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electrical_engineering_1:preparation_properties_proportions [2023/10/11 11:29] – mexleadminelectrical_engineering_1:preparation_properties_proportions [2024/10/10 15:17] (aktuell) – mexleadmin
Zeile 55: Zeile 55:
  
 ~~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. $1~{{{\rm m}}\over{{\rm s}}}$.
Zeile 100: Zeile 100:
  
 ~~PAGEBREAK~~ ~~CLEARFIX~~ ~~PAGEBREAK~~ ~~CLEARFIX~~
-==== Physical equations  ====+==== Physical Equations  ====
  
   * Physical equations allow a connection of physical quantities.   * Physical equations allow a connection of physical quantities.
Zeile 110: Zeile 110:
 <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 $1$.
 \\ \\ \\ \\
Zeile 124: Zeile 124:
 <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"> 
Zeile 288: Zeile 288:
 {{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 ===
Zeile 332: Zeile 332:
   * 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:
     * $a = {{1} \over {4\pi\cdot\varepsilon}}$     * $a = {{1} \over {4\pi\cdot\varepsilon}}$
Zeile 345: Zeile 345:
  
 <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>
Zeile 395: Zeile 395:
 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>
  
Zeile 430: Zeile 430:
 <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>
  
Zeile 633: Zeile 633:
 <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>
Zeile 647: Zeile 647:
 </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>
Zeile 661: Zeile 661:
 </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>
Zeile 677: Zeile 677:
 <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>
Zeile 734: Zeile 734:
 $R(\vartheta) = R_0 + c\cdot (\vartheta - \vartheta_0)$ $R(\vartheta) = R_0 + c\cdot (\vartheta - \vartheta_0)$
  
-  *  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>
Zeile 778: Zeile 779:
 A series expansion can again be applied: $R(T) \sim {\rm e}^{{\rm A} + {{\rm B}\over{T}} + {{\rm C}\over{T^2}} + ...}$. 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}}} = {{{\rm exp} \left({{\rm B}\over{T}}\right)} \over {{\rm exp} \left({{\rm B}\over{298.15 ~{\rm K}}}\right)}} $ with $R_{25}=R(T_{25})$ ${{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 $R_{25}=R(T_{25})$
  
Zeile 841: Zeile 842:
 <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>.
Zeile 856: Zeile 857:
 <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 864: 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?
 </WRAP></WRAP></panel> </WRAP></WRAP></panel>
  
Zeile 881: Zeile 884:
  
 <WRAP><callout> <WRAP><callout>
-=== 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.