Import Question JSON

Current Question (ID: 16657)

Question:

$A \ 5 \ \text{A} \ \text{fuse wire can withstand a maximum power of} \ 1 \ \text{W in a circuit. The resistance of the fuse wire is:}$

Options:

1. $5 \ \Omega$
2. $0.04 \ \Omega$
3. $0.2 \ \Omega$
4. $0.4 \ \Omega$

Solution:

$\text{Hint:} \ P = I^2 R$ $\text{Step: Find the resistance of the fuse wire.}$ $\text{The power dissipated in a resistor (or fuse wire) is given by:}$ $\Rightarrow P = I^2 R \Rightarrow R = \frac{P}{I^2}$ $\text{Substituting the known values we get,}$ $\Rightarrow R = \frac{1}{5^2} \Rightarrow R = \frac{1}{25}$ $\Rightarrow R = 0.04 \ \Omega$ $\text{Hence, option (2) is the correct answer.}$

Import JSON File

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
}