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--- electrical_engineering_1:task_rj0r6j4apumukrj6_with_calculation [2023/02/12 05:58] – mexleadmin
+++ electrical_engineering_1:task_rj0r6j4apumukrj6_with_calculation [Unbekanntes Datum] (aktuell) – gelöscht - Externe Bearbeitung (Unbekanntes Datum) 127.0.0.1
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-{{tag>resistivity power exam_ee1_WS2022}}
- ~~#~~ test
-<panel type="info" > <WRAP group><WRAP column 2%>{{fa>pencil?32}}</WRAP><WRAP column 92%>
-<fs x-large>**Exercise ~~#~~ : Resistance of a Wire by Resistivity** \\ (written test, approx. 6% of a 60-minute written test, WS2022) \\ \\ </fs>
-A heating element made of a Nichrome wire with a round cross-section is used in an electric oven. \\
-Nichrome is a common Nickel Chromium alloy for heating elements. \\
-The Nichrome wire has a resistivity of $1.10\cdot 10^{-6} \Omega m$. \\
-The heating element is $3 m$ long and has a diameter of $3.57 mm$. \\ \\
-. Calculate the resistance $R$ of the heating element.
-<button size="xs" type="link" collapse="RJ0R6J4APUMUKRJ6_1_path">{{icon>eye}} Solution</button><collapse id="RJ0R6J4APUMUKRJ6_1_path" collapsed="true">
-\begin{align*}
-R &= \rho \cdot \frac{l}{A} && | \text{with  } A = r^2 \cdot \pi = \frac{1}{4} d^2 \cdot \pi \\
-R &= \rho \cdot \frac{4 \cdot l}{d^2 \cdot \pi} && \\
-R &= 1.10\cdot 10^{-6} \Omega m \cdot \frac{4 \cdot 3m}{(3.57\cdot 10^{-3}m)^2 \cdot \pi} && \\
-\end{align*}
-</collapse>
-<button size="xs" type="link" collapse="RJ0R6J4APUMUKRJ6_1_solution">{{icon>eye}} Final result</button><collapse id="RJ0R6J4APUMUKRJ6_1_solution" collapsed="true">
-\begin{align*}
-R &= 0.33 \Omega \\
-\end{align*}
- \\
-</collapse>
-. The heating element is used to heat the oven to a temperature of $180°C$. For this, a power dissipation (= heat flow) of $P=40 W$ is necessary. \\ Calculate the current $I$ needed to operate it.
-<button size="xs" type="link" collapse="RJ0R6J4APUMUKRJ6_2_path">{{icon>eye}} Solution</button><collapse id="RJ0R6J4APUMUKRJ6_2_path" collapsed="true">
-\begin{align*}
-P = U \cdot I = R \cdot I^2  \quad \rightarrow \quad I= \sqrt{\frac{P}{R}} = \sqrt{\frac{40 W}{0.33 \Omega}}
-\end{align*}
-</collapse>
-<button size="xs" type="link" collapse="RJ0R6J4APUMUKRJ6_2_solution">{{icon>eye}} Final result</button><collapse id="RJ0R6J4APUMUKRJ6_2_solution" collapsed="true">
-\begin{align*}
-I = 11 A
-\end{align*}
- \\
-</collapse>
-</WRAP></WRAP></panel>

resistivity power exam ee1 ws2022