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electrical_engineering_and_electronics_1:block01 [2025/09/28 14:40] – mexleadminelectrical_engineering_and_electronics_1:block01 [2026/03/05 13:57] (current) – mexleadmin
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-====== Block 01 — Physical quantities and SI system ======+====== Block 01 — Physical Quantities and SI System ======
  
-===== Learning objectives =====+===== 1.0 Intro ===== 
 + 
 +==== 1.0.1 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 =====+==== 1.0.2 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?” 
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   - Wrap-up (5 min): Summary table; common pitfalls checklist.   - Wrap-up (5 min): Summary table; common pitfalls checklist.
  
-===== Conceptual overview =====+==== 1.0.3 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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   </callout>   </callout>
  
-===== Core content =====+===== 1.1 Core Content =====
  
-==== SI base quantities and units ====+==== 1.1.1 SI Base Quantities and Units ====
 <WRAP right 50%> <WRAP right 50%>
 <tabcaption baseSI| SI base quantities (SI) > <tabcaption baseSI| SI base quantities (SI) >
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 ~~PAGEBREAK~~ ~~CLEARFIX~~ ~~PAGEBREAK~~ ~~CLEARFIX~~
-==== Common derived quantities ====+==== 1.1.2 Common derived Quantities ====
  
   * Besides the basic quantities, there are also quantities derived from them, e.g. $[F] = [m]\cdot [a] \rightarrow 1~{\rm N} = 1 ~{\rm kg} \cdot {{1 ~{\rm m}}\over{1 ~{\rm s}^2}}$.   * Besides the basic quantities, there are also quantities derived from them, e.g. $[F] = [m]\cdot [a] \rightarrow 1~{\rm N} = 1 ~{\rm kg} \cdot {{1 ~{\rm m}}\over{1 ~{\rm s}^2}}$.
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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.
  
-==== Prefixes ====+==== 1.1.3 Prefixes ====
 <WRAP right 50%> <WRAP right 50%>
 <tabcaption prefix1 | Prefixes I> <tabcaption prefix1 | Prefixes I>
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   * Use prefixes to keep magnitudes practical (see <tabref prefix1> and <tabref prefix2>).   * Use prefixes to keep magnitudes practical (see <tabref prefix1> and <tabref prefix2>).
   * Instead of writing zeroes for like in $0.000000004 ~\rm C $ is is easier to write $4 \rm ~nC $.   * 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''+  * For calculation it is often easier to write $4 ~\rm nC  = 4 \cdot 10^{-9} ~C$ or the notation $\rm 4e-9 ~C$
  
 ~~PAGEBREAK~~ ~~CLEARFIX~~ ~~PAGEBREAK~~ ~~CLEARFIX~~
-==== Physical equations ====+==== 1.1.4 Physical Equations ====
  
   * Physical equations allow a connection of physical quantities.   * Physical equations allow a connection of physical quantities.
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 <WRAP half column> <WRAP half column>
 <callout color="gray"> <callout color="gray">
-==== Quantity Equations ====+ 
 +==== 1.1.5 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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 <callout color="gray"> <callout color="gray">
  
-==== normalized Quantity Equations ====+==== 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. In normalized quantity equations, the measured value or calculated value of a quantity equation is divided by a reference value.
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 </callout> </callout>
  
-==== Letters for physical quantities ====+==== 1.1.7 Letters for physical Quantities ====
 <WRAP right 50%> <WRAP right 50%>
 <tabcaption tab03| greek letters > <tabcaption tab03| greek letters >
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 ~~PAGEBREAK~~ ~~CLEARFIX~~ ~~PAGEBREAK~~ ~~CLEARFIX~~
  
-==== Notation & units ====+==== 1.1.8 Notation & Units ====
 The course consistently uses the following symbols, units, and typical values: The course consistently uses the following symbols, units, and typical values:
  
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 </tabcaption> </tabcaption>
  
-===== Common pitfalls & misconceptions =====+===== 1.2 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 ===== +===== 1.3 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~@# 
 +  - $W=mgs$ with $m=100~\rm{kg},\,g=9.81~\rm{m/s^2},\,s=2~\rm{m}$  
 +  - $W=100\cdot9.81\cdot2~\rm{Nm}=1962~\rm{J}$ 
 +#@ResultEnd_HTML@# 
 +#@TaskEnd_HTML@# 
  
 #@TaskTitle_HTML@##@Lvl_HTML@#~~#@ee1_taskctr#~~.1  Conversion  #@TaskTitle_HTML@##@Lvl_HTML@#~~#@ee1_taskctr#~~.1  Conversion 
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 Convert $47~\rm{k\Omega}$ to $\rm{M\Omega}$ and $\Omega$. Convert $47~\rm{k\Omega}$ to $\rm{M\Omega}$ and $\Omega$.
  
-#@ResultBegin_HTML~conv1~@#+#@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@# #@ResultEnd_HTML@#
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 Which is larger: $5~\rm{mA}$ or $4500~\rm{\mu A}$?  Which is larger: $5~\rm{mA}$ or $4500~\rm{\mu A}$? 
  
-#@ResultBegin_HTML~conv2~@#+#@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.
  
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 True/False: $1~\rm{V}=1~\rm{Nm/As}$. True/False: $1~\rm{V}=1~\rm{Nm/As}$.
  
-#@ResultBegin_HTML~conv2~@#+#@ResultBegin_HTML~conv4~@#
 True (from $W=U \cdot Q$). True (from $W=U \cdot Q$).
 #@ResultEnd_HTML@# #@ResultEnd_HTML@#