Import Question JSON

Current Question (ID: 20167)

Question:

$\text{In the following circuit, the switch } S \text{ is closed at } t = 0. \text{ The charge on the capacitor } C_1 \text{ as a function of time will be given by:}$ $\left( \text{take } C_{eq} = \frac{C_1 C_2}{C_1 + C_2} \right)$

Options:

1. $C_1 E \left[ 1 - e^{-tR/C_1} \right]$
2. $C_{eq} E \ e^{-t/RC_{eq}}$
3. $C_{eq} E \left[ 1 - e^{-t/RC_{eq}} \right]$
4. $C_2 E \left[ 1 - e^{-t/RC_2} \right]$

Solution:

$\text{Hint: } Q = C_{eq} V$

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
}