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Current Question (ID: 19646)

Question:

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

Options:

1. $5 \times 10^{-4} \, ^\circ \text{C}^{-1}$
2. $2 \times 10^{-4} \, ^\circ \text{C}^{-1}$
3. $1 \times 10^{-4} \, ^\circ \text{C}^{-1}$
4. $0.5 \times 10^{-4} \, ^\circ \text{C}^{-1}$

Solution:

$\text{Hint: } R = R_0[1 + \alpha \Delta T]$

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Upload a JSON file containing LaTeX/MathJax formatted question, options, and solution.

Expected JSON Format:

{
  "question": "The mass of carbon present in 0.5 mole of $\\mathrm{K}_4[\\mathrm{Fe(CN)}_6]$ is:",
  "options": [
    {
      "id": 1,
      "text": "1.8 g"
    },
    {
      "id": 2,
      "text": "18 g"
    },
    {
      "id": 3,
      "text": "3.6 g"
    },
    {
      "id": 4,
      "text": "36 g"
    }
  ],
  "solution": "\\begin{align}\n&\\text{Hint: Mole concept}\\\\\n&1 \\text{ mole of } \\mathrm{K}_4[\\mathrm{Fe(CN)}_6] = 6 \\text{ moles of carbon atom}\\\\\n&0.5 \\text{ mole of } \\mathrm{K}_4[\\mathrm{Fe(CN)}_6] = 6 \\times 0.5 \\text{ mol} = 3 \\text{ mol}\\\\\n&1 \\text{ mol of carbon} = 12 \\text{ g}\\\\\n&3 \\text{ mol carbon} = 12 \\times 3 = 36 \\text{ g}\\\\\n&\\text{Hence, 36 g mass of carbon present in 0.5 mole of } \\mathrm{K}_4[\\mathrm{Fe(CN)}_6].\n\\end{align}",
  "correct_answer": 4
}