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 $500\,^oC$ more than room temperature. What is the temperature coefficient resistance of the heating element?
JEE MAIN 2018, Diffcult
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Resistance after temperature increases by $500\,{\,^o}C\,\,i.e.,\,{R_t}\, = \,\frac{V}{I}\, = \frac{{220}}{2}\, = 110\,\Omega $ $R_0 = 100$ (given) temperature coefficient of resistance, $\alpha = ?$
using $R_t = R_0( 1 + \alpha t)$
$110 = 100 (1 + \alpha 500)$
$\alpha \, = \,\frac{{10}}{{100 \times 500}}$ or, $\alpha \, = \,2 \times {10^{ - 4}}\,\,{^o C^{ - 1}}$
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