Import Question JSON

Current Question (ID: 20562)

Question:

$\text{Find the power factor of the given } AC \text{ circuit.}$ $L = \frac{1}{10\pi} \text{ H}$ $C = \frac{1}{1000\pi} \text{ F}$ $R = 10 \ \Omega$

Options:

1. 0.75
2. 0.5
3. 1
4. \text{none of the above}

Solution:

$\text{Hint: } \cos \phi = \frac{R}{Z}$ $X_L = \omega L = 100\pi \times \frac{1}{10\pi} = 10 \Omega$ $X_C = \frac{1}{\omega C} = \frac{1}{100\pi \times \frac{1}{1000\pi}} = 10 \Omega$ $R = 10 \Omega$ $\cos \phi = \frac{R}{Z} = \frac{10}{\sqrt{(10 - 10)^2 + (10)^2}} = 1$

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
}