Import Question JSON

Current Question (ID: 20259)

Question:

$\text{What is the ratio of potential difference across } C_1 \text{ and } C_2 \text{ at steady state for the given circuit?}$

Options:

1. $4 : 5$
2. $2 : 5$
3. $1 : 4$
4. $3 : 1$

Solution:

$\text{Hint: When the capacitors are in steady state, no current passes through them.}$ $\text{At steady state } R_{\text{eq}} = 6 + 2 + 8 = 16 \Omega$ $i_{\text{battery}} = \frac{4}{16} = \frac{1}{4} \text{ A}$ $\Delta V_{C_1} = \frac{1}{4} \times 8 = 2 \text{ V}$ $\Delta V_{C_2} = \frac{1}{4} \times 10 = \frac{5}{2} \text{ V}$

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
}