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--- electrical_engineering_1:preparation_properties_proportions [2022/10/05 09:03]
tfischer [Tabelle]
+++ electrical_engineering_1:preparation_properties_proportions [2023/10/12 03:48] (aktuell)
mexleadmin [Bearbeiten - Panel]
@@ Zeile 1: / Zeile 1: @@
-====== 1. Preparation, Properties and Proportions ======
+#@DefLvlBegin_HTML~1,1.~@#
+====== 1 Preparation, Properties, and Proportions ======
 ===== 1.1 Physical Proportions =====
@@ Zeile 7: / Zeile 9: @@
 By the end of this section, you will be able to:
-  - know the basic physical quantities and the associated SI units.
+  - know the fundamental physical quantities and the associated SI units.
-  - know the most important prefixes. Be able to assign a power of ten to the respective abbreviation (G, M, k, d, c, m, µ, n).
+  - know the most important prefixes. Be able to assign a power of ten to the respective abbreviation (${\rm G}$, ${\rm M}$, ${\rm k}$, ${\rm d}$, ${\rm c}$, ${\rm m}$, ${\rm µ}$, ${\rm n}$).
-  - insert given numerical values and units into an existing quantity equation. From this you should be able to calculate the correct result using a calculator.
+  - insert given numerical values and units into an existing quantity equation. From this, you should be able to calculate the correct result using a calculator.
   - assign the Greek letters.
   - always calculate with numerical value and unit.
@@ Zeile 16: / Zeile 18: @@
 <WRAP>
-A nice 10 minute intro into some of the main topics of this chapter
+A nice 10-minute intro into some of the main topics of this chapter
 {{youtube>IOb3-JZPY0Y}}
 </WRAP>
@@ Zeile 30: / Zeile 32: @@
 <tabcaption tab01| SI-System>
-^ Base quantity           ^ Name      ^ Unit  ^ Definition                       ^
+^ Base quantity           ^ Name      ^ Unit         ^ Definition                       ^
-| Time                    | Second    | s     | Oscillation of $Cs$-Atom         |
+| Time                    | Second    | ${\rm s}$     | Oscillation of $Cs$-Atom         |
-| Length                  | Meter     | m     | by s und speed of light          |
+| Length                  | Meter     | ${\rm m}$     | by s und speed of light          |
-| el. Current             | Ampere    | A     | by s and elementary charge       |
+| el. Current             | Ampere    | ${\rm A}$     | by s and elementary charge       |
-| Mass                    | Kilogram  | kg    | still by kg prototype            |
+| Mass                    | Kilogram  | ${\rm kg}$    | still by kg prototype            |
-| Temperature             | Kelvin    | K     | by triple point of water         |
+| Temperature             | Kelvin    | ${\rm K}$     | by triple point of water         |
-| amount of \\ substance  | Mol       | mol   | via number of $^{12}C$ nuclides  |
+| amount of \\ substance  | Mol       | ${\rm mol}$   | via number of $^{12}C$ nuclides  |
-| luminous \\ intensity   | Candela   | cd    | via given radiant intensity      |
+| luminous \\ intensity   | Candela   | ${\rm cd}$    | via given radiant intensity      |
 </tabcaption>
 </WRAP>
@@ Zeile 43: / Zeile 45: @@
   * 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. $metre$ for length.
+  * 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. <tabref tab01> ) 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. $I = 2 A$
+  * 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 $I = 2\cdot 1A$
+    * 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 A$ is the (measurement) unit, here: Ampere
+    * $ [I] = 1~{\rm A}$ is the (measurement) unit, here: ${\rm Ampere}$
 ~~PAGEBREAK~~ ~~CLEARFIX~~
-==== derived quantities, SI units and prefixes ====
+==== derived quantities, SI units, and prefixes ====
-<WRAP>
+  * Besides the basic quantities, there are also quantities derived from them, e.g. $1~{{{\rm m}}\over{{\rm s}}}$.
-Importance of orders of magnitude in engineering (when the given examples in the video are unclear: we will get into this.)
+  * SI units should be preferred for calculations. These can be derived from the basic quantities **without a numerical factor**.
-{{youtube>jjvIy04PwYI}}
+    * The pressure unit bar (${\rm bar}$) is an SI unit.
-</WRAP>
+    * 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>.
 <WRAP>
 <tabcaption tab02| Prefixes I>
 ^ prefix ^ prefix symbol ^ meaning^
-| Yotta  | Y             | $10^{24}$   |
+| Yotta  | ${\rm Y}$      | $10^{24}$   |
-| Zetta  | Z             | $10^{21}$   |
+| Zetta  | ${\rm Z}$      | $10^{21}$   |
-| Exa    | E             | $10^{18}$   |
+| Exa    | ${\rm E}$      | $10^{18}$   |
-| Peta   | P             | $10^{15}$   |
+| Peta   | ${\rm P}$      | $10^{15}$   |
-| Tera   | T             | $10^{12}$   |
+| Tera   | ${\rm T}$      | $10^{12}$   |
-| Giga   | G             | $10^{9}$    |
+| Giga   | ${\rm G}$      | $10^{9}$    |
-| Mega   | M             | $10^{6}$    |
+| Mega   | ${\rm M}$      | $10^{6}$    |
-| Kilo   | k             | $10^{3}$    |
+| Kilo   | ${\rm k}$      | $10^{3}$    |
-| Hecto  | h             | $10^{2}$    |
+| Hecto  | ${\rm h}$      | $10^{2}$    |
-| Deka   | de            | $10^{1}$    |
+| Deka   | ${\rm de}$     | $10^{1}$    |
 </tabcaption>
 <tabcaption tab02| Prefixes II>
 ^ prefix ^ prefix symbol ^ meaning^
-| Deci   | d             | $10^{-1}$   |
+| Deci   | ${\rm d}$      | $10^{-1}$   |
-| Centi  | c             | $10^{-2}$   |
+| Centi  | ${\rm c}$      | $10^{-2}$   |
-| Milli  | m             | $10^{-3}$   |
+| Milli  | ${\rm m}$      | $10^{-3}$   |
-| Micro  | u, $\mu$      | $10^{-6}$   |
+| Micro  | ${\rm u}$, $µ$  | $10^{-6}$   |
-| Nano   | n             | $10^{-9}$   |
+| Nano   | ${\rm n}$      | $10^{-9}$   |
-| Piko   | p             | $10^{-12}$  |
+| Piko   | ${\rm p}$      | $10^{-12}$  |
-| Femto  | f             | $10^{-15}$   |
+| Femto  | ${\rm f}$      | $10^{-15}$   |
-| Atto   | a             | $10^{-18}$   |
+| Atto   | ${\rm a}$      | $10^{-18}$   |
-| Zeppto | z             | $10^{-21}$   |
+| Zeppto | ${\rm z}$      | $10^{-21}$   |
-| Yocto  | y             | $10^{-24}$   |
+| Yocto  | ${\rm y}$      | $10^{-24}$   |
 </tabcaption>
 </WRAP>
+<WRAP>
-  * Besides the basic quantities, there are also quantities derived from them, e.g. $1{{m}\over{s}}$.
+\\
-  * SI units should be preferred for calculations. These can be derived from the basic quantities **without a numerical factor**.
+Importance of orders of magnitude in engineering (when the given examples in the video are unclear: we will get into this.)
-    * The pressure unit bar ($bar$) is an SI unit.
+{{youtube>jjvIy04PwYI}}
-    * BUT: The obsolete pressure unit atmospheric ($=1.013 bar$) is **__not__** an SI unit.
+</WRAP>
-  *  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>.
 ~~PAGEBREAK~~ ~~CLEARFIX~~
@@ Zeile 102: / Zeile 104: @@
   * Physical equations allow a connection of physical quantities.
   * There are two types of physical equations to distinguish (at least in German):
-    * Quantity equations (Größengleichungen )
+    * Quantity equations (in German: //Größengleichungen// )
-    * Normalized quantity equations (also called related quantity equations, normierte Größengleichungen)
+    * Normalized quantity equations (also called related quantity equations, in German //normierte Größengleichungen//)
 <WRAP>
@@ Zeile 109: / Zeile 111: @@
 === Quantity equations ===
-he vast majority of physical equations result in a physical unit that is not equal to $1$.
+The vast majority of physical equations result in a physical unit that does not equal $1$.
 \\ \\
-Example: Force $F = m \cdot a$ with $[F] = kg \cdot {{m}\over{s^2}}$
+Example: Force $F = m \cdot a$ with $[{\rm F}] = 1~\rm kg \cdot {{{\rm m}}\over{{\rm s}^2}}$
 \\ \\
@@ Zeile 127: / Zeile 129: @@
 This results in a dimensionless quantity relative to the reference value.
-Example: Efficiency $\eta = {{P_{out}}\over{P_{in}}}$
+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 reference value are often used:
+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)
@@ Zeile 140: / Zeile 142: @@
 <callout title="Example for a quantity equation">
-Let a body with the mass $m = 100kg$ be given. The body is lifted by the height $s=2m$. \\
+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?
@@ Zeile 148: / Zeile 150: @@
 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 $m=100kg$, $s=2m$ and $g=9.81{{m}\over{s^2}}$
+\\ $W = m \cdot g \cdot s \quad\quad$ where $m=100~{\rm kg}$, $s=2~m$ and $g=9.81~{{{\rm m}}\over{{\rm s}^2}}$
-\\ $W = 100kg \cdot 9.81{{m}\over{s^2}} \cdot 2m $
+\\ $W = 100~kg \cdot 9.81 ~{{{\rm m}}\over{{\rm s}^2}} \cdot 2~{\rm m} $
-\\ $W = 100\cdot 9.81 \cdot 2 \;\; \cdot \;\; kg \cdot {{m}\over{s^2}} \cdot m$
+\\ $W = 100     \cdot 9.81 \cdot 2 \;\; \cdot \;\; {\rm kg} \cdot {{{\rm m}}\over{{\rm s}^2}}         \cdot {\rm m}$
-\\ $W = 1962 \quad\quad \cdot \quad\quad\; \left( kg \cdot {{m}\over{s^2}} \right) \cdot m $
+\\ $W = 1962 \quad\quad \cdot \quad\quad\;  \left( {\rm kg} \cdot {{{\rm m}}\over{{\rm s}^2}} \right) \cdot {\rm m} $
-\\ $W = 1962 Nm = 1962 J $
+\\ $W = 1962~{\rm Nm} = 1962~{\rm J} $
 </WRAP></WRAP>
@@ Zeile 159: / Zeile 161: @@
 ==== Letters for physical quantities ====
-<WRAP >
-<tabcaption tab03| greek letters >
-^ Uppercase letters  ^ Lowercase letters          ^ Name     ^
-| $A$                | $\alpha$                   | Alpha    |
-| $B$                | $\beta$                    | Beta     |
-| $\Gamma$           | $\gamma$                   | Gamma    |
-| $\Delta$           | $\delta$                   | Delta    |
-| $E$                | $\epsilon$, $\varepsilon$  | Epsilon  |
-| $Z$                | $\zeta$                    | Zeta     |
-| $H$                | $\eta$                     | Eta      |
-| $\Theta$           | $\theta$, $\vartheta$      | Theta    |
-| $I$                | $\iota$                    | Iota     |
-| $K$                | $\kappa$                   | Kappa    |
-| $\Lambda$          | $\lambda$                  | Lambda   |
-| $M$                | $\mu$                      | Mu       |
-| $N$                | $\nu$                      | Nu       |
-| $\Xi$              | $\xi$                      | Xi       |
-| $O$                | $\omicron$                 | Omicron  |
-| $\Pi$              | $\pi$                      | Pi       |
-| $R$                | $\rho$, $\varrho$          | Rho      |
-| $\Sigma$           | $\sigma$                   | Sigma    |
-| $T$                | $\tau$                     | Tau      |
-| $\Upsilon$         | $\upsilon$                 | Upsilon  |
-| $\Phi$             | $\phi$, $\varphi$          | Phi      |
-| $X$                | $\chi$                     | Chi      |
-| $\Psi$             | $\psi$                     | Psi      |
-| $\Omega$           | $\omega$                   | Omega    |
-</tabcaption>
-</WRAP>
 In physics and electrical engineering, the letters for physical quantities are often close to the English term.
 Thus explains $C$ for //**__C__**apacity//, $Q$ for //**__Q__**uantity// and $\varepsilon_0$ for the //**__E__**lectical 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 has not enough letters to avoid conflicts for the scope of physics .
+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 <tabref tab03>).
@@ Zeile 201: / Zeile 172: @@
   * or a time-dependent quantity, \\ e.g. the instantaneous voltage $u(t)$
+<WRAP hide>
 The relevant Greek letters for electrical engineering are described in the following video.
+</WRAP>
+<WRAP >
+<tabcaption tab03| greek letters >
+^ 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    |                                                              |
+| $\Delta$           | $\delta$                   | 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                        |
+</tabcaption>
+</WRAP>
 ~~PAGEBREAK~~ ~~CLEARFIX~~
 ==== Exercises ====
-<panel type="info" title="Exercise 1.1.1 Conversions I - precalculated example for the conversion of units"> <WRAP group><WRAP column 2%>{{fa>pencil?32}}</WRAP><WRAP column 92%>
+{{tagtopic>chapter1_1&nodate&nouser&noheader&nofooter&order=custom}}
-{{youtube>DLjHyd0pFos}}
-</WRAP></WRAP></panel>
-<panel type="info" title="Exercise 1.1.2 Conversions II"> <WRAP group><WRAP column 2%>{{fa>pencil?32}}</WRAP><WRAP column 92%>
-Convert the following values step by step:
-  * A vehicle speed of 80 km/h in m/s
-  * An energy of 60 joules in kWh (1 joule = 1 watt*second)
-  * The number of electrolytically deposited single positively charged copper ions of 1.2 coulombs (a copper ion has the charge of about $1.6 \cdot 10^{-19} C$)
-  * Absorbed energy of a small IoT consumer, which consumes 1 µW uniformly in 10 days
-</WRAP></WRAP></panel>
-<panel type="info" title="Exercise 1.1.3 Conversions III"> <WRAP group><WRAP column 2%>{{fa>pencil?32}}</WRAP><WRAP column 92%>
-Convert the following values step by step:
-How many minutes could an ideal battery with 10 kWh operate a consumer with 3W?
-</WRAP></WRAP></panel>
-<panel type="info" title="Exercise 1.1.4 Conversions IV"> <WRAP group><WRAP column 2%>{{fa>pencil?32}}</WRAP><WRAP column 92%>
-Convert the following values step by step:
-How much energy does an average household consume per day when consuming an average power of 500 W? How many chocolate bars (2000 kJ each) does this correspond to?
-</WRAP></WRAP></panel>
-===== 1.2 Introduction to the structure of matter =====
+===== 1.2 Introduction to the Structure of Matter =====
 <WRAP><callout>
@@ Zeile 239: / Zeile 223: @@
 ==== Elementary Charge ====
-<WRAP>
-<imgcaption BildNr0 | Atomic model according to Bohr / Sommerfeld>
-</imgcaption>
-{{drawio>Atommodell }}
-</WRAP>
 <WRAP>
 Charge in Matter
@@ Zeile 250: / Zeile 228: @@
 </WRAP>
-  * Explanation of the charge on the basis of the atomic models according to Bohr and Sommerfeld (see <imgref BildNr0>)
+  * Explanation of the charge based on the atomic models according to Bohr and Sommerfeld (see <imgref BildNr0>)
   * Atoms consist of
     * Atomic nucleus (with protons and neutrons)
     * Electron shell
   * Electrons are carriers of the elementary charge $|e|$
-  * elementary charge $|e| = 1.6022\cdot 10^{-19} C$
+  * elementary charge $|e| = 1.6022\cdot 10^{-19}~{\rm C}$
-  * Proton is the antagonist, i.e. has opposite charge
+  * Proton is the antagonist, i.e. has the opposite charge
   * Sign is arbitrarily chosen:
     * Electron charge: $-e$
     * proton charge: $+e$
-  * all charges on/in bodies can only occur as integer multiples of the elementary charge.
+  * All charges on/in bodies can only occur as integer multiples of the elementary charge.
   * Due to the small numerical value of $e$, the charge is considered as a continuum when viewed macroscopically.
+<WRAP>
+<imgcaption BildNr0 | Atomic model according to Bohr / Sommerfeld>
+</imgcaption>
+{{drawio>Atommodell.svg}}
+</WRAP>
 ==== Conductivity ====
@@ Zeile 279: / Zeile 264: @@
 === Semiconductor ===
-In semiconductors, charge carriers can be generated by heat and light irradiation. Often a small movement of electrons is already possible by room temperature.
+In semiconductors, charge carriers can be generated by heat and light irradiation. Often a small movement of electrons is already possible at room temperature.
 Examples:
   * Silicon
-  * diamond
+  * Diamond
 </callout>
@@ Zeile 292: / Zeile 277: @@
 In the insulator, charge carriers are firmly bound to the atomic shells.
-\\ \\ \\ \\
+\\ \\
 Examples:
@@ Zeile 301: / Zeile 286: @@
 ==== Exercises ====
-<panel type="info" title="Exercise 1.2.1 Charges I"> <WRAP group><WRAP column 2%>{{fa>pencil?32}}</WRAP><WRAP column 92%>
+{{tagtopic>chapter1_2&nodate&nouser&noheader&nofooter&order=custom}}
-How many electrons make up the charge of one coulomb?
-</WRAP></WRAP></panel>
-<panel type="info" title="Exercise  1.2.2 Charges II"> <WRAP group><WRAP column 2%>{{fa>pencil?32}}</WRAP><WRAP column 92%>
-A balloon has a charge of $Q=7nC$ on its surface. How many additional electrons are on the balloon?
-</WRAP></WRAP></panel>
 ===== 1.3 Effects of electric charges and current =====
@@ Zeile 320: / Zeile 299: @@
   * What effects of electric charges and current do you know?
-==== first approximation to the el. charge ====
+==== First Approximation to the el. Charge ====
 <WRAP>
 <imgcaption BildNr1 | Experiment 1 with two suspended charges>
 </imgcaption>
-{{drawio>Versuch1_Ladungen}}
+{{drawio>Versuch1_Ladungen.svg}}
 </WRAP>
   * first attempt (see <imgref BildNr1>):
     * Two charges ($Q_1$ and $Q_2$) are suspended at a distance of $r$.
-    * Charges are generated by high voltage source and transferred to the two test specimens
+    * Charges are generated by the high-voltage source and transferred to the two test specimens
   * Result
-    * samples with same charges $\rightarrow$ Repulsion
+    * samples with same charges $\rightarrow$ repulsion
     * samples with charges of different sign $\rightarrow$ attraction
   * Findings
@@ Zeile 343: / Zeile 322: @@
 Setup for own experiments \\
 {{url>https://phet.colorado.edu/sims/html/charges-and-fields/latest/charges-and-fields_de.html 500,400 noborder}} \\
-Take a charge ($+1nC$) and position it. Measure the field across a sample charge (a sensor).
+Take a charge ($+1~{\rm nC}$) and position it. Measure the field across a sample charge (a sensor).
 </WRAP>
 <WRAP>
-Experiment on Coulomb's law and some calculated exercises
+Experiment with Coulomb's law and some calculated exercises
 {{youtube>4ubqby1Id4g}}
 </WRAP>
-  * Qualitative investigation by means of a second experiment
+  * Qualitative investigation using a second experiment
     * two charges ($Q_1$ and $Q_2$) at distance $r$
     * additional measurement of the force $F_C$ (e.g. via spring balance)
   * Experiment results:
     * Force increases linearly with larger charge $Q_1$ or $Q_2$. \\ $ F_C \sim Q_1$ and $ F_C \sim Q_2$
-    * Force falls quadratically with greater distance $r$ \\ $ F_C \sim {1 \over {r^2}}$
+    * Force falls quadratic with greater distance $r$ \\ $ F_C \sim {1 \over {r^2}}$
     * with a proportionality factor $a$: \\ $ F_C = a \cdot {{Q_1 \cdot Q_2} \over {r^2}}$
   * Proportionality factor $a$
@@ Zeile 362: / Zeile 341: @@
     * $a$ thus becomes:
     * $a = {{1} \over {4\pi\cdot\varepsilon}}$
-    * $\varepsilon_0$ is the {{wp>Coulomb constant}} (also called eletric field constant). In a vacuum, $\varepsilon_0 = \varepsilon$.
+    * $\varepsilon_0$ is the {{wp>Coulomb constant}} (also called electric field constant). In a vacuum, $\varepsilon_0 = \varepsilon$.
   * The formula is similar to that of the gravitational force: $F_G = \gamma \cdot {{m_1 \cdot m_2} \over {r^2}}$
 <callout icon="fa fa-exclamation" color="red" title="Note!">
 The Coulomb force (in a vacuum) can be calculated via. \\ $\boxed{ F_C = {{1} \over {4\pi\cdot\varepsilon_0}} \cdot {{Q_1 \cdot Q_2} \over {r^2}} }$ \\
-where $\varepsilon_0 = 8.85 \cdot 10^{-12} \cdot {C^2 \over {m^2\cdot N}} = 8.85 \cdot 10^{-12} \cdot {{As} \over {Vm}}$
+where $\varepsilon_0 = 8.85 \cdot 10^{-12} \cdot ~{{\rm C}^2 \over {{\rm m}^2\cdot {\rm N}}} = 8.85 \cdot 10^{-12} \cdot ~{{{\rm As}} \over {{\rm Vm}}}$
 </callout>
 ~~PAGEBREAK~~ ~~CLEARFIX~~
-===== 1.4 Charge and current =====
+===== 1.4 Charge and Current =====
 <WRAP><callout>
@@ Zeile 398: / Zeile 377: @@
 ~~PAGEBREAK~~ ~~CLEARFIX~~
-==== qualitative View ====
+==== Qualitative View ====
 <WRAP>
 <imgcaption BildNr2 | Part of a Conductor >
 </imgcaption>
-{{drawio>Ladungen_im_Leiter}}
+{{drawio>Ladungen_im_Leiter.svg}}
 </WRAP>
@@ Zeile 408: / Zeile 387: @@
     * the above-mentioned conductor with a cross-section $A$ perpendicular to the conductor
     * the quantity of charges $\Delta Q = n \cdot e$, which in a certain period of time $\Delta t$, pass through the area $A$
-  * In the case of a uniform charge transport over a longer period of time, i.e. direct current (DC), the following applies:
+  * In the case of a uniform charge transport over a longer period, i.e. direct current (DC), the following applies:
-    * The amount of charges per time flowing through the surface is constant: \\ ${{\Delta Q} \over {\Delta t}} = const. = I$
+    * The amount of charges per time flowing through the surface is constant: \\ ${{\Delta Q} \over {\Delta t}} = {\rm const.} = I$
     * $I$ denotes the strength of the direct current.
-    * The unit of $I$ is the SI unit ampere: $1 A = {{1 C}\over{1 s}}$ . Thus, for the unit coulomb applies: $1 C = 1 A\cdot s$
+    * The unit of $I$ is the SI unit ${\rm Ampere}$: $1~{\rm A} = {{1~{\rm C}}\over{1~{\rm s}}}$ . Thus, for the unit coulomb applies: $1~{\rm C} = 1~{\rm A} \cdot {\rm s}$
 <callout icon="fa fa-comment" color="blue" title="Definition of current">
-The current of $1 A$ flows when an amount of charge of $1 C$ is transported in $1 s$ through the cross section of the conductor.
+The current of $1~{\rm A}$ flows when an amount of charge of $1~{\rm C}$ is transported in $1~{\rm s}$ through the cross-section of the conductor.
-Before 2019: The current of $1 A$ flows when two parallel conductors, each $1m$ long and $1m$ apart, exert a force of $F_C = 0.2\cdot 10^{-6} N$ on each other.
+Before 2019: The current of $1~{\rm A}$ flows when two parallel conductors, each $1~{\rm m}$ long and $1~{\rm m}$ apart, exert a force of $F_C = 0.2\cdot 10^{-6}~{\rm N}$ on each other.
 </callout>
@@ Zeile 423: / Zeile 402: @@
 </callout>
-==== Determination of the current direction====
+==== Direction of the Current ====
 <WRAP>
 <imgcaption BildNr4 | Part of a conductor with different charged charges>
 </imgcaption>
-{{drawio>pos_neg_Ladungen_im_Leiter}}
+{{drawio>pos_neg_Ladungen_im_Leiter.svg}}
 </WRAP>
@@ Zeile 448: / Zeile 427: @@
 </callout>
-<WRAP>
-<imgcaption BildNr8 | Electrodes on the diode>
-</imgcaption>
-{{drawio>Diode_Elektroden}}
-</WRAP>
 <callout icon="fa fa-comment" color="blue" title="Definition of electrodes (according to DIN5489)">
-An electrode is a connection (or pin) of an electrical component.
+An electrode is a connection (or pin) of an electrical component. \\
-As a rule, electrodes are characterized by the fact that a change of material takes place (e.g. metal->semiconductor, metal->liquid)
+As a rule, the dimension of an electrode is characterized by the fact that a change of material takes place (e.g. metal->semiconductor, metal->liquid). \\
-  * Anode: Electrode at which the current enters the component.
+The name of the electrode is given as follows:
-  * Cathode: Electrode at which the current exits the component.
+  * **A**node: Electrode at which the current enters the component.
+  * Cathode: Electrode at which the current exits the component. (in German //**K**athode//)
-As a mnemonic you can remember the structure, shape and electrodes of the diode (see <imgref BildNr8>).
+As a mnemonic, you can remember the structure, shape, and electrodes of the diode (see <imgref BildNr8>).
 </callout>
-~~PAGEBREAK~~ ~~CLEARFIX~~
-==== Exercises ====
-<panel type="info" title="Exercise 1.4.1 Determining the current from the charge per time"> <WRAP group><WRAP column 2%>{{fa>pencil?32}}</WRAP><WRAP column 92%>
 <WRAP>
-<imgcaption BildNr3 | Time course of the charge>
+<imgcaption BildNr8 | Electrodes on the diode>
 </imgcaption>
-{{drawio>Zeitverlauf_Ladung}}
+{{drawio>Diode_Elektroden.svg}}
 </WRAP>
-Let the charge gain per time on an object be given.
+~~PAGEBREAK~~ ~~CLEARFIX~~
-  * Determine from the diagram <imgref BildNr3> and plot them on the diagram.
+==== Exercises ====
-  * How could you proceed if the amount of charge on the object changes non-linearly?
-</WRAP></WRAP></panel>
+{{tagtopic>chapter1_4&nodate&nouser&noheader&nofooter&order=custom}}
-<panel type="info" title="Exercise 1.4.2 Electron flow"> <WRAP group><WRAP column 2%>{{fa>pencil?32}}</WRAP><WRAP column 92%>
-How many electrons pass through a control cross section of a metallic conductor when the current of $40mA$ flows for $4.5s$?
-</WRAP></WRAP></panel>
-===== 1.5 Voltage, potential and energy =====
+===== 1.5 Voltage, Potential, and Energy =====
 <WRAP><callout>
@@ Zeile 505: / Zeile 468: @@
 <imgcaption BildNr9 | Symbolic image of an electric circuit>
 </imgcaption>
-{{drawio>Symbolbild_Stromkreis}}
+{{drawio>Symbolbild_Stromkreis.svg}}
 </WRAP>
@@ Zeile 515: / Zeile 478: @@
   * $\rightarrow$ there is a turnover of energy.
   * The energy turnover is proportional to the amount of charge $q$ transported.
-  * In many cases, the "energetic path" from ① to ② hast to be characterized in charge-independent terms: \\ $\boxed{{W_{1,2}\over{q}} = U_{1,2}}$
+  * In many cases, the "energetic path" from ① to ② has to be characterized in charge-independent terms: \\ $\boxed{{W_{1,2}\over{q}} = U_{1,2}}$
-  * $V$ for Voltage is often used to denote the unit AND the quantity (in German $U$ is used for the quantity):
+  * V for Voltage is in the English literature often used to denote the unit ${\rm V}$ AS WELL AS the quantity $V$ (in German $U$ is used for the quantity):
   * e.g.
-    * $VCC = 5V$ : Voltage supply of an IC (__V__oltage __C__ommon __C__ollector),
+    * $VCC = 5~{\rm V}$ : Voltage supply of an IC (__V__oltage __C__ommon __C__ollector),
-    * $V_{S+} = 15V$ : Voltage supply of an operational amplifier (__V__oltage __S__upply plus).
+    * $V_{S+} = 15~{\rm V}$ : Voltage supply of an operational amplifier (__V__oltage __S__upply plus).
 ~~PAGEBREAK~~ ~~CLEARFIX~~
-==== Comparison mechanics to electrics ====
+==== Comparison: Mechanics vs Electrics ====
 <WRAP group><WRAP half column>
@@ Zeile 529: / Zeile 492: @@
 <imgcaption BildNr5 | Mechanical potential>
 </imgcaption>
-{{drawio>mechanisches_Potential}}
+{{drawio>mechanisches_Potential.svg}}
 </WRAP>
 === Mechanical System ===
@@ Zeile 545: / Zeile 508: @@
 <imgcaption BildNr6 | Electrical Potential>
 </imgcaption>
-{{drawio>elektrisches_Potential}}
+{{drawio>elektrisches_Potential.svg}}
 </WRAP>
 === Electrical System ===
@@ Zeile 573: / Zeile 536: @@
 <callout icon="fa fa-exclamation" color="red" title="Note:">
   * Voltage is always a potential difference.
-  * The unit of voltage is Volt: $1 V$
+  * The unit of voltage is ${\rm Volt}$: $1~{\rm V}$
 </callout>
 <callout icon="fa fa-comment" color="blue" title="Definition of voltage">
-A voltage of $1 V$ is present between two points if a charge of $1 C$ undergoes an energy change of $1J = 1Nm$ between these two points.
+A voltage of $1~{\rm V}$ is present between two points if a charge of $1~{\rm C}$ undergoes an energy change of $1~{\rm J} = 1~{\rm Nm}$ between these two points.
-From $W=U \cdot Q$ also the unit results: $1Nm = 1V\cdot As \rightarrow 1V = 1{{Nm}\over{As}}$
+From $W=U \cdot Q$ also the unit results: $1~{\rm Nm} = 1~ {\rm V} \cdot {\rm As} \rightarrow 1~ {\rm V} = 1~{{{\rm Nm}}\over{{\rm As}}}$
 </callout>
-==== voltage between two points ====
+==== Voltage between two Points ====
 For the voltage between two points, using what we know so far, we get the following definition:
@@ Zeile 596: / Zeile 559: @@
 ==== Exercises ====
-<panel type="info" title="Exercise 1.5.1 Direction of the voltage"> <WRAP group><WRAP column 2%>{{fa>pencil?32}}</WRAP><WRAP column 92%>
+#@TaskTitle_HTML@#1.5.1 Direction of the voltage
+#@TaskText_HTML@#
 <WRAP>
 <imgcaption BildNr21 | Example of conventional voltage specification>
 </imgcaption>
-{{drawio>BeispKonventionelleSpannungsangabe}}
+{{drawio>BeispKonventionelleSpannungsangabe.svg}}
 </WRAP>
-Explain whether the voltages $U_{Batt}$, $U_{12}$ and $U_{21}$ in <imgref BildNr21> are positive or negative according to the voltage definition.
+Explain whether the voltages $U_{\rm Batt}$, $U_{12}$ and $U_{21}$ in <imgref BildNr21> are positive or negative according to the voltage definition.
-~~PAGEBREAK~~ ~~CLEARFIX~~
-</WRAP></WRAP></panel>
+#@HiddenBegin_HTML~1,Hints~@#
+  * Which terminal has the higher potential?
+  * From where to where does the arrow point?
+#@HiddenEnd_HTML~1,Hints~@#
-===== 1.6 Resistance and conductance =====
+#@HiddenBegin_HTML~2,Result~@#
+  * ''+'' is the higher potential. Terminal 1 has the higher potential. $\varphi_1 > \varphi_2$
+  * For $U_{\rm Batt}$: The arrow starts at terminal 1 and ends at terminal 2. So $U_{\rm Batt}=U_{12}>0$
+  * $U_{21}<0$
+#@HiddenEnd_HTML~1l2,Result~@#
+#@TaskEnd_HTML@#
+===== 1.6 Resistance and Conductance =====
 <WRAP><callout>
@@ Zeile 627: / Zeile 604: @@
 <imgcaption BildNr11 | resistor as two-terminal component>
 </imgcaption>
-{{drawio>Widerstand_Zweitor}}
+{{drawio>Widerstand_Zweitor.svg}}
 </WRAP>
+Current flow generally requires an energy input first. This energy is at some point extracted from the electric circuit and is usually converted into heat.
+The reason for this conversion is the resistance e.g. of the conductor or other loads.
+A resistor is an electrical component with two connections (or terminals). Components with two terminals are called two-terminal networks or one-port networks (<imgref BildNr11>). Later in the semester, four-terminal networks will also be added.
 <WRAP>
-{{url>https://www.falstad.com/circuit/circuitjs.html?running=false&ctz=CQAgjCAMB0l3BWK0AsKAcYBs6CckB2SAZmPUixSxAUhpsgCgAnEAJgWuzo+rfXRRwcRmAJtwuCd3AEuWOnQL0ki5EgBqAewA2AFwCGAcwCmjI+0iD+1qyGKQUURsSKTpC9mycyIixgDultYC7JzsoUwARuyk4ChIbLjUDtRMQWze4J682f5AA 350,300 noborder}}
+{{url>https://www.falstad.com/circuit/circuitjs.html?running=false&ctz=CQAgjCAMB0l3BWK0AsKAcYBs6CckB2SAZmPUixSxAUhpsgCgAnEAJgWuzo+rfXRRwcRmAJtwuCd3AEuWOnQL0ki5EgBqAewA2AFwCGAcwCmjI+0iD+1qyGKQUURsSKTpC9mycyIixgDultYC7JzsoUwARuyk4ChIbLjUDtRMQWze4J682f5AA noborder}}
 </WRAP>
-Current flow generally requires energy input. This energy is extracted from the electric circuit and is usually converted into heat.
+In general, the cause-and-effect relationship is such that an applied voltage across the resistor produces the current flow. However, the reverse relationship also applies: as soon as an electric current flows across a resistor, a voltage drop is produced over the resistor.
-The reason for this is the resistance of the conductor.
+In electrical engineering, circuit diagrams use idealized components in a {{wp>Lumped-element model}}. The resistance of the wires is either neglected - if it is very small compared to all other resistance values - or drawn as a separate "lumped" resistor.
-A resistor is an electrical component with two connections (or terminals). Components with two terminals are called two-terminal network or one-port network (<imgref BildNr11>). In later in the semester, four-terminal network will also be added.
+The values of the resistors are standardized in such a way, that there is a fixed number of different values between $1~\Omega$ and $10~\Omega$ or between $10~\rm k\Omega$ and $100~\rm k\Omega$. These ranges, which cover values up to the tenfold number, are called decades. In general, the resistors are ordered in the so-called {{wp>E series of preferred numbers}}, like 6 values in a decade, which is named E6 (here: $1.0~\rm k\Omega$, $1.5~\rm k\Omega$, $2.2~\rm k\Omega$, $3.3~\rm k\Omega$, $4.7~\rm k\Omega$, $6.8~\rm k\Omega$). As higher the number (e.g. E24) more different values are available in a decade, and as more precise the given value is.
+For larger resistors with wires, the value is coded by four to six colored bands (see [[https://www.digikey.com/en/resources/conversion-calculators/conversion-calculator-resistor-color-code|conversion tool]]). For smaller resistors without wires, often numbers are printed onto the components ([[https://www.digikey.com/en/resources/conversion-calculators/conversion-calculator-smd-resistor-code|conversion tool]])
+<imgcaption BildNr13 | examples for a real 15kOhm resistor>
+</imgcaption>
+{{drawio>examplesForResistors.svg}}
-In general, the cause-and-effect relationship is such that an applied voltage across the resistor produces the current flow. However, the reverse relationship also applies: as soon as an electric current flows across a resistor, a voltage drop is produced across the resistor.
-In electrical engineering, circuit diagrams use idealized components in a {{wp>Lumped-element model}}. The resistance of the wires is either neglected - if it is very small compared to all other resistance values - or drawn as a separate resistor.
 ~~PAGEBREAK~~ ~~CLEARFIX~~
-==== Linearity of resistors ====
+==== Linearity of Resistors ====
 <WRAP group><WRAP half column>
 <callout color="grey">
@@ Zeile 648: / Zeile 636: @@
 <imgcaption BildNr13 | Linear resistors in the U-I diagram>
 </imgcaption>
-{{drawio>linearer_Widerstand_UI}}
+{{drawio>linearer_Widerstand_UI.svg}}
-  * For linear resistors, the resistance value is $R={{U_R}\over{I_R}}=const.$ and thus independent of $U_R$.
+  * For linear resistors, the resistance value is $R={{U_R}\over{I_R}}={\rm const.} $ and thus independent of $U_R$.
-  * **Ohm's law** results: \\ $\boxed{R={{U_R}\over{I_R}}}$ with unit $[R]={{[U_R]}\over{[I_R]}}= 1{{V}\over{A}}= 1\Omega$
+  * **Ohm's law** results: \\ $\boxed{R={{U_R}\over{I_R}}}$ with unit $[R]={{[U_R]}\over{[I_R]}}= 1{\rm {V}\over{A}}= 1~\Omega$
   * In <imgref BildNr13> the value $R$ can be read from the course of the straight line $R={{{\Delta U_R}}\over{\Delta I_R}}$
-  * The reciprocal value (inverse) of the resistance is called the conductance: $G={{1}\over{R}}$ with unit $1 S$ (Siemens). This value can be seen as a slope in the $U$-$I$ diagram.
+  * The reciprocal value (inverse) of the resistance is called the conductance: $G={{1}\over{R}}$ with unit $1~{\rm S}$ (${\rm Siemens}$). This value can be seen as a slope in the $U$-$I$ diagram.
 </callout>
@@ Zeile 662: / Zeile 650: @@
 <imgcaption BildNr14 | Non-linear resistors in the U-I diagram>
 </imgcaption>
-{{drawio>nichtlinearer_Widerstand_UI}}
+{{drawio>nichtlinearer_Widerstand_UI.svg}}
   * The point in the $U$-$I$ diagram in which a system rests is called the operating point. In the <imgref BildNr14> an operating point is marked with a circle in the left diagram.
   * For nonlinear resistors, the resistance value is $R={{U_R}\over{I_R(U_R)}}=f(U_R)$. This resistance value depends on the operating point.
-  * Often small changes around the operating point are of interest (e.g. for small disturbances of load machines). For this purpose, the differential resistance $r$ (also dynamic resistance) is determined: \\ $\boxed{r={{dU_R}\over{dI_R}} \approx{{\Delta U_R}\over{\Delta I_R}} }$ with unit $[R]=1\Omega$.
+  * Often small changes around the operating point are of interest (e.g. for small disturbances of load machines). For this purpose, the differential resistance $r$ (also dynamic resistance) is determined: \\ $\boxed{r={{{\rm d}U_R}\over{{\rm d}I_R}} \approx{{\Delta U_R}\over{\Delta I_R}} }$ with unit $[R]=1~\Omega$.
   * As with the resistor $R$, the reciprocal of the differential resistance $r$ is the differential conductance $g$.
-  * In <imgref BildNr14> the differential conductance $g$ can be read from the slope of the straight line at each point $g={{dI_R}\over{dU_R}}$
+  * In <imgref BildNr14> the differential conductance $g$ can be read from the slope of the straight line at each point $g={{{\rm d}I_R}\over{{\rm d}U_R}}$
 </callout>
 </WRAP></WRAP>
-==== Resistance as a material property ====
+==== Resistance as a material Property ====
 <WRAP>
@@ Zeile 689: / Zeile 677: @@
 <WRAP >
 <tabcaption tab04| Specific resistivity for different materials>
-^ Material           ^ $\rho$ in ${{\Omega\cdot {mm^2}}\over{m}}$ ^
+^ Material           ^ $\rho$ in ${{\Omega\cdot {{\rm mm}^2}}\over{{\rm m}}}$ ^
 | Silver               |  $1.59\cdot 10^{-2}$  |
 | Copper               |  $1.79\cdot 10^{-2}$  |
@@ Zeile 696: / Zeile 684: @@
 | Lead                 |  $2.1\cdot 10^{-1}$   |
 | Graphite             |  $8\cdot 10^{0}$      |
-| Battery acid (laed-acid battery) |  $1.5\cdot 10^4$      |
+| Battery Acid (Lead-acid Battery) |  $1.5\cdot 10^4$      |
 | Blood                |  $1.6\cdot 10^{6}$    |
-| (tap) water          |  $2 \cdot 10^{7}$     |
+| (Tap) Water          |  $2 \cdot 10^{7}$     |
 | Paper                |  $1\cdot 10^{15} ... 1\cdot 10^{17}$   |
@@ Zeile 706: / Zeile 694: @@
 <callout icon="fa fa-exclamation" color="red" title="Note:">
 The resistance can be calculated by \\ $\boxed{R = \rho \cdot {{l}\over{A}} } $
-  * $\rho$ is the material dependent resistivity with the unit: $[\rho]={{[R]\cdot[A]}\over{l}}=1{{\Omega\cdot m^{\not{2}}}\over{\not{m}}}=1 \Omega\cdot m$
+  * $\rho$ is the material dependent resistivity with the unit: $[\rho]={{[R]\cdot[A]}\over{l}}=1~{{\Omega\cdot {\rm m}^{\not{2}}}\over{\not{{\rm m}}}}=1~\Omega\cdot {\rm m}$
-  * Often, instead of $1 \Omega\cdot m$, the unit $1 {{\Omega\cdot {mm^2}}\over{m}}$ is used. It holds that $1 {{\Omega\cdot {mm^2}}\over{m}}= 10^{-6} \Omega m$
+  * Often, instead of $1~\Omega\cdot {\rm m}$, the unit $1~{{\Omega\cdot {{\rm mm}^2}}\over{{\rm m}}}$ is used. It holds that $1~{{\Omega\cdot {{\rm mm}^2}}\over{{\rm m}}}= 10^{-6}~\Omega {\rm m}$
 </callout>
-  * There exists also a specific conductance $\kappa$, given by the conductance $G$ : $G= \kappa \cdot {{A}\over{l}}$
+  * There exists also a specific conductance $\kappa$, given by the conductance $G$ : \\ $G= \kappa \cdot {{A}\over{l}}$
-    * The specific conductance $\kappa$ is the reciprocal of the specific resistance $\rho$: $\kappa={{1}\over{\rho}}$
+  * The specific conductance $\kappa$ is the reciprocal of the specific resistance $\rho$: \\ $\kappa={{1}\over{\rho}}$
-==== Temperature dependence of resistors ====
+==== Temperature Dependence of Resistors ====
 <WRAP>
 Explanation of the temperature dependence of resistors
 {{youtube>Xw7QXJ9sV6s}}
-<WRAP group><WRAP column>
-<imgcaption BildNr15 | Circuit for measuring the effect of temperature on a resistor>
-</imgcaption>
-{{drawio>Widerstand_Temperatur_Schaltung}}
-</WRAP></WRAP>
-<WRAP group><WRAP column>
-<imgcaption BildNr16 | Influence of temperature on resistance>
-</imgcaption>
-{{drawio>Widerstand_Temperatur}}
-</WRAP></WRAP>
-</WRAP>
 The resistance value is - apart from the influences of geometry and material mentioned so far - also influenced by other effects. These are e.g.:
   * Heat (thermoresistive effect, e.g. in the resistance thermometer)
-  * Light (photoresistive effect, e.g. in the component photo resistor)
+  * Light (photosensitive effect, e.g. in the component photoresistor)
   * Magnetic field (magnetoresistive effect, e.g. in hard disks)
   * Pressure (piezoresistive effect e.g. tire pressure sensor)
   * Chemical environment (chemoresistive effect e.g. chemical analysis of breathing air)
-In order to summarize these influences in a formula, the mathematical tool of {{wp>Taylor series}} is often used. This will be shown here practically for the thermoresistive effect. The thermoresistive effect, or the temperature dependence of the resistivity, is one of the most common (interference) influences in components.
+To summarize these influences in a formula, the mathematical tool of {{wp>Taylor series}} is often used.
+This will be shown here practically for the thermoresistive effect.
+The thermoresistive effect, or the temperature dependence of the resistivity, is one of the most common influences in components.
-The starting point for this is again an experiment. The ohmic resistance is to be determined as a function of temperature. For this purpose, the resistance is measured by means of a voltage source, a voltmeter (voltage measuring device) and an ammeter (current measuring device) and the temperature is changed (<imgref BildNr15>).
+The starting point for this is again an experiment. The ohmic resistance is to be determined as a function of temperature.
+For this purpose, the resistance is measured using a voltage source, a voltmeter (voltage measuring device), and an ammeter (current measuring device), and the temperature is changed (<imgref BildNr15>).
+<WRAP group><WRAP column>
+<imgcaption BildNr15 | Circuit for measuring the effect of temperature on a resistor>
+</imgcaption>
+{{drawio>Widerstand_Temperatur_Schaltung.svg}}
+</WRAP></WRAP>
 The result is a curve of the resistance $R$ versus the temperature $\vartheta$ as shown in <imgref BildNr16>.
-These is approximated in a first approximation by a linear progression around an operating point.
+As a first approximation is a linear progression around an operating point.
 This results in:
@@ Zeile 751: / Zeile 735: @@
   *  The constant is replaced by $c = R_0 \cdot \alpha$
-  *  $\alpha$ here is the linear temperature coefficient with unit: $ [\alpha] = {{1}\over{[\vartheta]}} = {{1}\over{K}} $
+  *  $\alpha$ here is the linear temperature coefficient with unit: $ [\alpha] = {{1}\over{[\vartheta]}} = {{1}\over{{\rm K}}} $
   *  Besides the linear term, it is also possible to increase the accuracy of the calculation of $R(\vartheta)$ with higher exponents of the temperature influence. This approach will be discussed in more detail in the mathematics section below.
   *  These temperature coefficients are described with Greek letters: $\alpha$, $\beta$, $\gamma$, ...
+<WRAP group><WRAP column>
+<imgcaption BildNr16 | Influence of temperature on resistance>
+</imgcaption>
+{{drawio>Widerstand_Temperatur.svg}}
+</WRAP></WRAP>
+</WRAP>
 ~~PAGEBREAK~~ ~~CLEARFIX~~
@@ Zeile 761: / Zeile 753: @@
 <imgcaption BildNr22 | Influence of temperature on resistance>
 </imgcaption>
-{{drawio>Widerstand_Temperaturkoeffizient}}
+{{drawio>Widerstand_Temperaturkoeffizient.svg}}
 </WRAP>
 The temperature dependence of the resistance is described by the following equation:
-$\boxed{ R(\vartheta) = R_0 (1 + \alpha \cdot (\vartheta - \vartheta_0) + \beta \cdot (\vartheta - \vartheta_0)^2 + \gamma \cdot (\vartheta - \vartheta_0)^3 + ...}$
+$\boxed{ R(\vartheta) = R_0 (1 + \alpha \cdot (\vartheta - \vartheta_0) + \beta \cdot (\vartheta - \vartheta_0)^2 + \gamma \cdot (\vartheta - \vartheta_0)^3 + ...)}$
 Where:
-  * $\alpha$ the (linear) temperature coefficient with unit: $ [\alpha] = {{1}\over{K}} $
+  * $\alpha$ the (linear) temperature coefficient with unit: $ [\alpha] = {{1}\over{{\rm K}}} $
-  * $\beta$ the (quadratic) temperature coefficient with unit: $ [\beta] = {{1}\over{K^2}} $
+  * $\beta$ the (quadratic) temperature coefficient with unit: $ [\beta] = {{1}\over{{\rm K}^2}} $
-  * $\gamma$ the temperature coefficient with unit: $ [\gamma] = {{1}\over{K^3}} $
+  * $\gamma$ the temperature coefficient with unit: $ [\gamma] = {{1}\over{{\rm K}^3}} $
-  * $\vartheta_0$ is the given reference temperature, usually $0°C$ or $25°C$.
+  * $\vartheta_0$ is the given reference temperature, usually $0~°{\rm C}$ or $25~°{\rm C}$.
 The further the temperature range deviates from the reference temperature, the more temperature coefficients are required to reproduce the actual curve (<imgref BildNr22>).
@@ Zeile 779: / Zeile 771: @@
 <callout icon="fa fa-info" color="grey" title="Outlook">
-In addition to the specification of the parameters $\alpha$,$\beta$, ..., the specification of $R_{25}$ and $B_{25}$ can occasionally be found.
+In addition to the specification of the parameters $\alpha$,$\beta$, ..., the specification of $R_{25}$ and $\rm B_{25}$ can occasionally be found.
-This is a different variant of approximation, which refers to the temperature of $25°C$.
+This is a different variant of approximation, which refers to the temperature of $25~°{\rm C}$.
-It is based on the {{wpde>Arrhenius equation}}, which links reaction kinetics to temperature in chemistry. For the temperature dependence of the resistance, the Arrhenius equation links the inhibition of carrier motion by lattice vibrations to the temperature $R(T) \sim e^{{B}\over{T}} $ .
+It is based on the {{wp>Arrhenius equation}}, which links reaction kinetics to temperature in chemistry.
+For the temperature dependence of the resistance, the Arrhenius equation links the inhibition of carrier motion by lattice vibrations to the temperature $R(T) \sim {\rm e}^{{\rm B}\over{T}} $ .
-A series expansion can again be applied: $R(T) \sim e^{A + {{B}\over{T}} + {{C}\over{T^2}} + ...}$.
+A series expansion can again be applied: $R(T) \sim {\rm e}^{{\rm A} + {{\rm B}\over{T}} + {{\rm C}\over{T^2}} + ...}$.
-However, often only $B$ is given. \\ By taking the ratio of any temperature $T$ and $T_{25}=298.15 K$ ($\hat{=} 25°C$) we get:
+However, often only $B$ is given. \\ By taking the ratio of any temperature $T$ and $T_{25}=298.15~{\rm K}$ ($\hat{=} 25~°{\rm C}$) we get:
-${{R(T)}\over{R_{25}}} = {{exp \left({{B}\over{T}}\right)} \over {exp \left({{B}\over{298.15 K}}\right)}} $ with $R_{25}=R(T_{25})$
+${{R(T)}\over{R_{25}}} = {{{\rm exp} \left({{\rm B}\over{T}}\right)} \over {{\rm exp} \left({{\rm B}\over{298.15 ~{\rm K}}}\right)}} $ with $R_{25}=R(T_{25})$
 This allows the final formula to be determined:
-$R(T) = R_{25} \cdot exp \left( B_{25} \cdot \left({{1}\over{T}} - {{1}\over{298.15 K}} \right) \right)  $
+$R(T) = R_{25} \cdot {\rm exp} \left( {\rm B}_{25} \cdot \left({{1}\over{T}} - {{1}\over{298.15~{\rm K}}} \right) \right)  $
 </callout>
-=== Types of temperature dependent resistors ===
+=== Types of temperature-dependent Resistors ===
-Besides the temperature dependence as a disturbing influence, there are also components which have been deliberately bred for a specific temperature influence.
+Besides the temperature dependence as a negative, disturbing influence, some components have been deliberately developed for a specific temperature influence.
-These are called thermistors (a portmanteau of __therm__ally sensitive res__istor__). Thermistors are basically divided into hot conductors and cold conductors.
+These are called thermistors (a portmanteau of __therm__ally sensitive res__istor__). Thermistors are divided into hot conductors and cold conductors.
-A special form of thermistors are materials that have been explicitly optimized for minimum temperature dependence (e.g. Constantan or Isaohm).
+A special form of thermistors is materials that have been explicitly optimized for minimum temperature dependence (e.g. Constantan or Isaohm).
 <WRAP group><WRAP half column><callout color="grey">
-=== NTC thermistor ===
-<imgcaption BildNr17 | NTC thermistor in the U-I-diagram>
+=== NTC Thermistor ===
-</imgcaption>
-{{drawio>Heissleiter_UI}}
   * As the name suggests, the NTC has a __n__egative __t__emperature __c__oefficient. This leads to lower resistance at higher temperatures.
-  * Such a NTC thermistor is also called Heißleiter in German ("hot conductor").
+  * Such an NTC thermistor is also called //Heißleiter// in German ("hot conductor").
   * Examples are semiconductors
   * Applications are inrush current limiters and temperature sensors. For the desired operating point, a strongly non-linear curve is selected there (e.g. fever thermometer).
-</callout></WRAP><WRAP half column><callout color="grey">
+<imgcaption BildNr17 | NTC thermistor in the U-I-diagram>
-=== PTC termistor ===
-<imgcaption BildNr18 | PTC thermistor in the U-I diagram>
 </imgcaption>
-{{drawio>Kaltleiter_UI}}
+{{drawio>Heissleiter_UI.svg}}
+</callout></WRAP><WRAP half column><callout color="grey">
+=== PTC Thermistor ===
   * As the name suggests, the PTC has a __p__ositive __t__emperature __c__oefficient. This leads to lower resistance at lower temperatures.
-  * Such a PTC thermistor is also called Kaltleiter in German ("cold conductor").
+  * Such a PTC thermistor is also called //Kaltleiter// in German ("cold conductor").
   * Examples are doped semiconductors or metals.
-  * Applications are temperature sensors. For this purpose they often offer a wide temperature range and good linearity (e.g. PT100 in the range of $-100°C$ to $200°C$).
+  * Applications are temperature sensors. For this purpose, they often offer a wide temperature range and good linearity (e.g. PT100 in the range of $-100~°{\rm C}$ to $200~°{\rm C}$).
   * [[https://www.geogebra.org/m/VVA2YUJQ#material/EQQm5kbT|Interactive example]] for PTC thermistors
+<imgcaption BildNr18 | PTC thermistor in the U-I diagram>
+</imgcaption>
+{{drawio>Kaltleiter_UI.svg}}
 </callout>
 </WRAP></WRAP>
-==== Resistor packages ====
+==== Resistor Packages ====
+The packages are not explained in detail here. The video shows the smaller available packages. In the 3rd semester and higher we will use 0603-size resistors.
 <WRAP>
 {{youtube>0NrrfotuANY}}
 </WRAP>
-The packages are not explained in detail here. The video shows the smaller available packages. In the 3rd semester and higher we will use 0603 size resistors.
 ~~PAGEBREAK~~ ~~CLEARFIX~~
@@ Zeile 847: / Zeile 841: @@
 <panel type="info" title="Exercise 1.6.2 Resistance of a pencil stroke"> <WRAP group><WRAP column 2%>{{fa>pencil?32}}</WRAP><WRAP column 92%>
-Assume that a soft pencil lead is 100% graphite. What is the resistance of a $5cm$ long and $0.2mm$ wide line if it has a height of $0.2\mu m$?
+Assume that a soft pencil lead is 100 % graphite. What is the resistance of a $5.0~{\rm cm}$ long and $0.20~{\rm mm}$ wide line if it has a height of $0.20~{\rm µm}$?
 The resistivity is given by <tabref tab04>.
+{{drawio>PencilStroke.svg}}
+<button size="xs" type="link" collapse="Loesung_1_6_1_1_Endergebnis">{{icon>eye}} Final result</button><collapse id="Loesung_1_6_1_1_Endergebnis" collapsed="true">
+\begin{align*}
+R = 10~{\rm k} \Omega
+\end{align*}</collapse>
 </WRAP></WRAP></panel>
 <panel type="info" title="Exercise 1.6.3 Resistance of a cylindrical coil"> <WRAP group><WRAP column 2%>{{fa>pencil?32}}</WRAP><WRAP column 92%>
-Let a cylindrical coil in the form of a multi-layer winding be given - this could for example occur in windings of a motor. The cylindrical coil has an inner diameter of $d_i=70mm$ and an outer diameter of $d_a = 120mm$. The number of turns is $n_W=1350$ turns, the wire diameter is $d=2.0mm$ and the specific conductivity of the wire is $\kappa_{Cu}=56 \cdot 10^6 {{S}\over{m}}$.
+Let a cylindrical coil in the form of a multi-layer winding be given - this could for example occur in windings of a motor.
+The cylindrical coil has an inner diameter of $d_{\rm i}=70~{\rm mm}$ and an outer diameter of $d_{\rm a} = 120~{\rm mm}$.
+The number of turns is $n_{\rm W}=1350$ turns, the wire diameter is $d=2.0~{\rm mm}$ and the specific conductivity of the wire is $\kappa_{\rm Cu}=56 \cdot 10^6 ~{{{\rm S}}\over{{\rm m}}}$.
-First calculate the wound wire length and then the ohmic resistance of the entire coil.
+First, calculate the wound wire length and then the ohmic resistance of the entire coil.
 </WRAP></WRAP></panel>
 <panel type="info" title="Exercise 1.6.4 Resistance of a supply line"> <WRAP group><WRAP column 2%>{{fa>pencil?32}}</WRAP><WRAP column 92%>
-The supply line to a consumer has to be replaced. Due to the application, the conductor resistance must remain the same.
+The power supply line to a consumer has to be replaced. Due to the application, the conductor resistance must remain the same.
-  * The old aluminium supply cable had a specific conductivity $\kappa_{Al}=33\cdot 10^6 {{S}\over{m}}$ and a cross-section $A_{Al}=115mm^2$.
+  * The old aluminium supply cable had a specific conductivity $\kappa_{\rm Al}=33\cdot 10^6 ~{\rm {S}\over{m}}$ and a cross-section $A_{\rm Al}=115~{\rm mm}^2$.
-  * The new copper supply cable has a specific conductivity $\kappa_{Cu}=56\cdot 10^6 {{S}\over{m}}$
+  * The new copper supply cable has a specific conductivity $\kappa_{\rm Cu}=56\cdot 10^6 ~{\rm {S}\over{m}}$
-Which wire cross-section $A_{Cu}$ must be selected ?
+Which wire cross-section $A_{\rm Cu}$ must be selected?
 </WRAP></WRAP></panel>
@@ Zeile 876: / Zeile 880: @@
 {{page>aufgabe_1.7.6_mit_rechnung&nofooter}}
-===== 1.7 Power and efficiency =====
+===== 1.7 Power and Efficiency =====
 <WRAP><callout>
@@ Zeile 885: / Zeile 889: @@
 <WRAP>
-A nice 10 minute intro into power and efficiency (a cutout from 2:40 to 12:15 from a full video of EEVblog)
+A nice 10-minute intro into power and efficiency (a cutout from 2:40 to 12:15 from a full video of EEVblog)
 {{youtube>fHoHYEZnVIg?start=160&end=735}}
 </WRAP>
-==== Determining the electrical power in a DC circuit ====
+==== Determining the electrical Power in a DC Circuit ====
-From chapter [[#1.5 Voltage, potential and energy]] it is known that a movement of a charge across a potential difference corresponds to a change in energy. Charge transport therefore automatically means energy expenditure. Often, however, the energy expenditure per unit of time is of interest.
+From chapter [[#1.5 Voltage, potential, and energy]] it is known that a movement of a charge across a potential difference corresponds to a change in energy.
+Charge transport therefore automatically means energy expenditure. Often, however, the energy expenditure per unit of time is of interest.
 <WRAP>
 <imgcaption BildNr19 |Course of power and energy>
 </imgcaption>
-{{drawio>LeistungEnergie}}
+{{drawio>LeistungEnergie.svg}}
 <imgcaption BildNr20 | Source and consumer>
 </imgcaption>
-{{drawio>QuelleVerbraucher}}
+{{drawio>QuelleVerbraucher.svg}}
 </WRAP>
 The energy expenditure per time unit represents the **power**: \\
-$\boxed{P={{\Delta W}\over{\Delta t}}}$ mwith unit $[P]={{[W]}\over{[t]}}=1 {{J}\over{s}} = 1 {{Nm}\over{s}} = 1 V\cdot A = 1 W$
+$\boxed{P={{\Delta W}\over{\Delta t}}}$ with the unit $[P]={{[W]}\over{[t]}}=1~{\rm {J}\over{s}} = 1~{\rm {Nm}\over{s}} = 1 ~{\rm V\cdot A} = 1~{\rm W}$
-For a constant power $P$ and an initial energy $W(t=0)=0$ holds: \\
+For a constant power $P$ and an initial energy $W(t=0~{\rm s})=0$ holds: \\
 $\boxed{W=P \cdot t}$ \\
 If the above restrictions do not apply, the generated/needed energy must be calculated via an integral.
-In addition to the current flow from the source to the consumer (and back), the power also flows from the source to the consumer.
+Besides the current flow from the source to the consumer (and back), also power flows from the source to the consumer.
+In the following circuit, the color code shows the incoming and outgoing power.
+<WRAP>
+{{url>https://www.falstad.com/circuit/circuitjs.html?running=true&ctz=CQAgjAzCAMB00IQVhAFlgDjBgTANgE5cCxojc0UVUokBTAWjDACgB3ECPDcMHEHNB7N+0FgDcBQgUjxThfGEtTQQKVRthIWAJ07de-LjxyylpMR2My5gk2bGocUAqrB5U4CAHZwHmCxOUJC+7p4hXp6OziCufp5xglDRwT4CEGBevkkBQbGqORE5KVnpmWDeKNjJgTERkOGV4Bg1AB6x-BUEft054TwAlgB2AMYA9gC2wwDmADoAzrOzQwAKY2x0OiztKnJdaBgF0FD9IGMArgAu02MzC0ur65u1J0jlEJ6oGN3VuTGobzKBx+LT+J2gnj6gOKL0omWcmQB8OOYLQEPiaMhKJKSIxuIaqJU4X8+P8YgARuBvL4CL4VAVvN0xO0cGBegQ5BAkCgcARuqc6AAbOgjS46AYjACGgoWAGUAJ7zS50CYsIA noborder}}
+</WRAP>
 If we only consider a __DC circuit__, the following energy is converted between the terminals (see also <imgref BildNr19> and <imgref BildNr20>): \\
@@ Zeile 916: / Zeile 925: @@
 This gives the power (i.e. energy converted per unit time): \\
-$\boxed{P=U_{12} \cdot I}$ with the unit $[P]= 1 V\cdot A = 1W \quad$ ... $W$ shere stands for watts.
+$\boxed{P=U_{12} \cdot I}$ with the unit $[P]= 1 ~{\rm V\cdot A} = 1~{\rm W} \quad$ ... ${\rm W}$ here stands for the physical unit watts.
 For ohmic resistors:
@@ Zeile 922: / Zeile 931: @@
 $\boxed{P=R\cdot I^2 = {{U_{12}^2}\over{R}}}$
-==== Nominal quantities of ohmic loads ====
+==== Nominal Quantities of ohmic Loads ====
 ^ Name of the nominal quantity ^ physical quantity ^ description^
-| Nominal power (= rated power)       | $P_N$               | $P_N$ is the power output of a device (consumer or generator) that is permissible in continuous operation. |
+| Nominal power (= rated power)       | $P_{\rm N}$               | $P_{\rm N}$ is the power output of a device (consumer or generator) that is permissible in continuous operation. |
-| Nominal current (= rated current)   | $I_N$               | $I_N$ is the current occurring during operation at rated power.                                            |
+| Nominal current (= rated current)   | $I_{\rm N}$               | $I_{\rm N}$ is the current occurring during operation at rated power.                                            |
-| Nominal voltage (= rated voltage)   | $U_N$               | $U_N$ is the voltage occurring during operation at rated power.                                            |
+| Nominal voltage (= rated voltage)   | $U_{\rm N}$               | $U_{\rm N}$ is the voltage occurring during operation at rated power.                                            |
 ==== Efficiency ====
-<WRAP>
+The usable (= outgoing) $P_{\rm O}$ power of a real system is always smaller than the supplied (incoming) power $P_{\rm I}$.
-<imgcaption BildNr23 | Power flow diagram>
+This is due to the fact, that there are additional losses in reality. \\
-</imgcaption>
+The difference is called power loss $P_{\rm loss}$. It is thus valid:
-{{drawio>Leistungsfluss}}
-</WRAP>
+$P_{\rm I} = P_{\rm O} + P_{\rm loss}$
-The usable (= outgoing) $P_A$ power is always smaller than the supplied (incoming) power $P_E$. The difference is called power loss $P_V$. It is thus valid:
+Instead of the power loss $P_{\rm loss}$, the efficiency $\eta$ is often given:
-$P_E = P_A + P_V$
+$\boxed{\eta = {{P_{\rm O}}\over{P_{\rm I}}}\overset{!}{<} 1}$
-Instead of the power loss $P_V$, the efficiency $\eta$ is often given:
+For systems connected in series (cf. <imgref BildNr23>), the total resistance is given by:
-$\boxed{\eta = {{P_{A}}\over{P_{E}}}\overset{!}{<} 1}$
+$\boxed{\eta = {{P_{\rm O}}\over{P_{\rm I}}} = {\not{P_{1}}\over{P_{\rm I}}}\cdot {\not{P_{2}}\over \not{P_{1}}}\cdot {{P_{\rm O}}\over \not{P_{2}}} = \eta_1 \cdot \eta_2 \cdot \eta_3}$
-For systems connected in series (cf. <imgref BildNr23>), the total resistance is given by:
+<WRAP>
+<imgcaption BildNr23 | Power flow diagram>
+</imgcaption>
+{{drawio>Leistungsfluss.svg}}
-$\boxed{\eta = {{P_{A}}\over{P_{E}}} = {\not{P_{1}}\over{P_{E}}}\cdot {\not{P_{2}}\over \not{P_{1}}}\cdot {{P_{A}}\over \not{P_{2}}} = \eta_1 \cdot \eta_3 \cdot \eta_3}$
+</WRAP>
 ~~PAGEBREAK~~ ~~CLEARFIX~~
@@ Zeile 956: / Zeile 967: @@
 <panel type="info" title="Exercise 1.7.1 Pre-calculated example of electrical power and energy"> <WRAP group><WRAP column 2%>{{fa>pencil?32}}</WRAP><WRAP column 92%>
-The first 5:20 minutes is a recap of the fundamentalc of calculation the electric power
+The first 5:20 minutes is a recap of the fundamentals of calculating the electric power
 {{youtube>41-37Kv_ljw}}
 ~~PAGEBREAK~~ ~~CLEARFIX~~
 </WRAP></WRAP></panel>
-<panel type="info" title="Exercise 1.7.2 Power"> <WRAP group><WRAP column 2%>{{fa>pencil?32}}</WRAP><WRAP column 92%>
+#@TaskTitle_HTML@#1.7.2 Power
+#@TaskText_HTML@#
-A SMD resistor is used on a circuit board for current measurement. The resistance value should be $R=0.2\Omega$, the maximum power $P_N=250 mW$.
+An SMD resistor is used on a circuit board for current measurement. The resistance value should be $R=0.20~\Omega$, and the maximum power $P_M=250 ~\rm mW $.
 What is the maximum current that can be measured?
-</WRAP></WRAP></panel>
+#@HiddenBegin_HTML~pow1,Solution~@#
+The formulas $R = {{U} \over {I}}$ and $P = {U} \cdot {I}$ can be combined to get:
+\begin{align*}
+P = R \cdot I^2
+\end{align*}
+This can be rearranged into
+\begin{align*}
+I = + \sqrt{ {{P} \over{R} } }
+\end{align*}
+#@HiddenEnd_HTML~pow1,Solution ~@#
+#@HiddenBegin_HTML~pow2,Result~@#
+\begin{align*}
+I = 1.118... ~{\rm A} \rightarrow I = 1.12 ~{\rm A}
+\end{align*}
+#@HiddenEnd_HTML~pow2,Result ~@#
+#@TaskEnd_HTML@#
 <panel type="info" title="Exercise 1.7.3 Power loss and efficiency I"> <WRAP group><WRAP column 2%>{{fa>pencil?32}}</WRAP><WRAP column 92%>
@@ Zeile 973: / Zeile 1008: @@
 <imgcaption BildNr29 | Sketch of the setup>
 </imgcaption>
-{{drawio>SkizzeBatteriemonitor}}
+{{drawio>SkizzeBatteriemonitor.svg}}
 </WRAP>
-  * The battery monitor BQ769x0 measures the charge and discharge currents of a lithium-ion battery by means of the voltage across a measuring resistor (shunt). In <imgref BildNr29> the analog-to-digital converter ($ADC$) of this chip is connected to the shunt $R\_S$ via the circuit board. Through the shunt the discharge current flows from the battery connection $BAT+$ to $OUT+$ and via $OUT-$ back to $BAT-$. The shunt shall be designed so that the bipolar measurement signals have a voltage level in the range of $-0.20 V$ to $+0.20 V$. The analog-to-digital converter has a resolution of $15uV$. The currents can be used to count the charge in the battery to determine the state of charge (SOC).
+  * The battery monitor BQ769x0 measures the charge and discharge currents of a lithium-ion battery using the voltage across a measuring resistor (shunt). In <imgref BildNr29> the analog-to-digital converter ($\rm ADC$) of this chip is connected to the shunt $\rm R\_S$ via the circuit board. Through the shunt, the discharge current flows from the battery connection $\rm BAT+$ to $\rm OUT+$ and via $\rm OUT-$ back to $\rm BAT-$. The shunt shall be designed so that the bipolar measurement signals have a voltage level in the range of $-0.20 ~{\rm V}$ to $+0.20 ~{\rm V}$. The analog-to-digital converter has a resolution of $15 ~{\rm uV}$. The currents can be used to count the charge in the battery to determine the state of charge ($\rm SOC$).
-  * Draw an equivalent circuit with voltage source (battery), measuring resistor and load resistor $R_L$. Also draw the measurement voltage and load voltage.
+  * Draw an equivalent circuit with a voltage source (battery), measuring resistor and load resistor $R_L$. Also, draw the measurement voltage and load voltage.
-  * The shunt should have a resistance value of $1m\Omega$. What maximum charge/discharge currents are still measurable? What minimum current change is measurable?
+  * The shunt should have a resistance value of $1~{\rm m}\Omega$. What maximum charge/discharge currents are still measurable? What minimum current change is measurable?
   * What power loss is generated at the shunt in the extreme case?
   * Now the efficiency is to be calculated
-    * Find the efficiency as a function of $R\_S$ and $R_L$. Note that the same current flows through both resistors.
+    * Find the efficiency as a function of $\rm R\_S$ and $R_\rm L$. Note that the same current flows through both resistors.
-    * Special task: The battery is to have a nominal voltage of $10V$ (3 cells) and the maximum discharge current is to flow. What efficiency results from the measurement alone?
+    * Special task: The battery is to have a nominal voltage of $10~{\rm V}$ (3 cells) and the maximum discharge current is to flow. What efficiency results from the measurement alone?
 </WRAP></WRAP></panel>
 <panel type="info" title="Exercise 1.7.4 Power loss and efficiency II"> <WRAP group><WRAP column 2%>{{fa>pencil?32}}</WRAP><WRAP column 92%>
-A water pump ($\eta_P = 60\%$) has an electric motor drive ($\eta_M=90\%$).
+A water pump ($\eta_\rm P = 60~\%$) has an electric motor drive ($\eta_\rm M=90~\%$).
-The pump has to pump $500l$ water per minute up to $12m$ difference in height.
+The pump has to pump $500~{\rm l}$ water per minute up to $12~{\rm m}$ difference in height.
   * What must be the rated power of the motor?
-  * What current does the motor draw from the $230V$ mains? (assumption: the 230V is a DC value and also the current is DC)
+  * What current does the motor draw from the $230~{\rm V}$ mains? (assumption: the $230~{\rm V}$ is a DC value and also the current is DC)
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 <panel type="info" title="Exercise 1.7.5 PPTC"> <WRAP group><WRAP column 2%>{{fa>pencil?32}}</WRAP><WRAP column 92%>
-Often, parts of a circuit have to be protected from overcurrent, since otherwise components could break. This is usually done by a fuse or a ciruit breaker, which open up the connection and therefore disable the path for the current. A problem with the commonly used fuses is, that once the fuse is blown (=it has been tripped) it has to be changed. \\
+Often, parts of a circuit have to be protected from over-current, since otherwise, components could break.
-Since opening up electronics and changing the fuse is not reasonable for consumer electronics, these products nowadays use {{wp>resettable fuse}}s. These consist of a polymer (="plastics") with conducting paths of graphite or carbon black in it. When more and more current is flowing, more and more heat is generated. At one distinct temperature, the polymer expands rapidly - which is also called phase change. This expansion moves the conducting paths appart. The system will stay in a state, where a minimum current is flowing, which maintains just enough heat dissipation for the expansion. This process is also reversable: When cooled down, the conducting paths gets re-connected. This components are also called **polymer positive temperature coefficient** component or PPTC. \\
+This is usually done by a fuse or a circuit breaker, which opens up the connection and therefore disables the path for the current.
-In the diagramm below the internal structure and the resistance over the temperature is shown (more details about the structure and function can be found [[https://onlinelibrary.wiley.com/doi/full/10.1002/app.49677|here]]).
+A problem with the commonly used fuses is, that once the fuse is blown (=it has been tripped) it has to be changed. \\
+Since opening up electronics and changing the fuse is not reasonable for consumer electronics, these products nowadays use {{wp>resettable fuse}}s.
+These consist of a polymer (="plastics") with conducting paths of graphite or carbon black in it.
+When more and more current is flowing, more and more heat is generated.
+ At one distinct temperature, the polymer expands rapidly - which is also called phase change.
+This expansion moves the conducting paths apart.
+The system will stay in a state, where a minimum current is flowing, which maintains just enough heat dissipation for the expansion.
+This process is also reversible: When cooled down, the conducting paths get re-connected.
+These components are also called **polymer positive temperature coefficient** components or PPTC. \\
+In the diagram below the internal structure and the resistance over the temperature are shown (more details about the structure and function can be found [[https://onlinelibrary.wiley.com/doi/full/10.1002/app.49677|here]]).
-{{drawio>PPTCfuse}}
+{{drawio>PPTCfuse.svg}}
-In the given circuit below, a fuse $F$ shall protect another component shown as $R_L$, which could be a motor or motor driver for example. In general, the fuse $F$ can be seen as a (temperature variable) resistance.
+In the given circuit below, a fuse $F$ shall protect another component shown as $R_\rm L$, which could be a motor or motor driver for example.
-The source voltage $U_S$ is $50V$ and $R_L=250\Omega$.
+In general, the fuse $F$ can be seen as a (temperature variable) resistance.
+The source voltage $U_\rm S$ is $50~{\rm V}$ and $R_{\rm L}=250~\Omega$.
-{{drawio>PPTCfusecircuit}}
+{{drawio>PPTCfusecircuit.svg}}
 For this fuse, the component "[[https://www.mouser.de/datasheet/2/643/ds_CP_0zcg_series-1960332.pdf|0ZCG0020AF2C]]"((the datasheet is not needed for this exercise)) is used.
-When this fuse trips, it has to carry nearly the full source voltage and dissipates a power of $0.8W$.
+When this fuse trips, it has to carry nearly the full source voltage and dissipates a power of $0.8~{\rm W}$.
-  * First assume that the fuse is not blown. The resistance of the fuse at this is $1 \Omega$, which is neglectable compared to $R_L$. What is the value of the current flowing through $R_L$?
+  * First assume that the fuse is not blown. The resistance of the fuse at this is $1~\Omega$, which is negligible compared to $R_{\rm L}$. What is the value of the current flowing through $R_{\rm L}$?
   * Assuming for the next questions that the fuse has to carry the full source voltage and the given power is dissipated.
     * Which value will the resistance of the fuse have?
     * What is the current flowing through the fuse, when it is tripped?
-    * Compare this resistance of the fuse with $R_L$. Is the assumption, that all of the voltage drops on the fuse is feasible?
+    * Compare this resistance of the fuse with $R_{\rm L}$. Is the assumption, that all of the voltage drops on the fuse feasible?
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 ~~PAGEBREAK~~ ~~CLEARFIX~~
-===== Further reading =====
+===== Further Reading =====
-  - [[http://omegataupodcast.net/303-das-si-system-der-einheiten/|Omega Tau Nr. 303]] : German Podcast with a researcher from the BTP ({{wpde>>Physikalisch-Technische Bundesanstalt}}, Germanys national standardisation institute) on the evolution of the SI unit system.
+  - [[http://omegataupodcast.net/303-das-si-system-der-einheiten/|Omega Tau Nr. 303]]: German Podcast with a researcher from the BTP ({{wpde>Physikalisch-Technische Bundesanstalt}}, Germany's national standardization institute) on the evolution of the SI unit system.
   - [[https://www.youtube.com/watch?v=KGJqykotjog&ab_channel=AtomsandSporks|How electric flow really works]]: No, there are no free electrons in the wire, and the electrons are not colliding with the atoms or atomic cores...
+#@DefLvlEnd_HTML~1,1.~@#