Import Question JSON

Current Question (ID: 17285)

Question:

$\text{Voltage and current in an AC circuit are given by } V = 5 \sin \left( 100 \pi t - \frac{\pi}{6} \right) \text{ V}$ $\text{and } I = 4 \sin \left( 100 \pi t + \frac{\pi}{6} \right) \text{ A.}$ $\text{Hence:}$

Options:

1. $\text{The voltage leads the current by } 30^\circ.$
2. $\text{The current leads the voltage by } 30^\circ.$
3. $\text{The current leads the voltage by } 60^\circ.$
4. $\text{The voltage leads the current by } 60^\circ.$

Solution:

$\phi_1 = \frac{\pi}{6}, \phi_2 = -\frac{\pi}{6}$ $\phi = \phi_1 - \phi_2$ $\phi = \frac{\pi}{6} - \left( -\frac{\pi}{6} \right) = \frac{2\pi}{6} = \frac{\pi}{3}$ $\text{Hence, current leads the voltage by } 60^\circ.$

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
}