JEE Mains · Physics · STD 12 - Current electricity
- JEE Mains 2018
- Hard
- MCQ
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?
Pick an option to check your answer.
Answer & Solution
Correct Answer
(C) \(2\, \times \,{10^{ - {4}}}\,\,{^oC^{ - 1}}\)
Step-by-step Solution
Detailed explanation
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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