Exercise EE1-04.R2

Prof. Dr. Thorsten Jungmann (last updated 2025-12-07)

Relates to EE1-04 Resistance

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Task

An electric heating element made of nickel-chromium wire (NiCr) is used in an industrial furnace. At room temperature ($T_1=20°\mathrm{C}$), the resistance of the heating element is $R_{20}=48\Omega$.

During operation, the heating wire heats up to a temperature of $T_2=800°\mathrm{C}$.

The temperature coefficient of NiCr is ${\alpha }_{20}=0.4\cdot 10^{-3}{\mathrm{K}}^{-1}$.

a) Calculate the resistance of the heating element at operating temperature.

b) The heating element is operated at a voltage of $U=230\mathrm{V}$. Calculate the current and the power in the cold state (at $20°\mathrm{C}$).

c) Calculate the current and the power in the hot state (at $800°\mathrm{C}$).

d) By what percentage does the power consumption change between the cold and the hot state?

Solution

a) $R_{800}=62.98\Omega \approx 63\Omega$
b) $I_{\mathrm{cold}}=4.79\mathrm{A}$, $P_{\mathrm{cold}}=1102\mathrm{W}$
c) $I_{\text{hot}}=3.65\mathrm{A}$, $P_{\text{hot}}=840\mathrm{W}$
d) Power decreases by approx. $24\%$

Complete solution