Question

An electric toaster uses nichrome for its heating element. When a negligibly small current passes through it, its resistance at room temperature $\left(27.0^{\circ} C \right)$ is found to be $75.3 \Omega$. When the toaster is connected to a $230 V$ supply, the current settles, after a few seconds to a steady value of $2.68\, A$. The temperature coefficient of resistance is $1.7 \times 10^{-4}{ }^{\circ} C ^{-1} .$ The steady temperature of the nichrome element is

• A. $747^{\circ} C$
• B. $847^{\circ} C$
• C. $897^{\circ} C$
• D. $927^{\circ} C$

Answer 1

Answer: (B)

$R_{2}=\frac{230 V }{2.68 A }=85.8 \Omega$
Using, $R_{2}=R_{1}\left[\left(1+\alpha\left(T_{2}-T_{1}\right)\right]\right.$
$85.8=75.3\left(1+\left(1.7 \times 10^{-4}\right)\left(T_{2}-27^{\circ} C \right)\right)$
$\Rightarrow T_{2}=\frac{(85.8-75.3)}{\left(75.3 \times 1.7 \times 10^{-4}\right)}+27$
$=820+27=847^{\circ} C .$