Import Question JSON

Current Question (ID: 17342)

Question:

$\text{If } q \text{ is the capacitor's charge and } i \text{ is the current at time } t, \text{ the voltage } V \text{ will be:}$

Options:

1. $L \frac{di}{dt} + iR - \frac{q}{C} = V$
2. $L \frac{di}{dt} - iR + \frac{q}{C} = V$
3. $L \frac{di}{dt} + iR + \frac{q}{C} = V$
4. $L \frac{di}{dt} - iR - \frac{q}{C} = V$

Solution:

$\text{Using the Kirchoff's law—}$ $V - iR - L \frac{di}{dt} - \frac{q}{C} = 0$ $\Rightarrow V = iR + L \frac{di}{dt} + \frac{q}{C}$

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
}