Question

A heating element has a resistance of $100 \, \Omega$ at room temperature. When it is connected to a supply of $220 \, V$ , a steady current of $2 \, A$ passes in it and temperature is $500{ }^{\circ} C$ more than the room temperature. The temperature coefficient of resistance of the heating element is

• A. $5 \times 10^{-4}{ }^{o} C ^{-1}$
• B. $2 \times 10^{-4}{ }^{o} C ^{-1}$
• C. $1 \times 10^{-4} \quad{ }^{o} C ^{-1}$
• D. $0.5 \times 10^{-4}{ }^{o} C ^{-1}$

Answer 1

Answer: (B)

Resistance of heating element after temperature increases by $500^{o}C=\frac{220}{2}=110 \, \Omega$ (from Ohm's law). The new resistance is related to the temperature coefficient of the heating element as $110=100 \, \left(\right.1+\alpha 500\left.\right)$
$\alpha=\frac{10}{100 \times 500} \Rightarrow \alpha=2 \times 10^{-4}{ }^{\circ} C ^{-1}$