Import Question JSON

Current Question (ID: 17328)

Question:

$\text{In a box } Z \text{ of unknown elements } (L \text{ or } R \text{ or any other combination}), \text{ an ac voltage } E = E_0 \sin(\omega t + \phi) \text{ is applied and the current in the circuit is found to be } I = I_0 \sin \left( \omega t + \phi + \frac{\pi}{4} \right). \text{ The unknown elements in the box could be:}$

Options:

1. $\text{Only the capacitor}$
2. $\text{Inductor and resistor both}$
3. $\text{Either capacitor, resistor, and an inductor or only capacitor and resistor}$
4. $\text{Only the resistor}$

Solution:

$\text{The total reactance of the circuit must be capacitive because the current leads the voltage.}$ $\text{Therefore, the box must contain either capacitor, resistor, and inductor or only capacitor and resistor.}$

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
}