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

• A. $967^{\circ} C$
• B. $867^{\circ} C$
• C. $853^{\circ} C$
• D. $937^{\circ} C$

Answer 1

Answer: (B)

Given, potential difference $=230\, V$
Initially current at $27^{\circ} C =I_{27^{\circ} C }=3.2\, A$
Finally current at $t^{\circ} C =I_{t^{\circ} C }=2.8\, A$
Room temperature $=27^{\circ} C$
Temperature coefficient of resistance
$\alpha=1.70 \times 10^{-4} /{ }^{\circ} C$
Resistance at $27^{\circ} C ,\, R_{27^{\circ} C }=\frac{V}{I_{27^{\circ} C }}=\frac{230}{3.2}$
$=\frac{2300}{32} \Omega$
Resistance at $t^{\circ} C ,\, R_{t^{\circ} C}=\frac{V}{I_{t^{\circ} C }}=\frac{230}{2.8}$
$=\frac{2300}{28} \Omega$
Temperature of coefficient of resistance
$\alpha=\frac{R_{t}-R_{27}}{R_{27}(t-27)}$
$\Rightarrow 1.7 \times 10^{-4}=\frac{\frac{2300}{28}-\frac{2300}{32}}{\frac{2300}{32}(t-32)}$
or $t-27=\frac{82.143-71.875}{71.875 \times 1.7 \times 10^{-4}}$
$=840.347$
or $t=840.3+27$
$=867.3^{\circ} C$
Thus, the steady temperature of heating element is $867.3^{\circ} C$.