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electrical_engineering_and_electronics_1:block01 [2025/09/27 14:23] – mexleadminelectrical_engineering_and_electronics_1:block01 [2025/09/29 21:52] (aktuell) – mexleadmin
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 ===== 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>
  
-===== SI base quantities and units =====+===== Core content ===== 
 + 
 +==== 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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     * 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 =====+==== Prefixes ====
 <WRAP right 50%> <WRAP right 50%>
 <tabcaption prefix1 | Prefixes I> <tabcaption prefix1 | Prefixes I>
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 ~~PAGEBREAK~~ ~~CLEARFIX~~ ~~PAGEBREAK~~ ~~CLEARFIX~~
-===== Physical equations =====+==== 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 ==== ==== 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 ====
  
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 </WRAP> </WRAP>
  
-===== Letters for physical quantities =====+<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 ====
 <WRAP right 50%> <WRAP right 50%>
 <tabcaption tab03| greek letters > <tabcaption tab03| greek letters >
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 ~~PAGEBREAK~~ ~~CLEARFIX~~ ~~PAGEBREAK~~ ~~CLEARFIX~~
  
-===== Notation & units =====+==== 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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 ===== 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~@# 
 +  - $W=mgs$ 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~1~@#+#@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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 Is $\eta=\dfrac{P_\rm{O}}{P_\rm{I}}$ dimensionless?  Is $\eta=\dfrac{P_\rm{O}}{P_\rm{I}}$ dimensionless? 
  
-#@ResultBegin_HTML~1~@#+#@ResultBegin_HTML~dim1~@#
 Yes. Units cancel ($\rm W/W$); normalized equation.  Yes. Units cancel ($\rm W/W$); normalized equation. 
 #@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~1~@#+#@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~1~@#+#@ResultBegin_HTML~conv4~@#
 True (from $W=U \cdot Q$). True (from $W=U \cdot Q$).
 #@ResultEnd_HTML@# #@ResultEnd_HTML@#