Import Question JSON

Current Question (ID: 20156)

Question:

$\text{Find the charge on the capacitor in the given circuit at steady state.}$

Options:

1. $\frac{40}{7} \, \mu\text{C}$
2. $\frac{20}{7} \, \mu\text{C}$
3. $\frac{60}{7} \, \mu\text{C}$
4. $\frac{10}{7} \, \mu\text{C}$

Solution:

$\text{Hint: } Q = CV_{AB}$ $V_A = 10 - \frac{10}{3} = \frac{20}{3} \, V$ $V_B = 10 - \frac{3}{7} \times 10 = \frac{40}{7} \, V$ $V_A - V_B = 20 \left[ \frac{1}{3} - \frac{2}{7} \right]$ $= \frac{20}{21} \, V$ $Q = CV_{AB}$ $= 6 \times \frac{20}{21} \, \mu\text{C}$ $= \frac{40}{7} \, \mu\text{C}$

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
}