Import Question JSON

Current Question (ID: 17025)

Question:

$\text{Two coils of 10 turns each are arranged such that the mutual inductance between them is 150 mH. The magnetic flux linked through one coil when 2 amperes current will flow in another coil, will be:}$ $1. \ 1 \times 10^{-3} \ \text{Wb}$ $2. \ 10 \times 10^{-3} \ \text{Wb}$ $3. \ 20 \times 10^{-3} \ \text{Wb}$ $4. \ 30 \times 10^{-3} \ \text{Wb}$

Options:

1. $1 \times 10^{-3} \ \text{Wb}$
2. $10 \times 10^{-3} \ \text{Wb}$
3. $20 \times 10^{-3} \ \text{Wb}$
4. $30 \times 10^{-3} \ \text{Wb}$

Solution:

$\text{Given:}$ $N_1 = N_2 = 10$ $M = 150 \ \text{mH}$ $I_2 = 2 \ \text{Amp}$ $\text{As } \phi_{12} = M I_2 = N_1 \phi_1$ $\phi_1 = \frac{M I_2}{N_1} = \frac{150}{10} \times 10^{-3} \times 2 = 30 \times 10^{-3} \ \text{Wb}$

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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
}