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 ${27.0}^{o}C$? Temperature coefficient of resistance of nichrome averaged over the temperature range involved is $1.70\times {10}^{-4}{}^o{C}^{-1}$.

Answer 1

V=230 volts
Initial current, $I_1=3.2A$
$R=V/I_1=71.9\Omega$
steady state current,
$I_2=2.8A$
$R_2=230/2.8=82.14\Omega$
$\alpha =1.7\times {10}^{-4},T_1={27}^{o}C$
coefficient of resistance$\alpha =\frac{R_2-R_1}{R_1(T_2-T_1)}$
$\Rightarrow T_2={867.5}^{o}C$