Answer to Question #149715 in Physics for Melza

Question

A heating element using nichrome connected to a 230 V supply draws an initial current of 3.2 A which settles after a few seconds to a steady value of 2.8 A. What is the steady temperature of the heating element if the room temperature is 27.0 °C? Temperature coefficient of resistance of nichrome averaged over the temperature range involved is 1.70 x 10-4 °C1.

Answer 1

$$R_1=\frac{U}{I_1}=\frac{230}{3.2}=71.9\Omega\\ R_2=\frac{U}{I_2}=\frac{230}{2.8}=82.1\Omega\\ \alpha=\frac{R_2-R_1}{R_1(T_2-T_1)}\\ 1.7\cdot10^{-4}=\frac{82.1-71.9}{71.9(T_2-27)}\\T_2=867.5\degree C$$