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| ee1:preparation_properties_proportions [2023/10/03 19:44] – mexleadmin | ee1:preparation_properties_proportions [2023/10/03 20:39] (aktuell) – mexleadmin | ||
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| Zeile 1: | Zeile 1: | ||
| # | # | ||
| - | ====== 1. Preparation, | + | ====== 1 Preparation, |
| ===== 1.1 Physical Proportions ===== | ===== 1.1 Physical Proportions ===== | ||
| Zeile 10: | Zeile 10: | ||
| By the end of this section, you will be able to: | By the end of this section, you will be able to: | ||
| - know the fundamental 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 (${\rm G}$, ${\rm M}$, ${\rm k}$, ${\rm d}$, ${\rm c}$, ${\rm m}$, ${\rm µ}$, ${\rm n}$). | + | - 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. | - assign the Greek letters. | ||
| Zeile 44: | Zeile 44: | ||
| * For practical applications of physical laws of nature, **physical quantities** are put into mathematical relationships. | * 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 | + | * There are basic quantities based on the SI system of units (French for Système |
| * In order to determine the basic quantities quantitatively (quantum = Latin for //how big//), **physical units** are defined, e.g. ${\rm metre}$ 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, | * In electrical engineering, | ||
| Zeile 83: | Zeile 83: | ||
| | Centi | ${\rm c}$ | $10^{-2}$ | | Centi | ${\rm c}$ | $10^{-2}$ | ||
| | Milli | ${\rm m}$ | $10^{-3}$ | | Milli | ${\rm m}$ | $10^{-3}$ | ||
| - | | Micro | ${\rm u}$, $µ$ | $10^{-6}$ | + | | Micro | ${\rm u}$, $µ$ | $10^{-6}$ |
| | Nano | ${\rm n}$ | $10^{-9}$ | | Nano | ${\rm n}$ | $10^{-9}$ | ||
| | Piko | ${\rm p}$ | $10^{-12}$ | | Piko | ${\rm p}$ | $10^{-12}$ | ||
| Zeile 104: | Zeile 104: | ||
| * Physical equations allow a connection of physical quantities. | * Physical equations allow a connection of physical quantities. | ||
| * There are two types of physical equations to distinguish (at least in German): | * There are two types of physical equations to distinguish (at least in German): | ||
| - | * Quantity equations (in German: //Größengleichungen// ) | + | * Quantity equations (in German: //Größengleichungen// ) |
| - | * Normalized quantity equations (also called related quantity equations, in German // | + | * Normalized quantity equations (also called related quantity equations, in German // |
| < | < | ||
| Zeile 210: | Zeile 210: | ||
| ==== Exercises ==== | ==== Exercises ==== | ||
| - | {{tagtopic> | + | {{tagtopic> |
| ===== 1.2 Introduction to the Structure of Matter ===== | ===== 1.2 Introduction to the Structure of Matter ===== | ||
| Zeile 475: | Zeile 475: | ||
| * Similar to the transport of a mass in the gravitational field, energy is needed to transport the charge in the " | * Similar to the transport of a mass in the gravitational field, energy is needed to transport the charge in the " | ||
| * We will look at the specific electric field in the next semester | * We will look at the specific electric field in the next semester | ||
| - | * A point charge $q$ is moved from electrode | + | * A point charge $q$ is moved from electrode |
| * $\rightarrow$ there is a turnover of energy. | * $\rightarrow$ there is a turnover of energy. | ||
| * The energy turnover is proportional to the amount of charge $q$ transported. | * The energy turnover is proportional to the amount of charge $q$ transported. | ||
| - | * In many cases, the " | + | * In many cases, the " |
| * 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): | * 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. | * e.g. | ||
| Zeile 554: | Zeile 554: | ||
| <callout icon=" | <callout icon=" | ||
| - | The voltage of $U_{12}$ along a path from point ① to ② becomes positive when the potential in ① is greater than the potential in ②. | + | The voltage of $U_{12}$ along a path from point â‘ |
| </ | </ | ||
| ==== Exercises ==== | ==== Exercises ==== | ||
| - | <panel type=" | + | # |
| + | # | ||
| < | < | ||
| Zeile 568: | Zeile 569: | ||
| Explain whether the voltages $U_{\rm Batt}$, $U_{12}$ and $U_{21}$ in <imgref BildNr21> | Explain whether the voltages $U_{\rm Batt}$, $U_{12}$ and $U_{21}$ in <imgref BildNr21> | ||
| - | ~~PAGEBREAK~~ ~~CLEARFIX~~ | + | |
| - | </WRAP></WRAP></panel> | + | # |
| + | * Which terminal has the higher potential? | ||
| + | * From where to where does the arrow point? | ||
| + | # | ||
| + | |||
| + | |||
| + | # | ||
| + | * '' | ||
| + | * For $U_{\rm Batt}$: The arrow starts at terminal 1 and ends at terminal 2. So $U_{\rm Batt}=U_{12}>0$ | ||
| + | * $U_{21}<0$ | ||
| + | # | ||
| + | |||
| + | # | ||
| Zeile 606: | Zeile 620: | ||
| In electrical engineering, | In electrical engineering, | ||
| - | 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: $1.0~\rm k\Omega$, | + | 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:// | For larger resistors with wires, the value is coded by four to six colored bands (see [[https:// | ||
| Zeile 625: | Zeile 639: | ||
| * 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 $R={{U_R}\over{I_R}}=const.$ and thus independent of $U_R$. | ||
| - | * **Ohm' | + | * **Ohm' |
| * In <imgref BildNr13> | * In <imgref BildNr13> | ||
| * The reciprocal value (inverse) of the resistance is called the conductance: | * The reciprocal value (inverse) of the resistance is called the conductance: | ||
| Zeile 749: | Zeile 763: | ||
| * $\beta$ the (quadratic) temperature coefficient with unit: $ [\beta] = {{1}\over{{\rm K}^2}} $ | * $\beta$ the (quadratic) temperature coefficient with unit: $ [\beta] = {{1}\over{{\rm K}^2}} $ | ||
| * $\gamma$ the temperature coefficient with unit: $ [\gamma] = {{1}\over{{\rm K}^3}} $ | * $\gamma$ the temperature coefficient with unit: $ [\gamma] = {{1}\over{{\rm K}^3}} $ | ||
| - | * $\vartheta_0$ is the given reference temperature, | + | * $\vartheta_0$ is the given reference temperature, |
| The further the temperature range deviates from the reference temperature, | The further the temperature range deviates from the reference temperature, | ||
| Zeile 757: | Zeile 771: | ||
| <callout icon=" | <callout icon=" | ||
| - | In addition to the specification of the parameters $\alpha$, | + | In addition to the specification of the parameters $\alpha$, |
| - | This is a different variant of approximation, | + | This is a different variant of approximation, |
| It is based on the {{wp> | It is based on the {{wp> | ||
| - | 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. \\ 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( | + | $R(T) = R_{25} \cdot {\rm exp} \left( |
| </ | </ | ||
| Zeile 784: | Zeile 798: | ||
| * As the name suggests, the NTC has a __n__egative __t__emperature __c__oefficient. This leads to lower resistance at higher temperatures. | * As the name suggests, the NTC has a __n__egative __t__emperature __c__oefficient. This leads to lower resistance at higher temperatures. | ||
| - | * Such an 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 | * 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). | * 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). | ||
| Zeile 798: | Zeile 812: | ||
| * Such a PTC thermistor is also called // | * Such a PTC thermistor is also called // | ||
| * Examples are doped semiconductors or metals. | * 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 $-100~°{\rm C}$ to $200~°{\rm C}$). | + | * 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:// | * [[https:// | ||
| Zeile 827: | Zeile 841: | ||
| <panel type=" | <panel type=" | ||
| - | 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 | + | 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 |
| The resistivity is given by <tabref tab04>. | The resistivity is given by <tabref tab04>. | ||
| Zeile 956: | Zeile 970: | ||
| </ | </ | ||
| - | <panel type=" | + | # |
| + | # | ||
| - | 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? | ||
| - | </ | + | # |
| + | 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*} | ||
| + | |||
| + | # | ||
| + | |||
| + | # | ||
| + | \begin{align*} | ||
| + | I = 1.118... ~{\rm A} \rightarrow I = 1.12 ~{\rm A} | ||
| + | \end{align*} | ||
| + | |||
| + | # | ||
| + | |||
| + | |||
| + | # | ||
| <panel type=" | <panel type=" | ||