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 \(867.5 °C\).