Unterschiede
Hier werden die Unterschiede zwischen zwei Versionen angezeigt.
| Beide Seiten der vorigen Revision Vorhergehende Überarbeitung Nächste Überarbeitung | Vorhergehende Überarbeitung | ||
| electrical_engineering_1:preparation_properties_proportions [2024/10/10 14:55] – mexleadmin | electrical_engineering_1:preparation_properties_proportions [2025/09/15 15:27] (aktuell) – mexleadmin | ||
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| ====== 1 Preparation, | ====== 1 Preparation, | ||
| Zeile 622: | Zeile 622: | ||
| 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:// | + | For larger resistors with wires, the value is coded by four to six colored bands (see __ BROKEN-LINK: |
| < | < | ||
| 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 (" | ||
| <WRAP group>< | <WRAP group>< | ||
| 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: |
| ${{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 883: | Zeile 884: | ||
| < | < | ||
| - | === 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 1041: | Zeile 1042: | ||
| This process is also reversible: When cooled down, the conducting paths get re-connected. | 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. \\ | 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:// | + | 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 __ BROKEN-LINK: |
| {{drawio> | {{drawio> | ||