Import Question JSON

Current Question (ID: 17316)

Question:

$A \ 50 \ \text{Hz} \ \text{AC source of} \ 20 \ \text{volts is connected across} \ R \ \text{and} \ C \ \text{as shown in the figure below. If the voltage across} \ R \ \text{is} \ 12 \ \text{volts, then the voltage across} \ C \ \text{will be:}$

Options:

1. $8 \ \text{V}$
2. $16 \ \text{V}$
3. $10 \ \text{V}$
4. $\text{not possible to determine unless values of} \ R \ \text{and} \ C \ \text{are given}$

Solution:

$V_C = \sqrt{V_S^2 - V_R^2} = \sqrt{20^2 - 12^2} = 16 \ \text{volt}$

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
}