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Current Question (ID: 17007)

Question:

$\text{A long solenoid has 1000 turns. When a current of } 4 \text{ A flows through it, the magnetic flux linked with each turn of the solenoid is } 4 \times 10^{-3} \text{ Wb. The self-inductance of the solenoid is:}$

Options:

1. $3 \text{ H}$
2. $2 \text{ H}$
3. $1 \text{ H}$
4. $4 \text{ H}$

Solution:

$\text{No of turns in solenoid, } N = 1000$ $\text{Value of current } = 4 \text{ A}$ $\text{Magnetic flux linked with each turn of the solenoid is, } \phi_B = 4 \times 10^{-3} \text{ Wb}$ $\text{The self-inductance of the solenoid can be expressed in the form of the following relation:}$ $L = \frac{\phi_B N}{I} \ldots (1)$ $\text{On substitution of the above-given values in the relation, we get}$ $L = \frac{4 \times 10^{-3} \times 1000}{4}$ $L = 1 \text{ H}$

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
}