{s}} \end{align*}

Solution steps

\begin{align*} v &= 80.00~{\rm {km}\over{h}} = 80~{\rm {1'000~m}\over{3'600~s}} = 80~{\rm {m}\over{3.6~s}} \\ &= 22.22~{\rm {m}\over{s}} \end{align*}

Result

\begin{align*} v = 22.22~{\rm {m}\over{s}} \end{align*}

2. An energy of $60.0~{\rm J}$ in ${\rm kWh}$ ($1~{\rm J} = 1~{\rm Joule} = 1~{\rm Watt}\cdot {\rm second}$).

Solution steps

\begin{align*} P = 60.0~{\rm J} = 60.0~{\rm Ws} = 0.06~{\rm kWs} = 0.0000167~{\rm kWh}= 1.67 \cdot 10^{-5}~{\rm kWh} \end{align*}

Result

\begin{align*} P = 1.67 \cdot 10^{-5}~{\rm kWh} \end{align*}

3. The number of electrolytically deposited single positively charged copper ions of $1.2 ~\rm Coulombs$ (a copper ion has the charge of about $1.6 \cdot 10^{-19}{\rm C}$)

Solution steps

\begin{align*} n_{\rm ions}= {{{\rm charge}}\over{{\rm charge\,per\,ion}}}={{1.2~{\rm C}}\over{1.6\cdot10^{-19}~{\rm C/ion}}}=7.5 \cdot 10^{18}~{\rm ions} \end{align*}

Result

\begin{align*} n_{\rm ions}= 7.5 \cdot 10^{18}~{\rm ions} \end{align*}

4. Absorbed energy of a small IoT consumer, which consumes $1~{\rm µW}$ uniformly in $10 ~\rm days$

Solution steps

\begin{align*} 10 ~{\rm days} &= 10 \cdot {{24 ~\rm h}\over{1 ~\rm day}} \cdot {{60 ~\rm min}\over{1 ~\rm h}} \cdot {{60 ~\rm s}\over{1 ~\rm min}} \\ &= 10 \cdot 24 \cdot 60 \cdot 60~{\rm s} \\ &= 864'000 ~{\rm s} \\ \\ W_{\rm absorbed} &= 1~{\rm µW} \cdot 864'000~{\rm s} \\ &= 864'000~{\rm µWs} \\ &= 864~{\rm mWs} \\ &= 0.864~{\rm Ws} \\ &= 0.864~{\rm J} \end{align*}

Result

\begin{align*} W_{\rm absorbed} = 0.864~{\rm Ws} = 0.864~{\rm J} \end{align*}

1 Conversion: Vacuum Cleaner

Your $18~{\rm V}$ vacuum cleaner is equipped with a $4.0~{\rm Ah}$ battery, it runs $15~{\rm minutes}$.
How much electrical power is consumed by the motor during this time on average?

Solution steps

\begin{align*} W &= 18~{\rm V} \cdot 4.0~{\rm Ah} = 72~{\rm Wh} \\ \\ t &= 15~{\rm min} = 0.25~{\rm h} \\ \\ P &= {{W } \over {t }} \\ &= {{72~\rm Wh} \over {0.25~\rm h }} = 288~{\rm W} \end{align*}

Result

\begin{align*} 288~{\rm W} \end{align*}

1 Conversions: Video on Prefixes

1 Conversion: Energy Consumption

Convert the following values step by step:

How much energy does an average household consume per day when consuming an average power of $ 500~{\rm W} $?
How many chocolate bars ($2'000~{\rm kJ}$ each) does this correspond to?

Solution steps

\begin{align*} W &= 500~{\rm W} \cdot 24~{\rm h} = 12000~{\rm Wh}= 43'200'000~{\rm Ws} = 43'200~{\rm kWs} &&= 43'200~{\rm kJ} \\ \text{Or: } W &= 0.5~{\rm kW} \cdot 24~{\rm h} = 12~{\rm kWh} = 43'200~{\rm kWs} &&= 43'200~{\rm kJ} \\ \\ n_{\rm bars} &={{43'200~{\rm kJ}}\over{2'000~{\rm kJ}}} = 21.6~{\rm chocolate~bars} \\ \end{align*}

Result

\begin{align*} 22~{\rm chocolate~bars} \end{align*}

1 Conversion: Energy, Power and Area

A Tesla Model 3 has an average power consumption of $ {{16~{\rm kWh}}\over{100~{\rm km}}}$ and an usable battery capacity of $60~{\rm kWh}$. Solar panels produces per $1~\rm m^2$ in average in December $0.2~{{{\rm kWh}}\over{{\rm m^{2}}}}$. The car is driven $50~{\rm km}$ per day. The size of a distinct solar module with $460~{\rm W_p}$ (Watt peak) is $1.9~{\rm m} \times 1.1~{\rm m}$.

1. What is the average power consumption of the car per day?

Solution steps

\begin{align*} {{W}\over{l}} &= {{16~{\rm kWh}}\over{100~{\rm km}}} = 0.16 {{~{\rm kWh}}\over{~{\rm km}}} \\ W &= 50~{\rm km} \cdot 0.16 {{~{\rm kWh}}\over{~{\rm km}}} = 8~{\rm kWh} \end{align*}

Result

\begin{align*} W = 8~{\rm kWh}\end{align*}

2. How many square meters (=$\rm m^2$) of solar panels are needed on average in December?

Solution steps

\begin{align*} A = {{8~{\rm kWh}}\over{0.2 {{~{\rm kWh}}\over{~{\rm m^{2}}}}}} = 40~{\rm m^{2}} \end{align*}

Result

\begin{align*} A=40~{\rm m^{2}} \end{align*}

3. How many panels are at least needed to cover this surface?

Solution steps

\begin{align*} A_{\rm panel} &= 1.9~{\rm m} \cdot 1.1~{\rm m} = 2.1~{\rm m^{2}} \\ n_{\rm panels} &= {{A }\over{ A_{\rm panel }}} = {{40~{\rm m^{2}}}\over{2.1~{\rm m^{2}/panel}}} \\ &= 19.04~{\rm panels} \rightarrow 20~{\rm panels} \end{align*}

Result

\begin{align*} n_{\rm panels} = 20~{\rm panels} \end{align*}

4. What is the combined $\rm kW_p$ of the panels you calculated in 3. ?

Solution steps

\begin{align*} P &= 20~{\rm panels} \cdot 460~{\rm kW_p / panel} \\ &= 9'200~{\rm kW_p} \end{align*}

Result

\begin{align*} P = 9'200~{\rm kW_p} \end{align*}

Embedded resources

A nice 10-minute intro into some of the main topics of this chapter

Short presentation of the SI units

Orders of magnitude and why prefixes matter.

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.

Table of Contents

Block 01 — Physical Quantities and SI System

1.0 Intro

1.0.1 Learning Objectives

1.0.2 90-minute plan

1.0.3 Conceptual overview

1.1 Core Content

1.1.1 SI Base Quantities and Units

1.1.2 Common derived Quantities

1.1.3 Prefixes

1.1.4 Physical Equations

1.1.5 Quantity Equations

1.1.6 Normalized Quantity Equations

Example for a quantity equation

1.1.7 Letters for physical Quantities

1.1.8 Notation & Units

1.2 Common Pitfalls & Misconceptions

1.3 Exercises

Quick checks

Longer exercises

Embedded resources

Mini-assignment / homework (optional)