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-===== Block 01 — Physical quantities and SI system =====+====== Block 01 — Physical quantities and SI system ======
  
-=== Learning objectives ===+===== Learning objectives =====
 <callout> <callout>
 +After this 90-minute block, you can
   * Use the SI base quantities, units, and symbols correctly; convert between units with prefixes.   * 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.   * Distinguish base vs. derived quantities; express key EE units (e.g. $\rm V$, $\rm \Omega$) in SI base units.
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 </callout> </callout>
  
-=== 90-minute plan ===+===== 90-minute plan =====
   - Warm-up (10 min):    - Warm-up (10 min): 
     - “What is the unit of conductivity? of energy?”      - “What is the unit of conductivity? of energy?” 
Zeile 22: Zeile 23:
   - Wrap-up (5 min): Summary table; common pitfalls checklist.   - Wrap-up (5 min): Summary table; common pitfalls checklist.
  
-=== Conceptual overview ===+===== Conceptual overview =====
 <callout icon="fa fa-lightbulb-o" color="blue"> <callout icon="fa fa-lightbulb-o" color="blue">
   - Units are the grammar of engineering and physics.    - Units are the grammar of engineering and physics. 
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   - 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., $I=2~\rm{A}$).    - 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., $I=2~\rm{A}$). 
   </callout>   </callout>
 +
 +===== Core content =====
  
 ==== SI base quantities and units ==== ==== SI base quantities and units ====
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     * The pressure unit bar (${\rm bar}$) is an SI unit.     * 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.     * 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 <tabref tab02>.+  *  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. We will see, that a lot of electrical quantities are derived quantities.
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 <WRAP half column> <WRAP half column>
 <callout color="gray"> <callout color="gray">
-=== Quantity Equations ===+ 
 +==== Quantity Equations ====
 The vast majority of physical equations result in a physical unit that does not equal $1$. The vast majority of physical equations result in a physical unit that does not equal $1$.
 \\ \\ \\ \\
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 <WRAP half column> <WRAP half column>
 <callout color="gray"> <callout color="gray">
-=== normalized Quantity Equations ===+ 
 +==== normalized Quantity Equations ====
  
 In normalized quantity equations, the measured value or calculated value of a quantity equation is divided by a reference value. In normalized quantity equations, the measured value or calculated value of a quantity equation is divided by a reference value.
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 </WRAP> </WRAP>
 </WRAP> </WRAP>
 +
 +<callout title="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:
 +<WRAP indent><WRAP indent>
 +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} $
 +</WRAP></WRAP>
 +
 +</callout>
  
 ==== Letters for physical quantities ==== ==== Letters for physical quantities ====
Zeile 195: Zeile 219:
 ~~PAGEBREAK~~ ~~CLEARFIX~~ ~~PAGEBREAK~~ ~~CLEARFIX~~
  
-==== Common pitfalls & misconceptions ====+==== Notation & units ==== 
 +The course consistently uses the following symbols, units, and typical values: 
 + 
 +<tabcaption notation | Course-wide notation and units> 
 +^ 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                      | $\rm A/Wb$               | — | — | 
 +</tabcaption> 
 + 
 +===== Common pitfalls & misconceptions =====
   * **Case matters:** $\rm M$ (mega, $10^6$) vs. $\rm m$ (milli, $10^{-3}$);   * **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);    * **Micro symbol:** use $\rm \mu$ (or ''u'' only when typing constraints exist); 
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   * **Normalized vs. quantity equations:** dimensionless ratios should cancel units; if not, something’s wrong.    * **Normalized vs. quantity equations:** dimensionless ratios should cancel units; if not, something’s wrong. 
  
-==== Exercises ==== +===== Exercises =====
-=== Worked example(s) ===+
  
-<callout> + 
-**1) Unit check (quantity equation):**   +==== Quick checks ==== 
-Show that $P=U\cdot I$ has unit watt.+ 
 +#@TaskTitle_HTML@##@Lvl_HTML@#~~#@ee1_taskctr#~~.1  Unit check (quantity equation)  
 +#@TaskText_HTML@#    
 + 
 +Show that $P=U\cdot I$ has unit watt. (Better to be calulcated after reading Block02) 
 + 
 +#@ResultBegin_HTML~conv1~@#
   - $[U]=\rm{V}=\rm{kg}\,\rm{m}^2\,\rm{s}^{-3}\,\rm{A}^{-1}$, $[I]=\rm{A}$.     - $[U]=\rm{V}=\rm{kg}\,\rm{m}^2\,\rm{s}^{-3}\,\rm{A}^{-1}$, $[I]=\rm{A}$.  
   - $[P]=[U][I]=\rm{kg}\,\rm{m}^2\,\rm{s}^{-3}=\rm{W}$.    - $[P]=[U][I]=\rm{kg}\,\rm{m}^2\,\rm{s}^{-3}=\rm{W}$. 
-</callout>+#@ResultEnd_HTML@# 
 +#@TaskEnd_HTML@# 
  
-<callout> +#@TaskTitle_HTML@##@Lvl_HTML@#~~#@ee1_taskctr#~~.2  Work from lifting (quantity equation)  
-**2) Prefix conversion:**   +#@TaskText_HTML@#   
-$3.3~\rm{mA}=3.3\times10^{-3}~\rm{A}=3300~\rm{\mu A}$. +
-</callout>+
  
-<callout> +How much energy is needed to lift 100 kg for 2 meters?
-**3) Work from lifting (quantity equation):**   +
-$W=mgs$ with $m=100~\rm{kg},\,g=9.81~\rm{m/s^2},\,s=2~\rm{m}$.   +
-$W=100\cdot9.81\cdot2~\rm{Nm}=1962~\rm{J}$. +
-</callout>+
  
-=== Quick checks === +#@ResultBegin_HTML~quant1~@# 
-<callout> +  - $W=mgs$ with $m=100~\rm{kg},\,g=9.81~\rm{m/s^2},\,s=2~\rm{m}$  
-Convert $47~\rm{k\Omega}$ to $\rm{M\Omega}$ and $\Omega$.  ++++ Answer|+  - $W=100\cdot9.81\cdot2~\rm{Nm}=1962~\rm{J}$ 
 +#@ResultEnd_HTML@# 
 +#@TaskEnd_HTML@#  
 + 
 +#@TaskTitle_HTML@##@Lvl_HTML@#~~#@ee1_taskctr#~~.1  Conversion  
 +#@TaskText_HTML@#    
 + 
 +Convert $47~\rm{k\Omega}$ to $\rm{M\Omega}$ and $\Omega$. 
 + 
 +#@ResultBegin_HTML~conv2~@#
 $47~\rm{k\Omega}=0.047~\rm{M\Omega}=47{,}000~\Omega$. $47~\rm{k\Omega}=0.047~\rm{M\Omega}=47{,}000~\Omega$.
-++++ +#@ResultEnd_HTML@# 
-</callout>+#@TaskEnd_HTML@# 
  
-<callout> +#@TaskTitle_HTML@##@Lvl_HTML@#~~#@ee1_taskctr#~~.2  Dimension 
-Is $\eta=\dfrac{P_\rm{O}}{P_\rm{I}}$ dimensionless?  ++++ Answer| +#@TaskText_HTML@#   
-Yes. Units cancel (W/W); normalized equation.  +
-++++ +
-</callout>+
  
-<callout> +Is $\eta=\dfrac{P_\rm{O}}{P_\rm{I}}$ dimensionless?  
-Which is larger: $5~\rm{mA}$ or $4500~\rm{\mu A}$?  ++++ Answer|+ 
 +#@ResultBegin_HTML~dim1~@# 
 +Yes. Units cancel ($\rm W/W$); normalized equation.  
 +#@ResultEnd_HTML@# 
 +#@TaskEnd_HTML@#  
 + 
 +#@TaskTitle_HTML@##@Lvl_HTML@#~~#@ee1_taskctr#~~.3  Conversion 
 +#@TaskText_HTML@#    
 + 
 +Which is larger: $5~\rm{mA}$ or $4500~\rm{\mu A}$?  
 + 
 +#@ResultBegin_HTML~conv3~@#
 $5~\rm{mA}=5000~\rm{\mu A}$, so $5~\rm{mA}$ is larger. $5~\rm{mA}=5000~\rm{\mu A}$, so $5~\rm{mA}$ is larger.
-++++ 
-</callout> 
  
-<callout> +#@ResultEnd_HTML@# 
-True/False: $1~\rm{V}=1~\rm{Nm/As}$.  ++++ Answer| +#@TaskEnd_HTML@#  
-True (from $W=UQ$). + 
-++++ +#@TaskTitle_HTML@##@Lvl_HTML@#~~#@ee1_taskctr#~~.4  Conversion 
-</callout>+#@TaskText_HTML@#    
 + 
 +True/False: $1~\rm{V}=1~\rm{Nm/As}$. 
 + 
 +#@ResultBegin_HTML~conv4~@# 
 +True (from $W=U \cdot Q$). 
 +#@ResultEnd_HTML@# 
 +#@TaskEnd_HTML@#  
 + 
 +==== Longer exercises ==== 
 + 
 +{{tagtopic>chapter1_1&nodate&nouser&noheader&nofooter&order=custom}}
  
-=== Embedded resources ===+===== Embedded resources =====
 \\ \\ \\ \\
 <WRAP column half> <WRAP column half>
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 ~~PAGEBREAK~~ ~~CLEARFIX~~ ~~PAGEBREAK~~ ~~CLEARFIX~~
  
-=== Mini-assignment / homework (optional) ===+===== Mini-assignment / homework (optional) =====
 List 10 everyday EE-relevant quantities (e.g., USB current, phone battery energy, LED forward voltage).  List 10 everyday EE-relevant quantities (e.g., USB current, phone battery energy, LED forward voltage). 
 For each:   For each: