Question

A heating element using nichrome connected to a $230V$ supply draws an initial current of $3.2,A$ which settles after a few seconds to a steady value of $2.8A$. 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 $=230V$
Initially current at $27^{\circ }C=I_{27^{\circ }C}=3.2A$
Finally current at $t^{\circ }C=I_{t^{\circ }C}=2.8A$
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 $867.3^{\circ }C$.