Import Question JSON

Current Question (ID: 20501)

Question:

$\text{A coil of inductance } 2 \text{ H having negligible resistance is connected to a source of supply whose voltage is given by } V = 3t \text{ volt.}$ $\text{(where } t \text{ is in second). If the voltage is applied when } t = 0, \text{ then the energy stored in the coil after } 4 \text{ s is:}$

Options:

1. $73 \text{ J}$
2. $36 \text{ J}$
3. $144 \text{ J}$
4. $288 \text{ J}$

Solution:

$\text{Hint: } \epsilon = \frac{L dI}{dt}$ $3 \int_0^4 t \, dt = 2 \int_0^4 dI$ $\frac{3}{2} \times 16 = 2I$ $I = 12$ $V = \frac{1}{2} LI^2 = \frac{1}{2} \times 2 \left(12\right)^2 = 144 \text{ J}$

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
}