Import Question JSON

Current Question (ID: 20557)

Question:

$\text{In an LC oscillating circuit with } L = 75 \text{ mH and } C = 30 \mu F. \text{ The maximum charge of capacitor is } 2.7 \times 10^{-4} C. \text{ Maximum current through the circuit will be:}$

Options:

1. $0.18 \text{ Amp}$
2. $0.24 \text{ Amp}$
3. $0.72 \text{ Amp}$
4. $0.92 \text{ Amp}$

Solution:

$\text{total energy} = \frac{q_{\text{max}}^2}{2C} = \frac{1}{2} L i_{\text{max}}^2$ $i_{\text{max}} = \frac{q_{\text{max}}}{\sqrt{\frac{L}{C}}} = \frac{2.7 \times 10^{-4}}{\sqrt{\frac{75 \times 10^{-3}}{30 \times 10^{-6}}}} = 0.18 \text{ Amp}$

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
}