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Current Question (ID: 17306)

Question:

$\text{A resistance of } 300 \, \Omega \text{ and an inductance of } \frac{1}{\pi} \, \text{henry are connected in series to an AC voltage of 20 volts and a 200 Hz frequency. The phase angle between the voltage and current will be:}$

Options:

1. $\tan^{-1} \frac{4}{3}$
2. $\tan^{-1} \frac{3}{4}$
3. $\tan^{-1} \frac{3}{2}$
4. $\tan^{-1} \frac{2}{5}$

Solution:

$\text{(1) Phase angle } \tan \phi = \frac{\omega L}{R} = \frac{2 \pi \times 200}{300} \times \frac{1}{\pi} = \frac{4}{3}$ $\therefore \phi = \tan^{-1} \frac{4}{3}$

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
}