Import Question JSON

Current Question (ID: 17041)

Question:

$\text{An inductor is connected to a direct voltage source through a switch. Then:}$

Options:

1. $\text{a very large emf is induced in inductor when the switch is closed.}$
2. $\text{a large emf is induced when the switch is opened.}$
3. $\text{a large emf is induced whether the switch is closed or opened.}$
4. $\text{no emf is induced whether the switch is closed or opened.}$

Solution:

$\text{Hint: Emf} = -\text{L} \frac{di}{dt}$ $\text{Step 1: When K is opened.}$ $\Delta I \rightarrow I_0 \text{ to } 0$ $\Delta t_1 \rightarrow \text{very small}$ $\frac{\Delta I}{\Delta t} \rightarrow \text{very large}$ $\text{Step 2: When K is closed.}$ $\Delta I \rightarrow 0 \rightarrow I_0$ $I = I_0 e^{-t/\tau}$ $\Delta t_2 \rightarrow \text{very large}$ $\frac{\Delta I}{\Delta t} = \text{very small}$

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
}