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electrical_engineering_1:preparation_properties_proportions [2023/05/31 09:26] – mexleadminelectrical_engineering_1:preparation_properties_proportions [2024/10/10 15:17] (aktuell) – mexleadmin
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 #@DefLvlBegin_HTML~1,1.~@#  #@DefLvlBegin_HTML~1,1.~@# 
  
-====== 1. Preparation, Properties, and Proportions ======+====== 1 Preparation, Properties, and Proportions ======
  
 ===== 1.1 Physical Proportions ===== ===== 1.1 Physical Proportions =====
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 ~~PAGEBREAK~~ ~~CLEARFIX~~ ~~PAGEBREAK~~ ~~CLEARFIX~~
-==== derived quantities, SI units, and prefixes ====+==== derived Quantities, SI Units, and Prefixes ====
  
   * Besides the basic quantities, there are also quantities derived from them, e.g. $1~{{{\rm m}}\over{{\rm s}}}$.   * Besides the basic quantities, there are also quantities derived from them, e.g. $1~{{{\rm m}}\over{{\rm s}}}$.
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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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 <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> <WRAP>
 <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.
Zeile 159: Zeile 159:
 </callout> </callout>
  
-==== Letters for physical quantities ====+==== Letters for physical Quantities ====
    
 In physics and electrical engineering, the letters for physical quantities are often close to the English term. In physics and electrical engineering, the letters for physical quantities are often close to the English term.
Zeile 248: Zeile 248:
    
  
-==== Conductivity ====+==== Conductivity of Matter ====
 <WRAP group><WRAP column third> <WRAP group><WRAP column third>
 <callout color="grey">  <callout color="grey"> 
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 {{tagtopic>chapter1_2&nodate&nouser&noheader&nofooter&order=custom}} {{tagtopic>chapter1_2&nodate&nouser&noheader&nofooter&order=custom}}
  
-===== 1.3 Effects of electric charges and current =====+===== 1.3 Effects of Electric Charges and Current =====
 <WRAP><callout> <WRAP><callout>
 === Learning Objectives === === Learning Objectives ===
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   * Qualitative investigation using a second experiment   * Qualitative investigation using a second experiment
     * two charges ($Q_1$ and $Q_2$) at distance $r$     * two charges ($Q_1$ and $Q_2$) at distance $r$
-    * additional measurement of the force $F_C$ (e.g. via spring balance)+    * additional measurement of the force $F_{\rm C}$ (e.g. via spring balance)
   * Experiment results:   * 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 increases linearly with larger charge $Q_1$ or $Q_2$. \\ $ F_{\rm C} \sim Q_1$ and $ F_{\rm C} \sim Q_2$ 
-    * Force falls quadratic with greater distance $r$ \\ $ F_C \sim {1 \over {r^2}}$ +    * Force falls quadratic with greater distance $r$ \\ $ F_{\rm C} \sim {1 \over {r^2}}$ 
-    * with a proportionality factor $a$: \\ $ F_C = a \cdot {{Q_1 \cdot Q_2} \over {r^2}}$+    * with a proportionality factor $a$: \\ $ F_{\rm C} = a \cdot {{Q_1 \cdot Q_2} \over {r^2}}$
   * Proportionality factor $a$   * Proportionality factor $a$
-  * The proportionality factor $a$ is defined in such a way that simpler relations arise in electrodynamics.+  * The proportionality factor $a$ is defined to create simpler relations in electrodynamics.
     * $a$ thus becomes:     * $a$ thus becomes:
     * $a = {{1} \over {4\pi\cdot\varepsilon}}$     * $a = {{1} \over {4\pi\cdot\varepsilon}}$
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 <callout icon="fa fa-exclamation" color="red" title="Note!"> <callout icon="fa fa-exclamation" color="red" title="Note!">
-The Coulomb force (in a vacuum) can be calculated via. \\ $\boxed{ F_C = {{1} \over {4\pi\cdot\varepsilon_0}} \cdot {{Q_1 \cdot Q_2} \over {r^2}} }$ \\+The Coulomb force (in a vacuum) can be calculated via. \\ $\boxed{ F_{\rm C} = {{1} \over {4\pi\cdot\varepsilon_0}} \cdot {{Q_1 \cdot Q_2} \over {r^2}} }$ \\
 where $\varepsilon_0 = 8.85 \cdot 10^{-12} \cdot ~{{\rm C}^2 \over {{\rm m}^2\cdot {\rm N}}} = 8.85 \cdot 10^{-12} \cdot ~{{{\rm As}} \over {{\rm Vm}}}$ 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> </callout>
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 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. 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 $1~{\rm A}$ 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.+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 $F_{\rm L} = 0.2\cdot 10^{-6}~{\rm N}$ on each other.
 </callout> </callout>
  
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 <callout icon="fa fa-comment" color="blue" title="Definition of electrodes (according to DIN5489)"> <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, the dimension of an electrode is characterized by the fact that a change of material takes place (e.g. metal->semiconductor, metal->liquid). \\+Looking at a component, the electrode is characterized as the homogenous part of the component, where the charges come in / move out (usually made out of metal). \\
 The name of the electrode is given as follows:  The name of the electrode is given as follows: 
   * **A**node: Electrode at which the current enters 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//)   * 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 diode's structure, shape, and electrodes (see <imgref BildNr8>).
 </callout> </callout>
  
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 ==== Exercises ==== ==== 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> <WRAP>
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 Explain whether the voltages $U_{\rm Batt}$, $U_{12}$ 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~@# 
 + 
 + 
 +#@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@# 
  
  
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 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. 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.
  
-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.+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]]) 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]])
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 <WRAP group><WRAP half column> <WRAP group><WRAP half column>
 <callout color="grey"> <callout color="grey">
-===  Linear resistors ==+===  Linear Resistors ==
 <imgcaption BildNr13 | Linear resistors in the U-I diagram> <imgcaption BildNr13 | Linear resistors in the U-I diagram>
 </imgcaption> </imgcaption>
 {{drawio>linearer_Widerstand_UI.svg}} {{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 $R={{{\Delta U_R}}\over{\Delta I_R}}$   * 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 $1~{\rm S}$ (${\rm Siemens}$). 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.
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 </WRAP><WRAP half column> </WRAP><WRAP half column>
 <callout color="grey"> <callout color="grey">
-=== Non-linear resistors  ===+=== Non-linear Resistors  ===
 <imgcaption BildNr14 | Non-linear resistors in the U-I diagram> <imgcaption BildNr14 | Non-linear resistors in the U-I diagram>
 </imgcaption> </imgcaption>
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   * 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.   * 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.   * 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 $g$.   * 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> </callout>
  
 </WRAP></WRAP> </WRAP></WRAP>
  
-==== Resistance as a material Property ====+==== Resistance as a Material Property ====
  
 <WRAP> <WRAP>
-Clear explanation of resistivity+Good explanation of resistivity
 {{youtube>dRtNvUQC7c8}} {{youtube>dRtNvUQC7c8}}
 </WRAP> </WRAP>
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 <WRAP > <WRAP >
 <tabcaption tab04| Specific resistivity for different materials> <tabcaption tab04| Specific resistivity for different materials>
-^ Material           ^ $\rho$ in ${{\Omega\cdot {{\rm mm}^2}}\over{{\rm m}}}$ ^  +^ Material                          ^ $\rho$ in ${{\Omega\cdot {{\rm mm}^2}}\over{{\rm m}}}$  ^ 
-| Silver               |  $1.59\cdot 10^{-2}$  |  +| Silver                            |  $1.59\cdot 10^{-2}$                                    | 
-| Copper               |  $1.79\cdot 10^{-2}$  |  +| Copper                            |  $1.79\cdot 10^{-2}$                                    | 
-| Aluminium            |  $2.78\cdot 10^{-2}$  |  +| Gold                              |  $2.2\cdot 10^{-2}$                                     | 
-| Gold                 |  $2.2\cdot 10^{-2}$   |  +| Aluminium                         |  $2.78\cdot 10^{-2}$                                    | 
-| Lead                 |  $2.1\cdot 10^{-1}$   |  +| Lead                              |  $2.1\cdot 10^{-1}$                                     | 
-| Graphite             |  $8\cdot 10^{0}$      |  +| Graphite                          |  $8\cdot 10^{0}$                                        | 
-| Battery Acid (Lead-acid Battery) |  $1.5\cdot 10^4$      |  +| Battery Acid (Lead-acid Battery)  |  $1.5\cdot 10^4$                                        | 
-| Blood                |  $1.6\cdot 10^{6}$    |  +| Blood                             |  $1.6\cdot 10^{6}$                                      | 
-| (Tap) Water          |  $2 \cdot 10^{7}$     |  +| (Tap) Water                       |  $2 \cdot 10^{7}$                                       | 
-| Paper                |  $1\cdot 10^{15} ... 1\cdot 10^{17}$   | +| Paper                             |  $1\cdot 10^{15} ... 1\cdot 10^{17}$                    |
  
 </tabcaption> </tabcaption>
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 $R(\vartheta) = R_0 + c\cdot (\vartheta - \vartheta_0)$ $R(\vartheta) = R_0 + c\cdot (\vartheta - \vartheta_0)$
  
-  *  The constant is replaced by $c = R_0 \cdot \alpha$ +  * 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{{\rm 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. +  * 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: $\alpha$, $\beta$, $\gamma$, ...+  * These temperature coefficients are described with Greek letters: $\alpha$, $\beta$, $\gamma$, ... 
 +  * Sometimes in the datasheets the value $\alpha$ is named as TCR ("Temperature Coefficient of Resistance"), for example {{electrical_engineering_1:tmp64-q1.pdf|here}}.
  
 <WRAP group><WRAP column> <WRAP group><WRAP column>
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 <callout icon="fa fa-info" color="grey" title="Outlook"> <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 $25~°{\rm C}$.  This is a different variant of approximation, which refers to the temperature of $25~°{\rm C}$. 
 It is based on the {{wp>Arrhenius equation}}, which links reaction kinetics to temperature in chemistry.  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 e^{{B}\over{T}} $ .+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 $T_{25}=298.15~{\rm K}$ ($\hat{=} 25~°{\rm C}$) we get: +However, often only $B$ is given, for example {{electrical_engineering_1:datasheet_ntcgs103jx103dt8.pdf|here}}. \\ 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 ~{\rm 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: 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~{\rm 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> </callout>
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 <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%> <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 $5.0~{\rm cm}$ long and $0.20~{\rm mm}$ wide line if it has a height of $0.20~{\rm µm}$?+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>. The resistivity is given by <tabref tab04>.
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 <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%> <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 $d_i=70~{\rm mm}$ and an outer diameter of $d_a = 120~{\rm mm}$. The number of turns is $n_W=1350$ turns, the wire diameter is $d=2.0~{\rm mm}$ and the specific conductivity of the wire is $\kappa_{Cu}=56 \cdot 10^6 ~{{{\rm S}}\over{{\rm m}}}$.+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.
Zeile 850: Zeile 867:
  
 The power 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 $\kappa_{Al}=33\cdot 10^6 ~{\rm {S}\over{m}}$ and a cross-section $A_{Al}=115~{\rm mm}^2$. +  * 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 $\kappa_{Cu}=56\cdot 10^6 ~{\rm {S}\over{m}}$+  * 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?
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Zeile 867: Zeile 884:
  
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-=== Goal ===+=== Learning Objectives ===
 After this lesson you should be able to: After this lesson you should be able to:
   - Be able to calculate the electrical power and energy across a resistor.   - Be able to calculate the electrical power and energy across a resistor.
Zeile 956: Zeile 973:
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-<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@#
  
-An SMD resistor is used on a circuit board for current measurement. The resistance value should be $R=0.2~\Omega$, and the maximum power $P_M=250 ~\rm 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? 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@# 
  
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Zeile 1007: Zeile 1048:
 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.  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. 
 In general, the fuse $F$ can be seen as a (temperature variable) resistance. In general, the fuse $F$ can be seen as a (temperature variable) resistance.
-The source voltage $U_\rm S$ is $50~{\rm V}$ and $R_L=250~\Omega$. +The source voltage $U_\rm S$ is $50~{\rm V}$ and $R_{\rm L}=250~\Omega$. 
  
 {{drawio>PPTCfusecircuit.svg}} {{drawio>PPTCfusecircuit.svg}}
Zeile 1013: Zeile 1054:
 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.  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 $0.8~{\rm W}$. 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 negligible 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.   * 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?     * Which value will the resistance of the fuse have?
     * What is the current flowing through the fuse, when it is tripped?     * 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 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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