{{tag>resistivity power exam_ee1_WS2022}}{{include_n>1000}}
 
#@TaskTitle_HTML@##@Lvl_HTML@#~~#@ee1_taskctr#~~ Resistance of a Wire by Resistivity\\
<fs medium>(written test, approx. 6 % of a 60-minute written test, WS2022)</fs> #@TaskText_HTML@#

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 $1.10\cdot 10^{-6} ~\Omega \rm{m}$.\\
The heating element is $3 ~\rm{m}$ long and has a diameter of $3.57 ~\rm{mm}$.\\
1. Calculate the resistance $R$ of the heating element.

#@PathBegin_HTML~1~@# \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 \rm{m} \cdot \frac{4 \cdot 3~\rm{m}}{(3.57\cdot 10^{-3}~\rm{m})^2 \cdot \pi} && \\ \end{align*} #@PathEnd_HTML~1~@#

#@ResultBegin_HTML~1~@# \begin{align*} R &= 0.33 ~\Omega \\ \end{align*} #@ResultEnd_HTML~1~@#

2. The heating element is used to heat the oven to a temperature of $180~°\rm{C}$. For this, a power dissipation (= heat flow) of $P=40 ~\rm{W}$ is necessary.\\
Calculate the current $I$ needed to operate it.

#@PathBegin_HTML~2~@# \begin{align*} P = U \cdot I = R \cdot I^2 \quad \rightarrow \quad I= \sqrt{\frac{P}{R}} = \sqrt{\frac{40 ~\rm{W}}{0.33 ~\Omega}} \end{align*} #@PathEnd_HTML~2~@#

#@ResultBegin_HTML~2~@# \begin{align*} I = 11 ~\rm{A} \end{align*} #@ResultEnd_HTML~2~@#

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