Dies ist eine alte Version des Dokuments!
Exercise 1 : Resistance of a Wire by Resistivity
(written test, approx. 6% of a 60-minute written test, WS2022)
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 $3.57 mm$.
1. Calculate the resistance $R$ of the heating element.
\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*}
\begin{align*}
R &= 0.33 \Omega \\
\end{align*}
2. 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.
\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*}
\begin{align*}
I = 11 A
\end{align*}