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electrical_engineering_1:task_70jjg4yzznocarsq_with_calculation [2023/02/11 23:23] – mexleadminelectrical_engineering_1:task_70jjg4yzznocarsq_with_calculation [Unbekanntes Datum] (aktuell) – gelöscht - Externe Bearbeitung (Unbekanntes Datum) 127.0.0.1
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-{{tag>resistivity power exam_WS2022}} 
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-<fs x-large>**Exercise ~~#~~ : Temperature-dependent Resistance** \\ (written test, approx. 6% of a 60-minute written test, WS2022) \\ \\ </fs> 
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-A thermistor is used as a temperature sensor in a refrigeration system. The thermistor has a resistance of $10 k\Omega$ at $+25 °C$. \\ 
-The temperature coefficients are: $\alpha=0.01 {{1}\over{K}}$ and $\beta=71 \cdot 10^{-6}{{1}\over{K^2}}$  \\  
-The temperature inside the refrigeration system can reach down to $-40 °C$.  
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-1. Calculate the resistance of the thermistor at $-40 °C$.  
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-<button size="xs" type="link" collapse="70jjg4yzznocarsq_1_path">{{icon>eye}} Solution</button><collapse id="70jjg4yzznocarsq_1_path" collapsed="true"> 
-\begin{align*} 
-R &= R_0 \cdot (1 + \alpha \cdot \Delta T + \beta \cdot \Delta T^2) && | \text{with  } T = T_{end} - T_{start}\\ 
-R &= 10 k\Omega \cdot (1 + 0.01 {{1}\over{K}} \cdot (-40°C - 25°C) + 71 \cdot 10^{-6}{{1}\over{K^2}} \cdot (-40°C - 25°C)^2) \\ 
-\end{align*} 
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-\begin{align*} 
-R &= 6.5 k\Omega \\ 
-\end{align*} 
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-2. Additionally, explain which effect a resistive temperature sensor can have on the refrigeration system.  
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-Resistors transfer electrical energy out of the circuit and generate heat. Therefore, a resistive sensor might heat up the refrigeration system. \\ \\ 
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-3. Regarding question 2.: Given a constant sensor voltage, would a sensor with tenfold the resistance be better or worse? Give an explanation for you answer.  
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-The power of the resistor $P = U \cdot I = R \cdot I^2 = {{U^2}\over{R}}$ is equivalent with the heat flow. \\  
-Therefore, with constant $U$ and increasing $R$ the power decreases. Ten times more resistance decreases the heat flow to one tenth. 
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