Import Question JSON

Current Question (ID: 17308)

Question:

$\text{A 44 mH inductor is connected to a 220 V, 50 Hz AC supply. The RMS value of the current in the circuit is:}$

Options:

1. $1.0 \text{ A}$
2. $15 \text{ A}$
3. $15.92 \text{ A}$
4. $14.29 \text{ A}$

Solution:

$\text{Hint: When AC current goes through inductor then reactance is equal,}$ $X_L = L \omega.$ $\text{Step 1: Using the relation, } i_{\text{rms}} = \frac{V_{\text{rms}}}{L \omega}.$ $i_{\text{rms}} = \frac{V_{\text{rms}}}{L \omega}$ $= \frac{220}{44 \times 10^{-3} \times 2 \pi \times 50}$ $= 15.92 \text{ A}.$

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
}