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 $1.70 × 10^{−4} °C^{ −1}$.

Answer 1

Supply voltage, $V = 230\,V$
Initial current drawn, $I_1 = 3.2\,A$
Initial resistance = $R_1$, which is given by the relation,
$R_1 =\frac{ V}{I}$
$R_1 = \frac{230}{3.2}$
$R_1 = 71.87 Ω$
Steady state value of the current, $I_2 = 2.8 \,A$
Resistance at the steady state = $R_2$, which is given as 
$R_2 = \frac{230}{2.8} = 82.14 \,Ω$
Temperature co-efficient of nichrome, $α = 1.70 × 10^{−4 }°C^{−1}$
Initial temperature of nichrome, $T_1= 27.0 °C$
Study state temperature reached by nichrome = $T_2$
$T_2$ can be obtained by the relation for $α$, 
$α = \frac{R_2 - R_1}{R_1(T_2-T_1)}$
$T_2 - 27 °C = \frac{82.14 \times 71.87}{71.87 \times 1.7 \times 10^{-4} }= 840.5$
$T_2 = 840.5 + 27$
$T_2 = 867.5 °C$
Therefore, the steady temperature of the heating element is $867.5 °C$.