Import Question JSON

Current Question (ID: 12062)

Question:

The current in a wire varies with time according to the equation I = (4 + 2t), where I is in ampere and t is in seconds. The quantity of charge which has passed through a cross-section of the wire during the time t = 2 s to t = 6 s will be:

Options:

1. 60 C
2. 24 C
3. 48 C
4. 30 C

Solution:

Hint: Use, i = dq/dt. Step 1: Find the charge flowing in time dt. Given, i = 4 + 2t As, i = dq/dt = (4 + 2t) dq = (4 + 2t) dt Step 2: Integrate on both sides to calculate (q1 - q2). ∫q2q1 dq = ∫62 (4 + 2t) dt [q]q2q1 = [4t + t²]62 (q1 - q2) = 48 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
}